"Fossies" - the Fresh Open Source Software Archive

Member "KASH3-lib-archindep-2008-07-31/lib/__DOC.g" (3 Sep 2008, 1821771 Bytes) of package /linux/misc/old/KASH3-lib-archindep-2008-07-31.tar.gz:

    1 __DOC := rec(keys:=Dry([
    2 "f896a5",
    3 "95e4b1",
    4 "5d80db",
    5 "4546ad",
    6 "575f80",
    7 "cfb542",
    8 "881f04",
    9 "7251a6",
   10 "a0823b",
   11 "b2cb94",
   12 "c4f2b5",
   13 "143f84",
   14 "ac2569",
   15 "8024dd",
   16 "b49bbf",
   17 "c7a0ee",
   18 "3b1b6a",
   19 "636b79",
   20 "bde31f",
   21 "1630a6",
   22 "2ae099",
   23 "e10eac",
   24 "f6116f",
   25 "3b8353",
   26 "7834fe",
   27 "6a9bd1",
   28 "c8a315",
   29 "aa13b4",
   30 "0b6f20",
   31 "2625da",
   32 "887cf1",
   33 "2dded0",
   34 "f78331",
   35 "6da1f1",
   36 "d81c63",
   37 "b9f653",
   38 "697229",
   39 "19c302",
   40 "1ed908",
   41 "96e0c5",
   42 "6a4b57",
   43 "de4e08",
   44 "1543ee",
   45 "deb7d2",
   46 "57fa02",
   47 "8b67a5",
   48 "1a2112",
   49 "398368",
   50 "f16dd2",
   51 "b922b7",
   52 "b588e0",
   53 "214893",
   54 "2809b1",
   55 "efdf43",
   56 "3557f0",
   57 "7081f0",
   58 "37c247",
   59 "e9863c",
   60 "d8eb79",
   61 "455bb8",
   62 "5447d9",
   63 "b428bb",
   64 "2e722c",
   65 "d6a98a",
   66 "144d2d",
   67 "ad4301",
   68 "66b097",
   69 "ea1698",
   70 "f9320a",
   71 "3e2598",
   72 "2a0f5b",
   73 "9528e2",
   74 "51dd36",
   75 "3729c0",
   76 "4ecb42",
   77 "199ebf",
   78 "03ff1b",
   79 "4a46b0",
   80 "14d69d",
   81 "3c99b9",
   82 "0f6520",
   83 "1fbd2d",
   84 "7de892",
   85 "335b78",
   86 "72db5a",
   87 "dcc5e1",
   88 "39607a",
   89 "f81ead",
   90 "ad5189",
   91 "1bdd5d",
   92 "4a4a6e",
   93 "fbad9f",
   94 "43bf9a",
   95 "0730f5",
   96 "68305c",
   97 "fc8a38",
   98 "36bbdd",
   99 "ab6670",
  100 "e60d0d",
  101 "650413",
  102 "efc75e",
  103 "90fb03",
  104 "d34ecf",
  105 "96b3e7",
  106 "7ef2be",
  107 "72dcb5",
  108 "1cc237",
  109 "d1d7cb",
  110 "aeb167",
  111 "98a11b",
  112 "ab7b5e",
  113 "ec51e2",
  114 "ca03d1",
  115 "b12aa7",
  116 "32de83",
  117 "26ec35",
  118 "637982",
  119 "871abd",
  120 "f2d081",
  121 "1b2275",
  122 "ead233",
  123 "c601cc",
  124 "0ce1d5",
  125 "c025b1",
  126 "8eb302",
  127 "bb5501",
  128 "2b0f66",
  129 "cf988f",
  130 "07c92e",
  131 "b7306d",
  132 "fa766e",
  133 "1f9485",
  134 "62d20c",
  135 "dcca85",
  136 "a0add0",
  137 "8b4255",
  138 "b464a5",
  139 "0c44c7",
  140 "3109b6",
  141 "79a28e",
  142 "2ad5c7",
  143 "ebcb64",
  144 "4a2939",
  145 "5ec41d",
  146 "90d41a",
  147 "1c4f4b",
  148 "1160f6",
  149 "88de41",
  150 "d07f27",
  151 "849310",
  152 "afd6a2",
  153 "367094",
  154 "c34314",
  155 "1b771b",
  156 "3196a1",
  157 "8cb8bb",
  158 "966a95",
  159 "cefa10",
  160 "cf9331",
  161 "c13e31",
  162 "a3cff8",
  163 "a283e8",
  164 "196729",
  165 "d691ad",
  166 "afca37",
  167 "52ee65",
  168 "9df99d",
  169 "7a1f45",
  170 "954a96",
  171 "cc967a",
  172 "04d6e2",
  173 "0f386d",
  174 "8a7886",
  175 "c3156e",
  176 "909f99",
  177 "0f462d",
  178 "c032ad",
  179 "065765",
  180 "32096c",
  181 "ca73ab",
  182 "e0184a",
  183 "f3f65b",
  184 "4a6ac6",
  185 "153d7a",
  186 "1b9919",
  187 "14048e",
  188 "27e1eb",
  189 "12d7db",
  190 "5974c9",
  191 "adf18d",
  192 "c70f5c",
  193 "f49c4a",
  194 "55939c",
  195 "80071c",
  196 "d86b75",
  197 "ed8fcc",
  198 "dde0bc",
  199 "f904e2",
  200 "4d7a41",
  201 "fe08ce",
  202 "d038c9",
  203 "2df183",
  204 "306f68",
  205 "16264b",
  206 "2656fb",
  207 "9a3bee",
  208 "1d3c71",
  209 "8be19d",
  210 "2e50e8",
  211 "52a693",
  212 "9e54fd",
  213 "17c2d1",
  214 "3ae997",
  215 "454b97",
  216 "2afd97",
  217 "06161c",
  218 "fc2dbf",
  219 "3836b4",
  220 "16397d",
  221 "a5a791",
  222 "8ee1cd",
  223 "4af2c5",
  224 "2a4d61",
  225 "f68093",
  226 "65cacd",
  227 "be3460",
  228 "60e26c",
  229 "566c1e",
  230 "22d77a",
  231 "fcb739",
  232 "cff7d0",
  233 "f8c01e",
  234 "9eede6",
  235 "707dde",
  236 "79fde2",
  237 "90ccd6",
  238 "76ce42",
  239 "bdc1fd",
  240 "749950",
  241 "e854e6",
  242 "83082f",
  243 "7e4ac6",
  244 "79731e",
  245 "010b85",
  246 "b520c7",
  247 "058bfd",
  248 "2582ff",
  249 "a1fdaa",
  250 "58ab0e",
  251 "8d5179",
  252 "6e06f6",
  253 "57c950",
  254 "0d5fda",
  255 "b5fb63",
  256 "538a8c",
  257 "a3e705",
  258 "c92634",
  259 "ed35c2",
  260 "a26b37",
  261 "ab46c5",
  262 "afac3c",
  263 "ead637",
  264 "65d8e9",
  265 "9b982b",
  266 "08ba89",
  267 "54eb9f",
  268 "51a70b",
  269 "4c47dd",
  270 "6ce6c5",
  271 "bc0792",
  272 "61074f",
  273 "7d5323",
  274 "fd2d29",
  275 "bd102f",
  276 "7cc48c",
  277 "7acb1d",
  278 "2d83c5",
  279 "1352b4",
  280 "1a564a",
  281 "61057a",
  282 "cc954c",
  283 "716b03",
  284 "33ff40",
  285 "a9e585",
  286 "82f7c4",
  287 "dfa314",
  288 "8f26c3",
  289 "55e26b",
  290 "6f0af0",
  291 "71e03d",
  292 "c16201",
  293 "aa88e2",
  294 "ee3f72",
  295 "93f01f",
  296 "4e3050",
  297 "51e100",
  298 "96758c",
  299 "46626e",
  300 "ea70c0",
  301 "ee0a32",
  302 "de2e6c",
  303 "bd482b",
  304 "2ee348",
  305 "cf4269",
  306 "120c98",
  307 "86383f",
  308 "5b5c8d",
  309 "1f60ed",
  310 "5d2a18",
  311 "97f2d4",
  312 "6708e8",
  313 "8d5ec6",
  314 "a6ea5b",
  315 "f2b426",
  316 "a946db",
  317 "1a92f7",
  318 "6b513a",
  319 "fdca38",
  320 "548853",
  321 "5345a1",
  322 "e292e9",
  323 "b38c0e",
  324 "f03e60",
  325 "1b536b",
  326 "94b4b7",
  327 "296081",
  328 "e28cd6",
  329 "c6d89b",
  330 "1322a4",
  331 "e63d5b",
  332 "edab48",
  333 "dbaff7",
  334 "1362af",
  335 "7d6800",
  336 "a8d39a",
  337 "567a74",
  338 "675095",
  339 "a5b5a6",
  340 "3b4186",
  341 "cd7ab2",
  342 "39cdfc",
  343 "1eaf4c",
  344 "c5c1d4",
  345 "088b6b",
  346 "99775d",
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  348 "579958",
  349 "a3fe4c",
  350 "b9714c",
  351 "1b29b5",
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  353 "135a15",
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  359 "86055e",
  360 "062463",
  361 "8bab25",
  362 "6bcd2e",
  363 "9d9291",
  364 "a3f4c7",
  365 "b39c6c",
  366 "c2fce0",
  367 "e5b910",
  368 "187ae4",
  369 "42f968",
  370 "2dd4da",
  371 "141812",
  372 "6869ff",
  373 "e0443c",
  374 "1a0a18",
  375 "ee8c2e",
  376 "ce5458",
  377 "487c0f",
  378 "a8a50b",
  379 "63c9db",
  380 "3943fc",
  381 "c5f8b8",
  382 "60328f",
  383 "8dd900",
  384 "09db15",
  385 "03e031",
  386 "dea687",
  387 "6a788f",
  388 "885945",
  389 "a9c98d",
  390 "006396",
  391 "5e69c1",
  392 "90cf6e",
  393 "14eea5",
  394 "fdb426",
  395 "d1103e",
  396 "e8fd95",
  397 "bbfd6e",
  398 "9aa461",
  399 "94dbb3",
  400 "5f9aec",
  401 "f9e752",
  402 "f63716",
  403 "bf9496",
  404 "69d342",
  405 "bd9934",
  406 "430302",
  407 "fe5666",
  408 "b19e9b",
  409 "d27408",
  410 "ff2f7d",
  411 "99b3fa",
  412 "b9a29c",
  413 "116c84",
  414 "9a6451",
  415 "6c8bc0",
  416 "a848e9",
  417 "1f37ab",
  418 "1361ce",
  419 "28c8d2",
  420 "ba191d",
  421 "1f84f1",
  422 "e139be",
  423 "da2302",
  424 "2184f2",
  425 "057455",
  426 "889a24",
  427 "a58e00",
  428 "fed97c",
  429 "b209ca",
  430 "130ccf",
  431 "564416",
  432 "883c6f",
  433 "c11247",
  434 "dc0712",
  435 "f3a0cf",
  436 "38af93",
  437 "719540",
  438 "1eb812",
  439 "d5bdc1",
  440 "64d3bf",
  441 "6ed7ac",
  442 "9bd2a8",
  443 "b2084c",
  444 "3c64b7",
  445 "545d6d",
  446 "772456",
  447 "2371d9",
  448 "dc0dae",
  449 "d7d7b2",
  450 "2bbd7f",
  451 "40738e",
  452 "67ab80",
  453 "e6e4de",
  454 "b89a5e",
  455 "5f9914",
  456 "191cfd",
  457 "47a5d6",
  458 "a53da3",
  459 "d9093f",
  460 "a4c200",
  461 "80ef57",
  462 "9da624",
  463 "890b10",
  464 "55a86d",
  465 "d311d7",
  466 "5f76dc",
  467 "23ff06",
  468 "acacf0",
  469 "cc9e0a",
  470 "1c07a1",
  471 "c89f1d",
  472 "df84c5",
  473 "9efff3",
  474 "6ce3e4",
  475 "5f50a9",
  476 "fd316b",
  477 "c8309c",
  478 "87c7ba",
  479 "18316f",
  480 "72c468",
  481 "c77aaf",
  482 "3eb458",
  483 "b8e53c",
  484 "d19437",
  485 "66baf1",
  486 "f0ca70",
  487 "20475b",
  488 "f307dc",
  489 "584386",
  490 "a41a54",
  491 "7cc02b",
  492 "fb76d0",
  493 "c401e7",
  494 "a2c7a5",
  495 "4ce650",
  496 "63b663",
  497 "ff2ad4",
  498 "17cebe",
  499 "71a37f",
  500 "64a650",
  501 "6ee450",
  502 "d78dd5",
  503 "9a31fa",
  504 "1e319c",
  505 "bbb6f8",
  506 "c757b8",
  507 "bef35b",
  508 "228580",
  509 "20711c",
  510 "6ff760",
  511 "7421d8",
  512 "4b4b22",
  513 "12da23",
  514 "eae08f",
  515 "d97a93",
  516 "2c586c",
  517 "75db40",
  518 "416e8f",
  519 "50625c",
  520 "56efc7",
  521 "d717ba",
  522 "af0655",
  523 "b4dc97",
  524 "bfcc9d",
  525 "676767",
  526 "4c2cbf",
  527 "c61e27",
  528 "ff057b",
  529 "737a5c",
  530 "3d04c7",
  531 "0c7daf",
  532 "f2726a",
  533 "f77154",
  534 "c2bf1d",
  535 "9ce6f1",
  536 "48446e",
  537 "ddfe0a",
  538 "6e0860",
  539 "cdd7b9",
  540 "b132f6",
  541 "54aba9",
  542 "c647c8",
  543 "58e6f5",
  544 "dfffc7",
  545 "1ca758",
  546 "5104be",
  547 "77833f",
  548 "78c4e6",
  549 "ba88f2",
  550 "5412b3",
  551 "829cf9",
  552 "fb7bf1",
  553 "0cce58",
  554 "22ce53",
  555 "109b0a",
  556 "5d0a7e",
  557 "49bff8",
  558 "1e1fcb",
  559 "781c13",
  560 "238a94",
  561 "ca36a7",
  562 "e51526",
  563 "553b27",
  564 "e6b0c9",
  565 "3d7eec",
  566 "e9735a",
  567 "08af13",
  568 "8e0999",
  569 "cb6ee8",
  570 "e5f5c1",
  571 "44a57f",
  572 "065a64",
  573 "ca50f2",
  574 "7ccbe9",
  575 "63f63f",
  576 "e1edd4",
  577 "71a89b",
  578 "47d84d",
  579 "c6023b",
  580 "3d613e",
  581 "44eb5e",
  582 "0a5141",
  583 "857ad1",
  584 "8c651b",
  585 "3105af",
  586 "5a626d",
  587 "c6a6b4",
  588 "90f13e",
  589 "7fa635",
  590 "d081cf",
  591 "d79561",
  592 "0ba7f4",
  593 "6a7a0a",
  594 "8fc1fe",
  595 "22cc35",
  596 "aaebb6",
  597 "012cb4",
  598 "a90850",
  599 "b2bd3e",
  600 "cca8e5",
  601 "ebba2d",
  602 "104c32",
  603 "dd3d18",
  604 "43c40a",
  605 "98045c",
  606 "435133",
  607 "3cb492",
  608 "f50b6d",
  609 "b73aba",
  610 "4bbc46",
  611 "854628",
  612 "d58beb",
  613 "3d0a34",
  614 "a51c13",
  615 "610ebf",
  616 "86ccf4",
  617 "865a97",
  618 "68af7a",
  619 "c7ceac",
  620 "96aeae",
  621 "2ace92",
  622 "8d5e14",
  623 "b95c14",
  624 "f482da",
  625 "93a1f1",
  626 "6dd570",
  627 "9076b2",
  628 "f62937",
  629 "f71924",
  630 "a48882",
  631 "4d409d",
  632 "c47b27",
  633 "a58de7",
  634 "09c43b",
  635 "a14ca0",
  636 "3f6d35",
  637 "d8744b",
  638 "732fb7",
  639 "6c1e5d",
  640 "036011",
  641 "a5c47e",
  642 "f8b58f",
  643 "ebd6fd",
  644 "7bce36",
  645 "6c3f92",
  646 "aa5a05",
  647 "363c30",
  648 "ff53a6",
  649 "f49ea9",
  650 "9735a1",
  651 "2ff489",
  652 "579169",
  653 "0a2873",
  654 "0239d5",
  655 "bc5c24",
  656 "01efb4",
  657 "5b7e45",
  658 "0b3a0f",
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  660 "c3d4cc",
  661 "c444d7",
  662 "5fd5aa",
  663 "029925",
  664 "5ee102",
  665 "2fc756",
  666 "b3e6b7",
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  668 "df130f",
  669 "c11b40",
  670 "db238a",
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  672 "aa40a9",
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  674 "190e40",
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  678 "3f93bc",
  679 "53741c",
  680 "3226cf",
  681 "e0b9fb",
  682 "0a36a8",
  683 "4e999a",
  684 "ab07d2",
  685 "0fb7b1",
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  691 "ffb49c",
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  702 "37a6d4",
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  710 "201232",
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  715 "2b17aa",
  716 "3f3f5a",
  717 "411b3d",
  718 "52b500",
  719 "842773",
  720 "24c8ae",
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  722 "faf5d3",
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  724 "7555e6",
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  726 "5191e5",
  727 "f0d448",
  728 "abdbbd",
  729 "8b5b8b",
  730 "a50f07",
  731 "3ef04b",
  732 "666ec6",
  733 "c07ec4",
  734 "515d6c",
  735 "1ed557",
  736 "38ce56",
  737 "afdabf",
  738 "7f5af5",
  739 "61f668",
  740 "9a0a4f",
  741 "bb303d",
  742 "3f8be1",
  743 "21a10d",
  744 "65d6ec",
  745 "7ced20",
  746 "20d162",
  747 "da80fb",
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  749 "c6a2ad",
  750 "352716",
  751 "1a5084",
  752 "8e8436",
  753 "a3e6ae",
  754 "beb919",
  755 "83979c",
  756 "cd5f0d",
  757 "1b8042",
  758 "0788b8",
  759 "95a84a",
  760 "e968f5",
  761 "3c1a13",
  762 "4c75c1",
  763 "506f16",
  764 "f7438f",
  765 "427bfe",
  766 "e23789",
  767 "79388e",
  768 "242972",
  769 "fb3d53",
  770 "d29e53",
  771 "71c558",
  772 "8b8cae",
  773 "ed0077",
  774 "a70dcb",
  775 "9baeb8",
  776 "817a72",
  777 "ed836f",
  778 "81b19d",
  779 "e6c18c",
  780 "fb83c5",
  781 "9f8a7c",
  782 "c548c3",
  783 "d32a59",
  784 "124d50",
  785 "bf8067",
  786 "7094e1",
  787 "8df859",
  788 "68090f",
  789 "ad4650",
  790 "0e9816",
  791 "2de91e",
  792 "21b5d9",
  793 "32016c",
  794 "eaba89",
  795 "831049",
  796 "9766e7",
  797 "7d88df",
  798 "18b8bd",
  799 "84fe43",
  800 "edce7d",
  801 "467a61",
  802 "70048b",
  803 "b24fc3",
  804 "578861",
  805 "cd16cb",
  806 "b14d2c",
  807 "69032c",
  808 "532bce",
  809 "fd0e13",
  810 "b7d483",
  811 "d1e0a8",
  812 "17b117",
  813 "b1ac9a",
  814 "70af9b",
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 3314 "38b62b",
 3315 "87379b",
 3316 "320b42",
 3317 "1ffdd0",
 3318 "30092e",
 3319 "e83203",
 3320 "bd8c26",
 3321 "e62572",
 3322 "ae4362",
 3323 "14c9f3",
 3324 "4519fc",
 3325 "13b80c",
 3326 "bdf45f",
 3327 "254a66",
 3328 "a95365",
 3329 "f55fdd",
 3330 "59fe3e",
 3331 "6e1a4d",
 3332 "8e984a",
 3333 "a9e9e4",
 3334 "f55160",
 3335 "24c6d5",
 3336 "49a3cc",
 3337 "b1c9d8",
 3338 "f6bc88",
 3339 "f2604f",
 3340 "83eb80",
 3341 "c93bdd",
 3342 "e49dc0",
 3343 "0aef1e",
 3344 "c87880",
 3345 "9de2d4",
 3346 "0dc7a4",
 3347 "2d59e1",
 3348 "eb496f",
 3349 "41445e",
 3350 "9c9f4e",
 3351 "cbec71",
 3352 "9579c0",
 3353 "78cfa9",
 3354 "f18de2",
 3355 "0be7f0",
 3356 "4b054b",
 3357 "dc3f33",
 3358 "618077",
 3359 "dfc01c",
 3360 "0ad917",
 3361 "fb4d07",
 3362 "f784c2",
 3363 "bb8323",
 3364 "74e8bb",
 3365 "275a70",
 3366 "e8c39c",
 3367 "1405df",
 3368 "570341",
 3369 "1ccb99",
 3370 "09d459",
 3371 "3f546b",
 3372 "95e032",
 3373 "19c8bb",
 3374 "c67a85",
 3375 "c3224d",
 3376 "ce4380",
 3377 "c6d56c",
 3378 "e8ef18",
 3379 "93fc71",
 3380 "32f457",
 3381 "e8285b",
 3382 "f87509",
 3383 "b6e78f",
 3384 "c4c5f1",
 3385 "66f323",
 3386 "d7b1df",
 3387 "06f79d",
 3388 "49b163",
 3389 "1cd196",
 3390 "aee64e",
 3391 "4476d6",
 3392 "65c10d",
 3393 "81cc80",
 3394 "44d2e9",
 3395 "1a7ad7",
 3396 "38a132",
 3397 "5aefda",
 3398 "b917fc",
 3399 "e41f4f",
 3400 "958f57",
 3401 "43eef9",
 3402 "6517f8",
 3403 "c0ac48",
 3404 "e1733a",
 3405 "3d4051",
 3406 "864033",
 3407 "5cd1b7",
 3408 "9c05d2",
 3409 "436028",
 3410 "5e2738",
 3411 "6d1225",
 3412 "53487a",
 3413 "3a0089",
 3414 "4c77e4",
 3415 "6a6ae0",
 3416 "64ea77",
 3417 "5423c0",
 3418 "ad6289",
 3419 "7cb0b3",
 3420 "bd2a3b",
 3421 "72086c",
 3422 "99b701",
 3423 "219440",
 3424 "748a9e",
 3425 "3b02b3",
 3426 "6fb1ec",
 3427 "289bab",
 3428 "842b64",
 3429 "4b9191",
 3430 "a343c0",
 3431 SUCCESS],rec(DupCheck:=FALSE)),
 3432     base:=[
 3433 rec(
 3434   kind := "FUNCTION",
 3435   name := "RetrieveDocumentation",
 3436   sin := [ [ string, "dochash" ] ],
 3437   sou := [ [ record ] ],
 3438   short := "Retrieve the current entry for `dochash' in the global documentation.\nUse this function to obtain the entire record from __DOC as is.",
 3439   ex := [ "RetrieveDocumentation(\"f896a5\");" ],
 3440   hash := "f896a5",
 3441   sig := "RetrieveDocumentation(<string> dochash)",
 3442   sog := " -> <record>",
 3443   docsrc := "docui.g",
 3444   sinflat := [ string ],
 3445   souflat := [ record ],
 3446   soghash := "275a70",
 3447   sig4hash := "RetrieveDocumentation(string)" ),
 3448 rec(
 3449   kind := "FUNCTION",
 3450   name := "ExistsDocumentation",
 3451   sin := [ [ string, "dochash" ] ],
 3452   sou := [ [ elt-alg^boo ] ],
 3453   short := "Return true iff documentation for 'dochash' is available.",
 3454   ex := [  ],
 3455   hash := "95e4b1",
 3456   sig := "ExistsDocumentation(<string> dochash)",
 3457   sog := " -> <elt-alg^boo>",
 3458   docsrc := "docui.g",
 3459   sinflat := [ string ],
 3460   souflat := [ elt-alg^boo ],
 3461   soghash := "5e8dd4",
 3462   sig4hash := "ExistsDocumentation(string)" ),
 3463 rec(
 3464   kind := "FUNCTION",
 3465   name := "DisplayDocSig",
 3466   sin := [ [ string, "dochash" ] ],
 3467   sou := [  ],
 3468   short := "Display name and signature for `dochash' which must be a valid hash in the internal documentation.",
 3469   see := [ "4546ad", "575f80" ],
 3470   ex := [ "DisplayDocSig(\"5d80db\");" ],
 3471   hash := "5d80db",
 3472   sig := "DisplayDocSig(<string> dochash)",
 3473   sog := "",
 3474   docsrc := "docui.g",
 3475   sinflat := [ string ],
 3476   souflat := [  ],
 3477   soghash := "da39a3",
 3478   sig4hash := "DisplayDocSig(string)" ),
 3479 rec(
 3480   kind := "FUNCTION",
 3481   name := "DisplayDocShort",
 3482   sin := [ [ string, "dochash" ] ],
 3483   sou := [  ],
 3484   short := "Display name, signature and shortdoc (if existing) for `dochash'.",
 3485   see := [ "5d80db", "575f80" ],
 3486   ex := [ "DisplayDocShort(\"4546ad\");" ],
 3487   hash := "4546ad",
 3488   sig := "DisplayDocShort(<string> dochash)",
 3489   sog := "",
 3490   docsrc := "docui.g",
 3491   sinflat := [ string ],
 3492   souflat := [  ],
 3493   soghash := "da39a3",
 3494   sig4hash := "DisplayDocShort(string)" ),
 3495 rec(
 3496   kind := "FUNCTION",
 3497   name := "DisplayDocComplete",
 3498   sin := [ [ string, "dochash" ] ],
 3499   sou := [  ],
 3500   short := "Display name, signature and everything else for `dochash'.",
 3501   see := [ "5d80db", "4546ad" ],
 3502   ex := [ "DisplayDocComplete(\"575f80\");" ],
 3503   hash := "575f80",
 3504   sig := "DisplayDocComplete(<string> dochash)",
 3505   sog := "",
 3506   docsrc := "docui.g",
 3507   sinflat := [ string ],
 3508   souflat := [  ],
 3509   soghash := "da39a3",
 3510   sig4hash := "DisplayDocComplete(string)" ),
 3511 rec(
 3512   kind := "FUNCTION",
 3513   name := "InstallMethod",
 3514   sin := [ [ record, "docrec" ], [ func, "body" ] ],
 3515   opt := [ [ elt-ord^rat, "Position", "Default: 1, negative numbers are ..." ] ],
 3516   sou := [ [  ] ],
 3517   short := "Install the function `body' to be executed when called with arguments as specified by `docrec'.sin.\nNote: `docrec' has to be a fully qualified documentation record, `MergeDocumentation' is called automatically.",
 3518   see := [ "a3cff8" ],
 3519   hash := "cfb542",
 3520   ex := [  ],
 3521   sig := "InstallMethod(<record> docrec, <func> body [, optargs])",
 3522   sog := "",
 3523   docsrc := "method.g",
 3524   sinflat := [ record, func ],
 3525   souflat := [  ],
 3526   soghash := "da39a3",
 3527   sig4hash := "InstallMethod(record,func)" ),
 3528 rec(
 3529   kind := "FUNCTION",
 3530   name := "List",
 3531   sin := [ [ list, "l" ], [ func, "f" ] ],
 3532   sou := [  ],
 3533   short := "Apply `f' to every member of `l' and return the list of return values.",
 3534   ex := [ "l:=[1,2,3,4];\nList(l,i->3*i);", "l:=[1,2,3,4];\nList(l,IsEven);" ],
 3535   see := [  ],
 3536   hash := "881f04",
 3537   sig := "List(<list> l, <func> f)",
 3538   sog := "",
 3539   docsrc := "init-methods.g",
 3540   sinflat := [ list, func ],
 3541   souflat := [  ],
 3542   soghash := "da39a3",
 3543   sig4hash := "List(list,func)" ),
 3544 rec(
 3545   kind := "FUNCTION",
 3546   name := "List",
 3547   sin := [ [ func, "f" ], [ list, "l" ] ],
 3548   sou := [  ],
 3549   short := "Apply `f' to every member of `l' and return the list of return values.",
 3550   ex := [ "l:=[1,2,3,4];\nList(i->3*i,l);", "l:=[1,2,3,4];\nList(IsEven,l);" ],
 3551   see := [  ],
 3552   hash := "7251a6",
 3553   sig := "List(<func> f, <list> l)",
 3554   sog := "",
 3555   docsrc := "init-methods.g",
 3556   sinflat := [ func, list ],
 3557   souflat := [  ],
 3558   soghash := "da39a3",
 3559   sig4hash := "List(func,list)" ),
 3560 rec(
 3561   kind := "FUNCTION",
 3562   docsrc := "string.c",
 3563   name := "Size",
 3564   sin := [ [ string, "S" ] ],
 3565   sou := [ [ elt-ord^rat ] ],
 3566   short := "Determine and return the number of characters in `S'.",
 3567   ex := [ "Size(\"foo\");" ],
 3568   see := [ "b2cb94" ],
 3569   hash := "a0823b",
 3570   sig := "Size(<string> S)",
 3571   sog := " -> <elt-ord^rat>",
 3572   sinflat := [ string ],
 3573   souflat := [ elt-ord^rat ],
 3574   soghash := "898213",
 3575   sig4hash := "Size(string)" ),
 3576 rec(
 3577   kind := "FUNCTION",
 3578   docsrc := "list.c",
 3579   name := "Size",
 3580   sin := [ [ list, "L" ] ],
 3581   sou := [ [ elt-ord^rat ] ],
 3582   short := "Determine and return the greatest position a value assigned to in `L'.",
 3583   ex := [ "Size([1,2,3]);", "Size([1,,,,,,,,2]);", "Size([1,2,,,,,,,]);" ],
 3584   see := [  ],
 3585   hash := "b2cb94",
 3586   sig := "Size(<list> L)",
 3587   sog := " -> <elt-ord^rat>",
 3588   sinflat := [ list ],
 3589   souflat := [ elt-ord^rat ],
 3590   soghash := "898213",
 3591   sig4hash := "Size(list)" ),
 3592 rec(
 3593   kind := "FUNCTION",
 3594   name := "Apply_",
 3595   sin := [ [ list, "l" ], [ func, "f" ] ],
 3596   sou := [  ],
 3597   short := "Apply 'f' to every member of `l' and replace the entry by the corresponding return value.\nNote: The previous contents of `l' will be lost.",
 3598   ex := [ "l:=[1,2,3,4];\nApply_(l,i->3*i); l;", "l:=[1,2,3,4];\nApply_(l,IsEven); l;" ],
 3599   see := [  ],
 3600   hash := "c4f2b5",
 3601   sig := "Apply_(<list> l, <func> f)",
 3602   sog := "",
 3603   docsrc := "init-methods.g",
 3604   sinflat := [ list, func ],
 3605   souflat := [  ],
 3606   soghash := "da39a3",
 3607   sig4hash := "Apply_(list,func)" ),
 3608 rec(
 3609   kind := "FUNCTION",
 3610   name := "Apply_",
 3611   sin := [ [ func, "f" ], [ list, "l" ] ],
 3612   sou := [  ],
 3613   short := "Apply 'f' to every member of `l' and replace the entry by the corresponding return value.\nNote: The previous contents of `l' will be lost.",
 3614   ex := [ "l:=[1,2,3,4];\nApply_(i->3*i,l); l;", "l:=[1,2,3,4];\nApply_(IsEven,l); l;" ],
 3615   see := [  ],
 3616   hash := "143f84",
 3617   sig := "Apply_(<func> f, <list> l)",
 3618   sog := "",
 3619   docsrc := "init-methods.g",
 3620   sinflat := [ func, list ],
 3621   souflat := [  ],
 3622   soghash := "da39a3",
 3623   sig4hash := "Apply_(func,list)" ),
 3624 rec(
 3625   kind := "FUNCTION",
 3626   name := "Apply",
 3627   sin := [ [ list, "l" ], [ func, "f" ] ],
 3628   sou := [ [ list, "r" ] ],
 3629   short := "Return the list where every member 'b' of 'l' is replaced by 'f' applied to 'b'.",
 3630   ex := [ "l:=[1,2,3,4];\nApply(l,i->3*i); l;", "l:=[1,2,3,4];\nApply(l,IsEven); l;" ],
 3631   see := [  ],
 3632   hash := "ac2569",
 3633   sig := "Apply(<list> l, <func> f)",
 3634   sog := " -> <list> r",
 3635   docsrc := "init-methods.g",
 3636   sinflat := [ list, func ],
 3637   souflat := [ list ],
 3638   soghash := "38b62b",
 3639   sig4hash := "Apply(list,func)" ),
 3640 rec(
 3641   kind := "FUNCTION",
 3642   name := "Apply",
 3643   sin := [ [ func, "f" ], [ list, "A" ] ],
 3644   sou := [ [ list, "r" ] ],
 3645   short := "Apply 'f' to every member of `A' and replace the entry by the corresponding return value.\nNote: The previous contents of `l' will be lost.",
 3646   ex := [ "l:=[1,2,3,4];\nApply(i->3*i,l); l;", "l:=[1,2,3,4];\nApply(IsEven,l); l;" ],
 3647   see := [  ],
 3648   hash := "8024dd",
 3649   sig := "Apply(<func> f, <list> A)",
 3650   sog := " -> <list> r",
 3651   docsrc := "init-methods.g",
 3652   sinflat := [ func, list ],
 3653   souflat := [ list ],
 3654   soghash := "38b62b",
 3655   sig4hash := "Apply(func,list)" ),
 3656 rec(
 3657   kind := "FUNCTION",
 3658   name := "Apply",
 3659   sin := [ [ func, "f" ], [ alist, "A" ] ],
 3660   sou := [ [ alist, "r" ] ],
 3661   short := "Apply `f' to every member of `A' and return the alist of return values.",
 3662   ex := [ "l:=Alist([3,1],[6,2],[9,3],[12,4]);\nApply(i->3*i,l);", "l:=[1,2,3,4];\nApply(IsEven,l);" ],
 3663   see := [  ],
 3664   hash := "b49bbf",
 3665   sig := "Apply(<func> f, <alist> A)",
 3666   sog := " -> <alist> r",
 3667   docsrc := "init-methods.g",
 3668   sinflat := [ func, alist ],
 3669   souflat := [ alist ],
 3670   soghash := "4405bf",
 3671   sig4hash := "Apply(func,alist)" ),
 3672 rec(
 3673   kind := "FUNCTION",
 3674   name := "Apply",
 3675   sin := [ [ alist, "l" ], [ func, "f" ] ],
 3676   sou := [ [ alist, "r" ] ],
 3677   short := "Apply `f' to every member of `l' and return the alist of return values.",
 3678   ex := [ "l:=Alist([3,1],[6,2],[9,3],[12,4]);\nApply(l,i->3*i);", "l:=[1,2,3,4];\nApply(l,IsEven);" ],
 3679   see := [  ],
 3680   hash := "c7a0ee",
 3681   sig := "Apply(<alist> l, <func> f)",
 3682   sog := " -> <alist> r",
 3683   docsrc := "init-methods.g",
 3684   sinflat := [ alist, func ],
 3685   souflat := [ alist ],
 3686   soghash := "4405bf",
 3687   sig4hash := "Apply(alist,func)" ),
 3688 rec(
 3689   kind := "FUNCTION",
 3690   name := "Apply_",
 3691   sin := [ [ alist, "A" ], [ func, "f" ] ],
 3692   sou := [  ],
 3693   short := "Apply 'f' to every member of `A' and replace the entry by the corresponding return value.\nNote: The previous contents of `A' will be lost.",
 3694   ex := [ "l:=[1,2,3,4];\nApply_(l,i->3*i); l;", "l:=[1,2,3,4];\nApply_(l,IsEven); l;" ],
 3695   see := [  ],
 3696   hash := "3b1b6a",
 3697   sig := "Apply_(<alist> A, <func> f)",
 3698   sog := "",
 3699   docsrc := "init-methods.g",
 3700   sinflat := [ alist, func ],
 3701   souflat := [  ],
 3702   soghash := "da39a3",
 3703   sig4hash := "Apply_(alist,func)" ),
 3704 rec(
 3705   kind := "FUNCTION",
 3706   name := "Apply_",
 3707   sin := [ [ func, "f" ], [ alist, "A" ] ],
 3708   sou := [  ],
 3709   short := "Apply 'f' to every member of `A' and replace the entry by the corresponding return value.\nNote: The previous contents of `l' will be lost.",
 3710   ex := [ "l:=[1,2,3,4];\nApply_(i->3*i,l); l;", "l:=[1,2,3,4];\nApply_(IsEven,l); l;" ],
 3711   see := [  ],
 3712   hash := "636b79",
 3713   sig := "Apply_(<func> f, <alist> A)",
 3714   sog := "",
 3715   docsrc := "init-methods.g",
 3716   sinflat := [ func, alist ],
 3717   souflat := [  ],
 3718   soghash := "da39a3",
 3719   sig4hash := "Apply_(func,alist)" ),
 3720 rec(
 3721   kind := "FUNCTION",
 3722   name := "GetEntry",
 3723   sin := [ [ record, "r" ], [ string, "f" ] ],
 3724   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 3725               Default := FAILURE ) ] ],
 3726   sou := [ [ any ] ],
 3727   short := "Returns the element of `r' in the field `f' if it exists and fails otherwise.",
 3728   ex := [ "A:=rec(ac:=1,ad:=INFTY);\nGetEntry(A,\"ad\");\nGetEntry(A,\"ab\");" ],
 3729   see := [  ],
 3730   hash := "bde31f",
 3731   sig := "GetEntry(<record> r, <string> f [, optargs])",
 3732   sog := " -> <any>",
 3733   docsrc := "init-methods.g",
 3734   sinflat := [ record, string ],
 3735   souflat := [ any ],
 3736   soghash := "c5fe02",
 3737   sig4hash := "GetEntry(record,string)" ),
 3738 rec(
 3739   kind := "FUNCTION",
 3740   name := "GetEntry",
 3741   sin := [ [ list, "l" ], [ elt-ord^rat, "pos" ] ],
 3742   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 3743               Default := FAILURE ) ] ],
 3744   sou := [ [ any ] ],
 3745   short := "Returns the element of `l' at position `pos' if it exists and fails otherwise.",
 3746   ex := [ "A:=[2,3,5,7,11,13,17,19];\nGetEntry(A,2);\nGetEntry(A,44);" ],
 3747   see := [  ],
 3748   hash := "1630a6",
 3749   sig := "GetEntry(<list> l, <elt-ord^rat> pos [, optargs])",
 3750   sog := " -> <any>",
 3751   docsrc := "init-methods.g",
 3752   sinflat := [ list, elt-ord^rat ],
 3753   souflat := [ any ],
 3754   soghash := "c5fe02",
 3755   sig4hash := "GetEntry(list,elt-ord^rat)" ),
 3756 rec(
 3757   kind := "FUNCTION",
 3758   name := "Position",
 3759   sin := [ [ list, "L" ], [ any, "a" ] ],
 3760   opt := [ [ elt-ord^rat, "Start", "Determines the position where the search is started.", rec(
 3761               Default := 1 ) ], [ any, "Fail", "Determines what to return in case of failure.", rec(
 3762               Default := FAILURE ) ] ],
 3763   sou := [ [ elt-ord^rat ] ],
 3764   short := "Return the position of the first occurence of `a' in `L' if `a in L' is true, and FAILURE otherwise.",
 3765   ex := [ "L:=[1,,3,4];\nPosition(L,3); Position(L,1,rec(Start:=2)); Position(L,\"foo\");" ],
 3766   see := [  ],
 3767   hash := "2ae099",
 3768   sig := "Position(<list> L, <any> a [, optargs])",
 3769   sog := " -> <elt-ord^rat>",
 3770   docsrc := "init-methods.g",
 3771   sinflat := [ list, any ],
 3772   souflat := [ elt-ord^rat ],
 3773   soghash := "898213",
 3774   sig4hash := "Position(list,any)" ),
 3775 rec(
 3776   kind := "FUNCTION",
 3777   name := "Position",
 3778   sin := [ [ string, "S" ], [ char, "c" ] ],
 3779   opt := [ [ elt-ord^rat, "Start", "Determines the position where the search is started.", rec(
 3780               Default := 1 ) ], [ any, "Fail", "Determines what to return in case of failure.", rec(
 3781               Default := FAILURE ) ] ],
 3782   sou := [ [ elt-ord^rat ] ],
 3783   short := "Return the position of the first occurence of `c' in `S' if c is a character in the string `S', and FAILURE otherwise.",
 3784   ex := [ "S:=\"foobar\";\nPosition(S,'o'); Position(S,'f',rec(Start:=2)); Position(S,\"foo\");" ],
 3785   see := [  ],
 3786   hash := "e10eac",
 3787   sig := "Position(<string> S, <char> c [, optargs])",
 3788   sog := " -> <elt-ord^rat>",
 3789   docsrc := "init-methods.g",
 3790   sinflat := [ string, char ],
 3791   souflat := [ elt-ord^rat ],
 3792   soghash := "898213",
 3793   sig4hash := "Position(string,char)" ),
 3794 rec(
 3795   kind := "FUNCTION",
 3796   name := "Position",
 3797   sin := [ [ dry, "D" ], [ any, "a" ] ],
 3798   opt := [ [ elt-ord^rat, "Start", "Determines the position where the search is started.", rec(
 3799               Default := 1 ) ], [ any, "Fail", "Determines what to return in case of failure.", rec(
 3800               Default := FAILURE ) ] ],
 3801   sou := [ [ elt-ord^rat ] ],
 3802   short := "Return the position of the occurence of `a' in `D' if `a in D' is true, and FAILURE otherwise.",
 3803   ex := [ "D:=Dry([1,12,4,3]);\nPosition(D,12); Position(D,1,rec(Start:=2)); Position(D,\"foo\");" ],
 3804   see := [  ],
 3805   hash := "f6116f",
 3806   sig := "Position(<dry> D, <any> a [, optargs])",
 3807   sog := " -> <elt-ord^rat>",
 3808   docsrc := "init-methods.g",
 3809   sinflat := [ dry, any ],
 3810   souflat := [ elt-ord^rat ],
 3811   soghash := "898213",
 3812   sig4hash := "Position(dry,any)" ),
 3813 rec(
 3814   kind := "FUNCTION",
 3815   name := "Position",
 3816   sin := [ [ alist, "A" ], [ any, "a" ] ],
 3817   opt := [ [ elt-ord^rat, "Start", "Determines the position where the search is started.", rec(
 3818               Default := 1 ) ], [ any, "Fail", "Determines what to return in case of failure.", rec(
 3819               Default := FAILURE ) ] ],
 3820   sou := [ [ elt-ord^rat ] ],
 3821   short := "Return the position of the occurence of `a' in `A' if `a in A' is true, and FAILURE otherwise.",
 3822   ex := [ "A:=Alist([1,12],[3,4]);\nPosition(A,3); Position(A,1,rec(Start:=2)); Position(A,\"foo\");" ],
 3823   see := [  ],
 3824   hash := "3b8353",
 3825   sig := "Position(<alist> A, <any> a [, optargs])",
 3826   sog := " -> <elt-ord^rat>",
 3827   docsrc := "init-methods.g",
 3828   sinflat := [ alist, any ],
 3829   souflat := [ elt-ord^rat ],
 3830   soghash := "898213",
 3831   sig4hash := "Position(alist,any)" ),
 3832 rec(
 3833   kind := "FUNCTION",
 3834   name := "Mapconcat",
 3835   sin := [ [ func, "f" ], [ list, "l" ], [ string, "sep" ] ],
 3836   sou := [ [ string, "s" ] ],
 3837   short := "Apply `f' to every member of `l' to obtain a string. Then concatenate all these strings intermixed with `sep' and return the result.",
 3838   ex := [ "Stringify:=function(arg) return SPrint(arg[1]); end;\nMapconcat(Stringify,[E,1,\"test\"],\", \");" ],
 3839   see := [ "6a9bd1" ],
 3840   hash := "7834fe",
 3841   sig := "Mapconcat(<func> f, <list> l, <string> sep)",
 3842   sog := " -> <string> s",
 3843   docsrc := "init-methods.g",
 3844   sinflat := [ func, list, string ],
 3845   souflat := [ string ],
 3846   soghash := "ecb252",
 3847   sig4hash := "Mapconcat(func,list,string)" ),
 3848 rec(
 3849   kind := "FUNCTION",
 3850   name := "Mapconcat",
 3851   sin := [ [ func, "f" ], [ list, "l" ] ],
 3852   sou := [ [ string, "s" ] ],
 3853   short := "Apply `f' to every member of `l' to obtain a string. Then concatenate all these strings intermixed with a space and return the result.",
 3854   ex := [ "Stringify:=function(arg) return SPrint(arg[1]); end;\nMapconcat(Stringify,[E,1,\"test\"]);" ],
 3855   see := [ "7834fe" ],
 3856   hash := "6a9bd1",
 3857   sig := "Mapconcat(<func> f, <list> l)",
 3858   sog := " -> <string> s",
 3859   docsrc := "init-methods.g",
 3860   sinflat := [ func, list ],
 3861   souflat := [ string ],
 3862   soghash := "ecb252",
 3863   sig4hash := "Mapconcat(func,list)" ),
 3864 rec(
 3865   kind := "FUNCTION",
 3866   name := "Filtered",
 3867   sin := [ [ func, "pred" ], [ list, "l" ] ],
 3868   sou := [ [ list, "filt" ] ],
 3869   short := "Gather elements from `l' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 3870   ex := [ "Filtered(IsPrime,[1..100]);" ],
 3871   see := [  ],
 3872   hash := "c8a315",
 3873   sig := "Filtered(<func> pred, <list> l)",
 3874   sog := " -> <list> filt",
 3875   docsrc := "init-methods.g",
 3876   sinflat := [ func, list ],
 3877   souflat := [ list ],
 3878   soghash := "38b62b",
 3879   sig4hash := "Filtered(func,list)" ),
 3880 rec(
 3881   kind := "FUNCTION",
 3882   name := "Filtered",
 3883   sin := [ [ list, "l" ], [ func, "pred" ] ],
 3884   sou := [ [ list, "filt" ] ],
 3885   short := "Gather elements from `l' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 3886   ex := [ "Filtered([1..100],IsPrime);" ],
 3887   see := [  ],
 3888   hash := "aa13b4",
 3889   sig := "Filtered(<list> l, <func> pred)",
 3890   sog := " -> <list> filt",
 3891   docsrc := "init-methods.g",
 3892   sinflat := [ list, func ],
 3893   souflat := [ list ],
 3894   soghash := "38b62b",
 3895   sig4hash := "Filtered(list,func)" ),
 3896 rec(
 3897   kind := "FUNCTION",
 3898   name := "Butfirst",
 3899   sin := [ [ list, "l" ] ],
 3900   sou := [ [ list, "r" ] ],
 3901   short := "Return the list `l' without its first element.",
 3902   see := [ "2625da" ],
 3903   ex := [  ],
 3904   hash := "0b6f20",
 3905   sig := "Butfirst(<list> l)",
 3906   sog := " -> <list> r",
 3907   docsrc := "init-methods.g",
 3908   sinflat := [ list ],
 3909   souflat := [ list ],
 3910   soghash := "38b62b",
 3911   sig4hash := "Butfirst(list)" ),
 3912 rec(
 3913   kind := "FUNCTION",
 3914   name := "Butfirst_",
 3915   sin := [ [ list, "l" ] ],
 3916   sou := [ [ list, "r" ] ],
 3917   short := "Remove the first element from the list `l'.\nNote: `l' is modified by side-effect.",
 3918   see := [ "0b6f20" ],
 3919   ex := [  ],
 3920   hash := "2625da",
 3921   sig := "Butfirst_(<list> l)",
 3922   sog := " -> <list> r",
 3923   docsrc := "init-methods.g",
 3924   sinflat := [ list ],
 3925   souflat := [ list ],
 3926   soghash := "38b62b",
 3927   sig4hash := "Butfirst_(list)" ),
 3928 rec(
 3929   kind := "FUNCTION",
 3930   name := "First",
 3931   sin := [ [ list, "l" ] ],
 3932   sou := [ [ any, "f" ] ],
 3933   short := "Return the first element of the list `l'.",
 3934   see := [ "6da1f1" ],
 3935   hash := "887cf1",
 3936   ex := [  ],
 3937   sig := "First(<list> l)",
 3938   sog := " -> <any> f",
 3939   docsrc := "init-methods.g",
 3940   sinflat := [ list ],
 3941   souflat := [ any ],
 3942   soghash := "c5fe02",
 3943   sig4hash := "First(list)" ),
 3944 rec(
 3945   kind := "FUNCTION",
 3946   name := "Butlast",
 3947   sin := [ [ list, "l" ] ],
 3948   sou := [ [ list, "r" ] ],
 3949   short := "Return the list `l' without its last element.",
 3950   see := [ "f78331" ],
 3951   ex := [  ],
 3952   hash := "2dded0",
 3953   sig := "Butlast(<list> l)",
 3954   sog := " -> <list> r",
 3955   docsrc := "init-methods.g",
 3956   sinflat := [ list ],
 3957   souflat := [ list ],
 3958   soghash := "38b62b",
 3959   sig4hash := "Butlast(list)" ),
 3960 rec(
 3961   kind := "FUNCTION",
 3962   name := "Butlast_",
 3963   sin := [ [ list, "l" ] ],
 3964   sou := [ [ list, "r" ] ],
 3965   short := "Remove the last element from the list `l'.\nNote: `l' is modified by side-effect.",
 3966   see := [ "2dded0" ],
 3967   ex := [  ],
 3968   hash := "f78331",
 3969   sig := "Butlast_(<list> l)",
 3970   sog := " -> <list> r",
 3971   docsrc := "init-methods.g",
 3972   sinflat := [ list ],
 3973   souflat := [ list ],
 3974   soghash := "38b62b",
 3975   sig4hash := "Butlast_(list)" ),
 3976 rec(
 3977   kind := "FUNCTION",
 3978   name := "Last",
 3979   sin := [ [ list, "l" ] ],
 3980   sou := [ [ any, "r" ] ],
 3981   short := "Return the last element of the list `l'.",
 3982   see := [ "887cf1" ],
 3983   hash := "6da1f1",
 3984   ex := [  ],
 3985   sig := "Last(<list> l)",
 3986   sog := " -> <any> r",
 3987   docsrc := "init-methods.g",
 3988   sinflat := [ list ],
 3989   souflat := [ any ],
 3990   soghash := "c5fe02",
 3991   sig4hash := "Last(list)" ),
 3992 rec(
 3993   kind := "FUNCTION",
 3994   name := "Mapc",
 3995   sin := [ [ func, "f" ], [ list, "l" ] ],
 3996   sou := [  ],
 3997   short := "Apply 'f' on each element of 'l' _without_ modifying 'l'.",
 3998   ex := [  ],
 3999   hash := "d81c63",
 4000   sig := "Mapc(<func> f, <list> l)",
 4001   sog := "",
 4002   docsrc := "init-methods.g",
 4003   sinflat := [ func, list ],
 4004   souflat := [  ],
 4005   soghash := "da39a3",
 4006   sig4hash := "Mapc(func,list)" ),
 4007 rec(
 4008   kind := "FUNCTION",
 4009   name := "RunHookWithArg",
 4010   sin := [ [ list, "hook" ], [ any, "arg" ] ],
 4011   sou := [  ],
 4012   short := "Run each function of the list `hook' with `arg' as argument.\nThis is unlike Mapc which takes _one_ function which acts on a list of arguments.",
 4013   ex := [ "RunHookWithArg([i->i*2, i->i*3, i->i*4],2);" ],
 4014   hash := "b9f653",
 4015   sig := "RunHookWithArg(<list> hook, <any> arg)",
 4016   sog := "",
 4017   docsrc := "init-methods.g",
 4018   sinflat := [ list, any ],
 4019   souflat := [  ],
 4020   soghash := "da39a3",
 4021   sig4hash := "RunHookWithArg(list,any)" ),
 4022 rec(
 4023   kind := "FUNCTION",
 4024   name := "Concatenation",
 4025   sin := [ [ list, "l1" ], [ list, "l2" ] ],
 4026   sou := [ [ list, "l" ] ],
 4027   short := "Concatenate the lists `l1' and `l2' and return the result.",
 4028   ex := [ "Concatenation([1,2],[3,4]);" ],
 4029   see := [  ],
 4030   hash := "697229",
 4031   sig := "Concatenation(<list> l1, <list> l2)",
 4032   sog := " -> <list> l",
 4033   docsrc := "init-methods.g",
 4034   sinflat := [ list, list ],
 4035   souflat := [ list ],
 4036   soghash := "38b62b",
 4037   sig4hash := "Concatenation(list,list)" ),
 4038 rec(
 4039   kind := "FUNCTION",
 4040   name := "Flat",
 4041   sin := [ [ list, "l" ] ],
 4042   sou := [ [ list, "f" ] ],
 4043   short := "Flatten `l' by recursing into a nested list structure and fetching all atomary (i.e. non-lists) elements and return the result.",
 4044   ex := [ "l:=[[1],[2,3,4]];\nFlat(l);" ],
 4045   see := [  ],
 4046   hash := "19c302",
 4047   sig := "Flat(<list> l)",
 4048   sog := " -> <list> f",
 4049   docsrc := "init-methods.g",
 4050   sinflat := [ list ],
 4051   souflat := [ list ],
 4052   soghash := "38b62b",
 4053   sig4hash := "Flat(list)" ),
 4054 rec(
 4055   kind := "FUNCTION",
 4056   name := "Reversed",
 4057   sin := [ [ list, "l" ] ],
 4058   sou := [ [ list, "r" ] ],
 4059   short := "Reverse `l' and return the result.",
 4060   ex := [ "l:=[1,2,3,4];\nReversed(l);" ],
 4061   see := [  ],
 4062   hash := "1ed908",
 4063   sig := "Reversed(<list> l)",
 4064   sog := " -> <list> r",
 4065   docsrc := "init-methods.g",
 4066   sinflat := [ list ],
 4067   souflat := [ list ],
 4068   soghash := "38b62b",
 4069   sig4hash := "Reversed(list)" ),
 4070 rec(
 4071   kind := "FUNCTION",
 4072   name := "Filter",
 4073   sin := [ [ func, "pred" ] ],
 4074   sou := [ [ func, "filt" ] ],
 4075   short := "Construct a functional `filt(<list> l) -> <list>' which gathers elements from `l' which suffice the predicate function `pred' which has to have out-signature `-> elt-alg^boo'.",
 4076   ex := [ "f:=Filter(IsPrime);\nf([1..100]);\n" ],
 4077   see := [  ],
 4078   hash := "96e0c5",
 4079   sig := "Filter(<func> pred)",
 4080   sog := " -> <func> filt",
 4081   docsrc := "init-methods.g",
 4082   sinflat := [ func ],
 4083   souflat := [ func ],
 4084   soghash := "99fdb3",
 4085   sig4hash := "Filter(func)" ),
 4086 rec(
 4087   kind := "FUNCTION",
 4088   name := "Number",
 4089   sin := [ [ list, "l" ], [ func, "pred" ] ],
 4090   sou := [ [ elt-ord^rat ] ],
 4091   short := "Return the number of elements from `l' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4092   ex := [ "Number([1..100],IsPrime);" ],
 4093   see := [  ],
 4094   hash := "6a4b57",
 4095   sig := "Number(<list> l, <func> pred)",
 4096   sog := " -> <elt-ord^rat>",
 4097   docsrc := "init-methods.g",
 4098   sinflat := [ list, func ],
 4099   souflat := [ elt-ord^rat ],
 4100   soghash := "898213",
 4101   sig4hash := "Number(list,func)" ),
 4102 rec(
 4103   kind := "FUNCTION",
 4104   name := "Number",
 4105   sin := [ [ func, "pred" ], [ list, "l" ] ],
 4106   sou := [ [ elt-ord^rat ] ],
 4107   short := "Return the number of elements from `l' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4108   ex := [ "Number(IsPrime,[1..100]);" ],
 4109   see := [  ],
 4110   hash := "de4e08",
 4111   sig := "Number(<func> pred, <list> l)",
 4112   sog := " -> <elt-ord^rat>",
 4113   docsrc := "init-methods.g",
 4114   sinflat := [ func, list ],
 4115   souflat := [ elt-ord^rat ],
 4116   soghash := "898213",
 4117   sig4hash := "Number(func,list)" ),
 4118 rec(
 4119   kind := "FUNCTION",
 4120   name := "Number",
 4121   sin := [ [ list, "l" ] ],
 4122   sou := [ [ elt-ord^rat ] ],
 4123   short := "Count the number of elements in `l'.",
 4124   ex := [ "Number([101,102,103]);", "Number([1,2,3,,,,,,4]);" ],
 4125   see := [  ],
 4126   hash := "1543ee",
 4127   sig := "Number(<list> l)",
 4128   sog := " -> <elt-ord^rat>",
 4129   docsrc := "init-methods.g",
 4130   sinflat := [ list ],
 4131   souflat := [ elt-ord^rat ],
 4132   soghash := "898213",
 4133   sig4hash := "Number(list)" ),
 4134 rec(
 4135   kind := "FUNCTION",
 4136   name := "Number",
 4137   sin := [ [ func, "pred" ] ],
 4138   sou := [ [ func, "ctr" ] ],
 4139   short := "Construct a functional `ctr(<list> l) -> elt-ord^rat' which returns the number of elements from `l' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4140   ex := [ "f:=Number(IsPrime);\nf([1..100]);" ],
 4141   see := [  ],
 4142   hash := "deb7d2",
 4143   sig := "Number(<func> pred)",
 4144   sog := " -> <func> ctr",
 4145   docsrc := "init-methods.g",
 4146   sinflat := [ func ],
 4147   souflat := [ func ],
 4148   soghash := "99fdb3",
 4149   sig4hash := "Number(func)" ),
 4150 rec(
 4151   kind := "FUNCTION",
 4152   name := "Number",
 4153   sin := [ [ string, "s" ], [ func, "pred" ] ],
 4154   sou := [ [ elt-ord^rat ] ],
 4155   short := "Return the number of characters from `s' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4156   ex := [ "Number(\"some really random text\",i->i in \"aeiou\");" ],
 4157   see := [  ],
 4158   hash := "57fa02",
 4159   sig := "Number(<string> s, <func> pred)",
 4160   sog := " -> <elt-ord^rat>",
 4161   docsrc := "init-methods.g",
 4162   sinflat := [ string, func ],
 4163   souflat := [ elt-ord^rat ],
 4164   soghash := "898213",
 4165   sig4hash := "Number(string,func)" ),
 4166 rec(
 4167   kind := "FUNCTION",
 4168   name := "Number",
 4169   sin := [ [ func, "pred" ], [ string, "s" ] ],
 4170   sou := [ [ elt-ord^rat ] ],
 4171   short := "Return the number of characters from `s' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4172   ex := [ "Number(i->not i in \"aeiou\",\"hm, this is a demonstration text\");" ],
 4173   see := [  ],
 4174   hash := "8b67a5",
 4175   sig := "Number(<func> pred, <string> s)",
 4176   sog := " -> <elt-ord^rat>",
 4177   docsrc := "init-methods.g",
 4178   sinflat := [ func, string ],
 4179   souflat := [ elt-ord^rat ],
 4180   soghash := "898213",
 4181   sig4hash := "Number(func,string)" ),
 4182 rec(
 4183   kind := "FUNCTION",
 4184   name := "Number",
 4185   sin := [ [ string, "s" ] ],
 4186   sou := [ [ elt-ord^rat ] ],
 4187   short := "Count the number of characters in `s'.",
 4188   ex := [ "Number(\"How many characters do I have?\");" ],
 4189   see := [  ],
 4190   hash := "1a2112",
 4191   sig := "Number(<string> s)",
 4192   sog := " -> <elt-ord^rat>",
 4193   docsrc := "init-methods.g",
 4194   sinflat := [ string ],
 4195   souflat := [ elt-ord^rat ],
 4196   soghash := "898213",
 4197   sig4hash := "Number(string)" ),
 4198 rec(
 4199   kind := "FUNCTION",
 4200   name := "Number",
 4201   sin := [ [ seq(), "s" ], [ func, "pred" ] ],
 4202   sou := [ [ elt-ord^rat ] ],
 4203   short := "Return the number of elements from `s' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4204   ex := [ "Number(Sequence([1..100]),IsPrime);" ],
 4205   see := [  ],
 4206   hash := "398368",
 4207   sig := "Number(<seq()> s, <func> pred)",
 4208   sog := " -> <elt-ord^rat>",
 4209   docsrc := "init-methods.g",
 4210   sinflat := [ seq(), func ],
 4211   souflat := [ elt-ord^rat ],
 4212   soghash := "898213",
 4213   sig4hash := "Number(seq(),func)" ),
 4214 rec(
 4215   kind := "FUNCTION",
 4216   name := "Number",
 4217   sin := [ [ func, "pred" ], [ seq(), "s" ] ],
 4218   sou := [ [ elt-ord^rat ] ],
 4219   short := "Return the number of elements from `s' which suffice the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4220   ex := [ "Number(IsPrime,Sequence([1..100]));" ],
 4221   see := [  ],
 4222   hash := "f16dd2",
 4223   sig := "Number(<func> pred, <seq()> s)",
 4224   sog := " -> <elt-ord^rat>",
 4225   docsrc := "init-methods.g",
 4226   sinflat := [ func, seq() ],
 4227   souflat := [ elt-ord^rat ],
 4228   soghash := "898213",
 4229   sig4hash := "Number(func,seq())" ),
 4230 rec(
 4231   kind := "FUNCTION",
 4232   name := "Number",
 4233   sin := [ [ seq(), "s" ] ],
 4234   sou := [ [ elt-ord^rat ] ],
 4235   short := "Count the number of elements in `s'.",
 4236   ex := [ "Number(Sequence([101,102,103]));" ],
 4237   see := [  ],
 4238   hash := "b922b7",
 4239   sig := "Number(<seq()> s)",
 4240   sog := " -> <elt-ord^rat>",
 4241   docsrc := "init-methods.g",
 4242   sinflat := [ seq() ],
 4243   souflat := [ elt-ord^rat ],
 4244   soghash := "898213",
 4245   sig4hash := "Number(seq())" ),
 4246 rec(
 4247   kind := "FUNCTION",
 4248   name := "ForAll",
 4249   sin := [ [ list, "l" ], [ func, "pred" ] ],
 4250   sou := [ [ elt-alg^boo ] ],
 4251   short := "Return true iff every member of `l' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4252   ex := [ "ForAll([1..100],IsPrime);", "ForAll([2,4,6,8,100],IsEven);" ],
 4253   see := [  ],
 4254   hash := "b588e0",
 4255   sig := "ForAll(<list> l, <func> pred)",
 4256   sog := " -> <elt-alg^boo>",
 4257   docsrc := "init-methods.g",
 4258   sinflat := [ list, func ],
 4259   souflat := [ elt-alg^boo ],
 4260   soghash := "5e8dd4",
 4261   sig4hash := "ForAll(list,func)" ),
 4262 rec(
 4263   kind := "FUNCTION",
 4264   name := "ForAll",
 4265   sin := [ [ func, "pred" ], [ list, "l" ] ],
 4266   sou := [ [ elt-alg^boo ] ],
 4267   short := "Return true iff every member of `l' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4268   ex := [ "ForAll(IsPrime,[1..100]);", "ForAll(IsEven,[2,4,6,8,100]);" ],
 4269   see := [  ],
 4270   hash := "214893",
 4271   sig := "ForAll(<func> pred, <list> l)",
 4272   sog := " -> <elt-alg^boo>",
 4273   docsrc := "init-methods.g",
 4274   sinflat := [ func, list ],
 4275   souflat := [ elt-alg^boo ],
 4276   soghash := "5e8dd4",
 4277   sig4hash := "ForAll(func,list)" ),
 4278 rec(
 4279   kind := "FUNCTION",
 4280   name := "ForAll",
 4281   sin := [ [ func, "pred" ] ],
 4282   sou := [ [ func, "fa" ] ],
 4283   short := "Construct a functional `fa(<list> l) -> elt-alg^boo' which returns true iff every member of `l' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4284   ex := [ "l:=[Random(10),Random(10)];\nf:=ForAll(IsEven);\nl; f(l);" ],
 4285   see := [  ],
 4286   hash := "2809b1",
 4287   sig := "ForAll(<func> pred)",
 4288   sog := " -> <func> fa",
 4289   docsrc := "init-methods.g",
 4290   sinflat := [ func ],
 4291   souflat := [ func ],
 4292   soghash := "99fdb3",
 4293   sig4hash := "ForAll(func)" ),
 4294 rec(
 4295   kind := "FUNCTION",
 4296   name := "ForAll",
 4297   sin := [ [ seq(), "s" ], [ func, "pred" ] ],
 4298   sou := [ [ elt-alg^boo ] ],
 4299   short := "Return true iff every element of `s' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4300   ex := [ "ForAll(Sequence([1..100]),IsPrime);", "ForAll(Sequence([2,4,6,8,100]),IsEven);" ],
 4301   see := [ "b588e0" ],
 4302   hash := "efdf43",
 4303   sig := "ForAll(<seq()> s, <func> pred)",
 4304   sog := " -> <elt-alg^boo>",
 4305   docsrc := "init-methods.g",
 4306   sinflat := [ seq(), func ],
 4307   souflat := [ elt-alg^boo ],
 4308   soghash := "5e8dd4",
 4309   sig4hash := "ForAll(seq(),func)" ),
 4310 rec(
 4311   kind := "FUNCTION",
 4312   name := "ForAll",
 4313   sin := [ [ func, "pred" ], [ seq(), "s" ] ],
 4314   sou := [ [ elt-alg^boo ] ],
 4315   short := "Return true iff every element of `s' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4316   ex := [ "ForAll(IsPrime,Sequence([1..100]));", "ForAll(IsEven,Sequence([2,4,6,8,100]));" ],
 4317   see := [ "214893" ],
 4318   hash := "3557f0",
 4319   sig := "ForAll(<func> pred, <seq()> s)",
 4320   sog := " -> <elt-alg^boo>",
 4321   docsrc := "init-methods.g",
 4322   sinflat := [ func, seq() ],
 4323   souflat := [ elt-alg^boo ],
 4324   soghash := "5e8dd4",
 4325   sig4hash := "ForAll(func,seq())" ),
 4326 rec(
 4327   kind := "FUNCTION",
 4328   name := "ForAny",
 4329   sin := [ [ list, "l" ], [ func, "pred" ] ],
 4330   sou := [ [ elt-alg^boo ] ],
 4331   short := "Return true iff every member of `l' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4332   ex := [ "ForAny([1..100],IsPrime);", "ForAny([2,4,6,8,100],IsEven);" ],
 4333   see := [  ],
 4334   hash := "7081f0",
 4335   sig := "ForAny(<list> l, <func> pred)",
 4336   sog := " -> <elt-alg^boo>",
 4337   docsrc := "init-methods.g",
 4338   sinflat := [ list, func ],
 4339   souflat := [ elt-alg^boo ],
 4340   soghash := "5e8dd4",
 4341   sig4hash := "ForAny(list,func)" ),
 4342 rec(
 4343   kind := "FUNCTION",
 4344   name := "ForAny",
 4345   sin := [ [ func, "pred" ], [ list, "l" ] ],
 4346   sou := [ [ elt-alg^boo ] ],
 4347   short := "Return true iff every member of `l' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4348   ex := [ "ForAny(IsPrime,[1..100]);", "ForAny(IsOdd,[2,4,6,8,100]);" ],
 4349   see := [  ],
 4350   hash := "37c247",
 4351   sig := "ForAny(<func> pred, <list> l)",
 4352   sog := " -> <elt-alg^boo>",
 4353   docsrc := "init-methods.g",
 4354   sinflat := [ func, list ],
 4355   souflat := [ elt-alg^boo ],
 4356   soghash := "5e8dd4",
 4357   sig4hash := "ForAny(func,list)" ),
 4358 rec(
 4359   kind := "FUNCTION",
 4360   name := "ForAny",
 4361   sin := [ [ func, "pred" ] ],
 4362   sou := [ [ func, "fa" ] ],
 4363   short := "Construct a functional `fa(<list> l) -> elt-alg^boo' which returns true iff every member of `l' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4364   ex := [ "l:=[Random(1000)..1000+Random(1000)];\nf:=ForAny(IsPrime);\nl; f(l);" ],
 4365   see := [  ],
 4366   hash := "e9863c",
 4367   sig := "ForAny(<func> pred)",
 4368   sog := " -> <func> fa",
 4369   docsrc := "init-methods.g",
 4370   sinflat := [ func ],
 4371   souflat := [ func ],
 4372   soghash := "99fdb3",
 4373   sig4hash := "ForAny(func)" ),
 4374 rec(
 4375   kind := "FUNCTION",
 4376   name := "ForAny",
 4377   sin := [ [ seq(), "s" ], [ func, "pred" ] ],
 4378   sou := [ [ elt-alg^boo ] ],
 4379   short := "Return true iff every element of `s' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4380   ex := [ "ForAny(Sequence([1..100]),IsPrime);", "ForAny(Sequence([2,4,6,8,100]),IsEven);" ],
 4381   see := [ "7081f0" ],
 4382   hash := "d8eb79",
 4383   sig := "ForAny(<seq()> s, <func> pred)",
 4384   sog := " -> <elt-alg^boo>",
 4385   docsrc := "init-methods.g",
 4386   sinflat := [ seq(), func ],
 4387   souflat := [ elt-alg^boo ],
 4388   soghash := "5e8dd4",
 4389   sig4hash := "ForAny(seq(),func)" ),
 4390 rec(
 4391   kind := "FUNCTION",
 4392   name := "ForAny",
 4393   sin := [ [ func, "pred" ], [ seq(), "s" ] ],
 4394   sou := [ [ elt-alg^boo ] ],
 4395   short := "Return true iff every element of `s' suffices the predicate function `pred'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4396   ex := [ "ForAny(IsPrime,Sequence([1..100]));", "ForAny(IsOdd,Sequence([2,4,6,8,100]));" ],
 4397   see := [ "37c247" ],
 4398   hash := "455bb8",
 4399   sig := "ForAny(<func> pred, <seq()> s)",
 4400   sog := " -> <elt-alg^boo>",
 4401   docsrc := "init-methods.g",
 4402   sinflat := [ func, seq() ],
 4403   souflat := [ elt-alg^boo ],
 4404   soghash := "5e8dd4",
 4405   sig4hash := "ForAny(func,seq())" ),
 4406 rec(
 4407   kind := "FUNCTION",
 4408   name := "First",
 4409   sin := [ [ list, "l" ], [ func, "pred" ] ],
 4410   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4411               Default := FAILURE ) ] ],
 4412   sou := [ [ any ] ],
 4413   short := "Find the first element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4414   ex := [ "First([1..100],IsPrime);", "First([2,4,6,8,12,50,100],i->i mod 5=0);" ],
 4415   see := [ "ea1698" ],
 4416   hash := "5447d9",
 4417   sig := "First(<list> l, <func> pred [, optargs])",
 4418   sog := " -> <any>",
 4419   docsrc := "init-methods.g",
 4420   sinflat := [ list, func ],
 4421   souflat := [ any ],
 4422   soghash := "c5fe02",
 4423   sig4hash := "First(list,func)" ),
 4424 rec(
 4425   kind := "FUNCTION",
 4426   name := "First",
 4427   sin := [ [ func, "pred" ], [ list, "l" ] ],
 4428   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4429               Default := FAILURE ) ] ],
 4430   sou := [ [ any ] ],
 4431   short := "Find the first element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4432   ex := [ "First(IsPrime,[1..100]);", "First(IsOdd,[2,4,6,8,100]);" ],
 4433   see := [ "f9320a" ],
 4434   hash := "b428bb",
 4435   sig := "First(<func> pred, <list> l [, optargs])",
 4436   sog := " -> <any>",
 4437   docsrc := "init-methods.g",
 4438   sinflat := [ func, list ],
 4439   souflat := [ any ],
 4440   soghash := "c5fe02",
 4441   sig4hash := "First(func,list)" ),
 4442 rec(
 4443   kind := "FUNCTION",
 4444   name := "First",
 4445   sin := [ [ func, "pred" ] ],
 4446   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4447               Default := FAILURE ) ] ],
 4448   sou := [ [ func, "fir" ] ],
 4449   short := "Construct a functional `fir(<list> l) -> any' which finds and returns the first element which suffices the predicate function `pred' and returns it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4450   ex := [ "l:=[Random(1000)..1000+Random(1000)];\nf:=First(i->i mod 17=0);\nl; f(l);" ],
 4451   see := [ "3e2598" ],
 4452   hash := "2e722c",
 4453   sig := "First(<func> pred [, optargs])",
 4454   sog := " -> <func> fir",
 4455   docsrc := "init-methods.g",
 4456   sinflat := [ func ],
 4457   souflat := [ func ],
 4458   soghash := "99fdb3",
 4459   sig4hash := "First(func)" ),
 4460 rec(
 4461   kind := "FUNCTION",
 4462   name := "First",
 4463   sin := [ [ string, "s" ], [ func, "pred" ] ],
 4464   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4465               Default := FAILURE ) ] ],
 4466   sou := [ [ char ] ],
 4467   short := "Find the first character which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4468   ex := [ "First(\"abcdefzyx\",i->(i='d' or i='z'));" ],
 4469   see := [ "2a0f5b" ],
 4470   hash := "d6a98a",
 4471   sig := "First(<string> s, <func> pred [, optargs])",
 4472   sog := " -> <char>",
 4473   docsrc := "init-methods.g",
 4474   sinflat := [ string, func ],
 4475   souflat := [ char ],
 4476   soghash := "71fafc",
 4477   sig4hash := "First(string,func)" ),
 4478 rec(
 4479   kind := "FUNCTION",
 4480   name := "First",
 4481   sin := [ [ func, "pred" ], [ string, "s" ] ],
 4482   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4483               Default := FAILURE ) ] ],
 4484   sou := [ [ char ] ],
 4485   short := "Find the first character which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4486   ex := [ "First(i->(i='d' or i='z'),\"abcdefzyx\");" ],
 4487   see := [ "9528e2" ],
 4488   hash := "144d2d",
 4489   sig := "First(<func> pred, <string> s [, optargs])",
 4490   sog := " -> <char>",
 4491   docsrc := "init-methods.g",
 4492   sinflat := [ func, string ],
 4493   souflat := [ char ],
 4494   soghash := "71fafc",
 4495   sig4hash := "First(func,string)" ),
 4496 rec(
 4497   kind := "FUNCTION",
 4498   name := "First",
 4499   sin := [ [ seq(), "s" ], [ func, "pred" ] ],
 4500   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4501               Default := FAILURE ) ] ],
 4502   sou := [ [ any ] ],
 4503   short := "Find the first element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4504   ex := [ "First(Sequence([1..100]),IsPrime);", "First(Sequence([2,4,6,8,12,50,100]),i->i mod 5=0);" ],
 4505   see := [ "51dd36" ],
 4506   hash := "ad4301",
 4507   sig := "First(<seq()> s, <func> pred [, optargs])",
 4508   sog := " -> <any>",
 4509   docsrc := "init-methods.g",
 4510   sinflat := [ seq(), func ],
 4511   souflat := [ any ],
 4512   soghash := "c5fe02",
 4513   sig4hash := "First(seq(),func)" ),
 4514 rec(
 4515   kind := "FUNCTION",
 4516   name := "First",
 4517   sin := [ [ func, "pred" ], [ seq(), "s" ] ],
 4518   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4519               Default := FAILURE ) ] ],
 4520   sou := [ [ any ] ],
 4521   short := "Find the first element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4522   ex := [ "First(IsPrime,Sequence([1..100]));", "First(IsOdd,Sequence([2,4,6,8,100]));" ],
 4523   see := [ "f9320a" ],
 4524   hash := "66b097",
 4525   sig := "First(<func> pred, <seq()> s [, optargs])",
 4526   sog := " -> <any>",
 4527   docsrc := "init-methods.g",
 4528   sinflat := [ func, seq() ],
 4529   souflat := [ any ],
 4530   soghash := "c5fe02",
 4531   sig4hash := "First(func,seq())" ),
 4532 rec(
 4533   kind := "FUNCTION",
 4534   name := "Last",
 4535   sin := [ [ list, "l" ], [ func, "pred" ] ],
 4536   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4537               Default := FAILURE ) ] ],
 4538   sou := [ [ any ] ],
 4539   short := "Find the last element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4540   ex := [ "Last([1..100],IsPrime);", "Last([2,4,6,8,12,50,100],i->i mod 3=0);" ],
 4541   see := [ "5447d9" ],
 4542   hash := "ea1698",
 4543   sig := "Last(<list> l, <func> pred [, optargs])",
 4544   sog := " -> <any>",
 4545   docsrc := "init-methods.g",
 4546   sinflat := [ list, func ],
 4547   souflat := [ any ],
 4548   soghash := "c5fe02",
 4549   sig4hash := "Last(list,func)" ),
 4550 rec(
 4551   kind := "FUNCTION",
 4552   name := "Last",
 4553   sin := [ [ func, "pred" ], [ list, "l" ] ],
 4554   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4555               Default := FAILURE ) ] ],
 4556   sou := [ [ any ] ],
 4557   short := "Find the last element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4558   ex := [ "Last(IsPrime,[1..100]);", "Last(IsOdd,[2,4,6,8,100]);" ],
 4559   see := [ "b428bb" ],
 4560   hash := "f9320a",
 4561   sig := "Last(<func> pred, <list> l [, optargs])",
 4562   sog := " -> <any>",
 4563   docsrc := "init-methods.g",
 4564   sinflat := [ func, list ],
 4565   souflat := [ any ],
 4566   soghash := "c5fe02",
 4567   sig4hash := "Last(func,list)" ),
 4568 rec(
 4569   kind := "FUNCTION",
 4570   name := "Last",
 4571   sin := [ [ func, "pred" ] ],
 4572   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4573               Default := FAILURE ) ] ],
 4574   sou := [ [ func, "las" ] ],
 4575   short := "Construct a functional `las(<list> l) -> any' which finds and returns the last element which suffices the predicate function `pred' and returns it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4576   ex := [ "l:=[Random(1000)..1000+Random(1000)];\nf:=Last(i->i mod 17=0);\nl; f(l);" ],
 4577   see := [ "2e722c" ],
 4578   hash := "3e2598",
 4579   sig := "Last(<func> pred [, optargs])",
 4580   sog := " -> <func> las",
 4581   docsrc := "init-methods.g",
 4582   sinflat := [ func ],
 4583   souflat := [ func ],
 4584   soghash := "99fdb3",
 4585   sig4hash := "Last(func)" ),
 4586 rec(
 4587   kind := "FUNCTION",
 4588   name := "Last",
 4589   sin := [ [ string, "s" ], [ func, "pred" ] ],
 4590   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4591               Default := FAILURE ) ] ],
 4592   sou := [ [ char ] ],
 4593   short := "Find the last character which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4594   ex := [ "Last(\"test\",i->i<'s');" ],
 4595   see := [ "d6a98a" ],
 4596   hash := "2a0f5b",
 4597   sig := "Last(<string> s, <func> pred [, optargs])",
 4598   sog := " -> <char>",
 4599   docsrc := "init-methods.g",
 4600   sinflat := [ string, func ],
 4601   souflat := [ char ],
 4602   soghash := "71fafc",
 4603   sig4hash := "Last(string,func)" ),
 4604 rec(
 4605   kind := "FUNCTION",
 4606   name := "Last",
 4607   sin := [ [ func, "pred" ], [ string, "s" ] ],
 4608   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4609               Default := FAILURE ) ] ],
 4610   sou := [ [ char ] ],
 4611   short := "Find the last character which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4612   ex := [ "Last(i->i>'f',\"this is a demo.\");" ],
 4613   see := [ "144d2d" ],
 4614   hash := "9528e2",
 4615   sig := "Last(<func> pred, <string> s [, optargs])",
 4616   sog := " -> <char>",
 4617   docsrc := "init-methods.g",
 4618   sinflat := [ func, string ],
 4619   souflat := [ char ],
 4620   soghash := "71fafc",
 4621   sig4hash := "Last(func,string)" ),
 4622 rec(
 4623   kind := "FUNCTION",
 4624   name := "Last",
 4625   sin := [ [ seq(), "s" ], [ func, "pred" ] ],
 4626   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4627               Default := FAILURE ) ] ],
 4628   sou := [ [ any ] ],
 4629   short := "Find the last element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4630   ex := [ "Last(Sequence([1..100]),IsPrime);", "Last(Sequence([2,4,6,8,12,50,100]),i->i mod 3=0);" ],
 4631   see := [ "ad4301" ],
 4632   hash := "51dd36",
 4633   sig := "Last(<seq()> s, <func> pred [, optargs])",
 4634   sog := " -> <any>",
 4635   docsrc := "init-methods.g",
 4636   sinflat := [ seq(), func ],
 4637   souflat := [ any ],
 4638   soghash := "c5fe02",
 4639   sig4hash := "Last(seq(),func)" ),
 4640 rec(
 4641   kind := "FUNCTION",
 4642   name := "Last",
 4643   sin := [ [ func, "pred" ], [ seq(), "s" ] ],
 4644   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4645               Default := FAILURE ) ] ],
 4646   sou := [ [ any ] ],
 4647   short := "Find the last element which suffices the predicate function `pred' and return it.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4648   ex := [ "Last(IsPrime,Sequence([1..100]));", "Last(IsOdd,Sequence([2,4,6,8,100]));" ],
 4649   see := [ "66b097" ],
 4650   hash := "3729c0",
 4651   sig := "Last(<func> pred, <seq()> s [, optargs])",
 4652   sog := " -> <any>",
 4653   docsrc := "init-methods.g",
 4654   sinflat := [ func, seq() ],
 4655   souflat := [ any ],
 4656   soghash := "c5fe02",
 4657   sig4hash := "Last(func,seq())" ),
 4658 rec(
 4659   kind := "FUNCTION",
 4660   name := "PositionProperty",
 4661   sin := [ [ list, "l" ], [ func, "pred" ] ],
 4662   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4663               Default := FAILURE ) ] ],
 4664   sou := [ [ elt-ord^rat ] ],
 4665   short := "Return the position of the first element of `l' which suffices the predicate function `pred'.\nReturn FAILURE if no such element exists in `l'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4666   ex := [ "PositionProperty([50..100],IsPrime);", "PositionProperty([2,4,6,8,12,50,100],i->i mod 5=0);" ],
 4667   see := [  ],
 4668   hash := "4ecb42",
 4669   sig := "PositionProperty(<list> l, <func> pred [, optargs])",
 4670   sog := " -> <elt-ord^rat>",
 4671   docsrc := "init-methods.g",
 4672   sinflat := [ list, func ],
 4673   souflat := [ elt-ord^rat ],
 4674   soghash := "898213",
 4675   sig4hash := "PositionProperty(list,func)" ),
 4676 rec(
 4677   kind := "FUNCTION",
 4678   name := "PositionProperty",
 4679   sin := [ [ func, "pred" ], [ list, "l" ] ],
 4680   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4681               Default := FAILURE ) ] ],
 4682   sou := [ [ elt-ord^rat ] ],
 4683   short := "Return the position of the first element of `l' which suffices the predicate function `pred'.\nReturn FAILURE if no such element exists in `l'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4684   ex := [ "PositionProperty(IsPrime,[1..100]);", "PositionProperty(IsOdd,[2,4,6,8,100]);" ],
 4685   see := [  ],
 4686   hash := "199ebf",
 4687   sig := "PositionProperty(<func> pred, <list> l [, optargs])",
 4688   sog := " -> <elt-ord^rat>",
 4689   docsrc := "init-methods.g",
 4690   sinflat := [ func, list ],
 4691   souflat := [ elt-ord^rat ],
 4692   soghash := "898213",
 4693   sig4hash := "PositionProperty(func,list)" ),
 4694 rec(
 4695   kind := "FUNCTION",
 4696   name := "PositionProperty",
 4697   sin := [ [ func, "pred" ] ],
 4698   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4699               Default := FAILURE ) ] ],
 4700   sou := [ [ func, "pos" ] ],
 4701   short := "Construct a functional `pos(<list> l) -> elt-ord^rat' which returns the position of the first element of `l' which suffices the predicate function `pred'.\nReturn FAILURE if no such element exists in `l'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4702   ex := [ "l:=[Random(1000)..1000+Random(1000)];;\nf:=PositionProperty(i->i mod 17=0);;\nl; f(l);" ],
 4703   see := [  ],
 4704   hash := "03ff1b",
 4705   sig := "PositionProperty(<func> pred [, optargs])",
 4706   sog := " -> <func> pos",
 4707   docsrc := "init-methods.g",
 4708   sinflat := [ func ],
 4709   souflat := [ func ],
 4710   soghash := "99fdb3",
 4711   sig4hash := "PositionProperty(func)" ),
 4712 rec(
 4713   kind := "FUNCTION",
 4714   name := "PositionProperty",
 4715   sin := [ [ string, "s" ], [ func, "pred" ] ],
 4716   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4717               Default := FAILURE ) ] ],
 4718   sou := [ [ elt-ord^rat ] ],
 4719   short := "Return the position of the first character of `s' which suffices the predicate function `pred'.\nReturn FAILURE if no such character exists in `s'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4720   ex := [ "PositionProperty(\"some random text\",i->i in \"uvwxyz\");" ],
 4721   see := [  ],
 4722   hash := "4a46b0",
 4723   sig := "PositionProperty(<string> s, <func> pred [, optargs])",
 4724   sog := " -> <elt-ord^rat>",
 4725   docsrc := "init-methods.g",
 4726   sinflat := [ string, func ],
 4727   souflat := [ elt-ord^rat ],
 4728   soghash := "898213",
 4729   sig4hash := "PositionProperty(string,func)" ),
 4730 rec(
 4731   kind := "FUNCTION",
 4732   name := "PositionProperty",
 4733   sin := [ [ func, "pred" ], [ string, "s" ] ],
 4734   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4735               Default := FAILURE ) ] ],
 4736   sou := [ [ elt-ord^rat ] ],
 4737   short := "Return the position of the first character of `s' which suffices the predicate function `pred'.\nReturn FAILURE if no such character exists in `s'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4738   ex := [ "PositionProperty(i->i in \"aeiou\",\"some random text\");" ],
 4739   see := [  ],
 4740   hash := "14d69d",
 4741   sig := "PositionProperty(<func> pred, <string> s [, optargs])",
 4742   sog := " -> <elt-ord^rat>",
 4743   docsrc := "init-methods.g",
 4744   sinflat := [ func, string ],
 4745   souflat := [ elt-ord^rat ],
 4746   soghash := "898213",
 4747   sig4hash := "PositionProperty(func,string)" ),
 4748 rec(
 4749   kind := "FUNCTION",
 4750   name := "PositionProperty",
 4751   sin := [ [ seq(), "s" ], [ func, "pred" ] ],
 4752   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4753               Default := FAILURE ) ] ],
 4754   sou := [ [ elt-ord^rat ] ],
 4755   short := "Return the position of the first element of `s' which suffices the predicate function `pred'.\nReturn FAILURE if no such element exists in `s'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4756   ex := [ "PositionProperty(Sequence([50..100]),IsPrime);", "PositionProperty(Sequence([2,4,6,8,12,50,100]),i->i mod 5=0);" ],
 4757   see := [ "4ecb42" ],
 4758   hash := "3c99b9",
 4759   sig := "PositionProperty(<seq()> s, <func> pred [, optargs])",
 4760   sog := " -> <elt-ord^rat>",
 4761   docsrc := "init-methods.g",
 4762   sinflat := [ seq(), func ],
 4763   souflat := [ elt-ord^rat ],
 4764   soghash := "898213",
 4765   sig4hash := "PositionProperty(seq(),func)" ),
 4766 rec(
 4767   kind := "FUNCTION",
 4768   name := "PositionProperty",
 4769   sin := [ [ func, "pred" ], [ seq(), "s" ] ],
 4770   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 4771               Default := FAILURE ) ] ],
 4772   sou := [ [ elt-ord^rat ] ],
 4773   short := "Return the position of the first element of `s' which suffices the predicate function `pred'.\nReturn FAILURE if no such element exists in `s'.\nNote: Apparently `pred' must have `-> elt-alg^boo' out-signature.",
 4774   ex := [ "PositionProperty(IsPrime,Sequence([1..100]));", "PositionProperty(IsOdd,Sequence([2,4,6,8,100]));" ],
 4775   see := [ "199ebf" ],
 4776   hash := "0f6520",
 4777   sig := "PositionProperty(<func> pred, <seq()> s [, optargs])",
 4778   sog := " -> <elt-ord^rat>",
 4779   docsrc := "init-methods.g",
 4780   sinflat := [ func, seq() ],
 4781   souflat := [ elt-ord^rat ],
 4782   soghash := "898213",
 4783   sig4hash := "PositionProperty(func,seq())" ),
 4784 rec(
 4785   kind := "FUNCTION",
 4786   name := "Collected",
 4787   sin := [ [ list, "l" ] ],
 4788   sou := [ [ list, "coll" ] ],
 4789   short := "Document me!",
 4790   ex := [ "Collected([1,2,3,3,2,5,4,3,2,1,4,4,3]);" ],
 4791   see := [  ],
 4792   hash := "1fbd2d",
 4793   sig := "Collected(<list> l)",
 4794   sog := " -> <list> coll",
 4795   docsrc := "init-methods.g",
 4796   sinflat := [ list ],
 4797   souflat := [ list ],
 4798   soghash := "38b62b",
 4799   sig4hash := "Collected(list)" ),
 4800 rec(
 4801   kind := "FUNCTION",
 4802   name := "Cartesian",
 4803   sin := [ [ list, "l1" ], [ list, "l2" ] ],
 4804   sou := [ [ list, "l1xl2" ] ],
 4805   short := "Return list obtained by the cartesian product of `l1' and `l2'.",
 4806   ex := [ "Cartesian([1,2,3,4],[1,I]);" ],
 4807   see := [  ],
 4808   hash := "7de892",
 4809   sig := "Cartesian(<list> l1, <list> l2)",
 4810   sog := " -> <list> l1xl2",
 4811   docsrc := "init-methods.g",
 4812   sinflat := [ list, list ],
 4813   souflat := [ list ],
 4814   soghash := "38b62b",
 4815   sig4hash := "Cartesian(list,list)" ),
 4816 rec(
 4817   kind := "FUNCTION",
 4818   name := "Sort",
 4819   sin := [ [ list, "l" ] ],
 4820   sou := [  ],
 4821   short := "Sort `l'.",
 4822   ex := [ "A:=[1,14,3,7,2,1];\nSort(A); A;" ],
 4823   see := [  ],
 4824   hash := "335b78",
 4825   sig := "Sort(<list> l)",
 4826   sog := "",
 4827   docsrc := "init-methods.g",
 4828   sinflat := [ list ],
 4829   souflat := [  ],
 4830   soghash := "da39a3",
 4831   sig4hash := "Sort(list)" ),
 4832 rec(
 4833   kind := "FUNCTION",
 4834   name := "SortParallel",
 4835   sin := [ [ list, "l1" ], [ list, "l2" ] ],
 4836   sou := [  ],
 4837   short := "Document me!",
 4838   ex := [  ],
 4839   see := [  ],
 4840   hash := "72db5a",
 4841   sig := "SortParallel(<list> l1, <list> l2)",
 4842   sog := "",
 4843   docsrc := "init-methods.g",
 4844   sinflat := [ list, list ],
 4845   souflat := [  ],
 4846   soghash := "da39a3",
 4847   sig4hash := "SortParallel(list,list)" ),
 4848 rec(
 4849   kind := "FUNCTION",
 4850   name := "Permuted",
 4851   sin := [ [ list, "l" ], [ elt-grp^per, "perm" ] ],
 4852   sou := [  ],
 4853   short := "Document me!",
 4854   ex := [  ],
 4855   see := [  ],
 4856   hash := "dcc5e1",
 4857   sig := "Permuted(<list> l, <elt-grp^per> perm)",
 4858   sog := "",
 4859   docsrc := "init-methods.g",
 4860   sinflat := [ list, elt-grp^per ],
 4861   souflat := [  ],
 4862   soghash := "da39a3",
 4863   sig4hash := "Permuted(list,elt-grp^per)" ),
 4864 rec(
 4865   kind := "FUNCTION",
 4866   name := "PositionSorted",
 4867   sin := [ [ list, "l" ], [ any, "elm" ] ],
 4868   sou := [ [ elt-ord^rat ] ],
 4869   short := "Returns the position of `elm' in the sorted list `l'.",
 4870   ex := [ "A:=[2,3,5,7,11,13,17,19];\nPositionSorted(A,11);" ],
 4871   see := [  ],
 4872   hash := "39607a",
 4873   sig := "PositionSorted(<list> l, <any> elm)",
 4874   sog := " -> <elt-ord^rat>",
 4875   docsrc := "init-methods.g",
 4876   sinflat := [ list, any ],
 4877   souflat := [ elt-ord^rat ],
 4878   soghash := "898213",
 4879   sig4hash := "PositionSorted(list,any)" ),
 4880 rec(
 4881   kind := "FUNCTION",
 4882   name := "Product",
 4883   sin := [ [ list, "l" ] ],
 4884   sou := [ [ any ] ],
 4885   short := "Return the product of the elements of `l'.\nNote: `l' may consist of elements of different types. Generally `Product' works on everything `*' can operate on.",
 4886   ex := [ "Product([2,3,5,7]);", "Product([2,\"1,2 \",2]);" ],
 4887   see := [  ],
 4888   hash := "f81ead",
 4889   sig := "Product(<list> l)",
 4890   sog := " -> <any>",
 4891   docsrc := "init-methods.g",
 4892   sinflat := [ list ],
 4893   souflat := [ any ],
 4894   soghash := "c5fe02",
 4895   sig4hash := "Product(list)" ),
 4896 rec(
 4897   kind := "FUNCTION",
 4898   name := "Product",
 4899   sin := [ [ seq(), "S" ] ],
 4900   sou := [ [ any ] ],
 4901   short := "Return the product of the elements of `s'.",
 4902   ex := [ "Product( Sequence([1, 2, 3]) );\nProduct( Sequence([1..100]) );\nProduct( [1, 2, 3] );\nProduct( [1..100] );" ],
 4903   see := [ "f81ead" ],
 4904   hash := "ad5189",
 4905   sig := "Product(<seq()> S)",
 4906   sog := " -> <any>",
 4907   docsrc := "<internal>",
 4908   sinflat := [ seq() ],
 4909   souflat := [ any ],
 4910   soghash := "da39a3",
 4911   sig4hash := "Product(seq())" ),
 4912 rec(
 4913   kind := "FUNCTION",
 4914   name := "Product",
 4915   sin := [ [ tup(), "t" ] ],
 4916   sou := [ [ any ] ],
 4917   short := "Return the product of the elements of `t'.",
 4918   ex := [ "Product(Tuple([2,3,5,7]));", "Product(Tuple([2,\"a,b \",5]));" ],
 4919   see := [ "f81ead" ],
 4920   hash := "1bdd5d",
 4921   sig := "Product(<tup()> t)",
 4922   sog := " -> <any>",
 4923   docsrc := "init-methods.g",
 4924   sinflat := [ tup() ],
 4925   souflat := [ any ],
 4926   soghash := "c5fe02",
 4927   sig4hash := "Product(tup())" ),
 4928 rec(
 4929   kind := "FUNCTION",
 4930   name := "Product",
 4931   sin := [ [ list, "l" ], [ func, "f" ] ],
 4932   sou := [ [ any ] ],
 4933   short := "Document me!",
 4934   ex := [  ],
 4935   see := [  ],
 4936   hash := "4a4a6e",
 4937   sig := "Product(<list> l, <func> f)",
 4938   sog := " -> <any>",
 4939   docsrc := "init-methods.g",
 4940   sinflat := [ list, func ],
 4941   souflat := [ any ],
 4942   soghash := "c5fe02",
 4943   sig4hash := "Product(list,func)" ),
 4944 rec(
 4945   kind := "FUNCTION",
 4946   name := "Product",
 4947   sin := [ [ func, "l" ], [ list, "l" ] ],
 4948   sou := [ [ any ] ],
 4949   short := "Document me!",
 4950   ex := [  ],
 4951   see := [  ],
 4952   hash := "fbad9f",
 4953   sig := "Product(<func> l, <list> l)",
 4954   sog := " -> <any>",
 4955   docsrc := "init-methods.g",
 4956   sinflat := [ func, list ],
 4957   souflat := [ any ],
 4958   soghash := "c5fe02",
 4959   sig4hash := "Product(func,list)" ),
 4960 rec(
 4961   kind := "FUNCTION",
 4962   name := "Product",
 4963   sin := [ [ func, "l" ] ],
 4964   sou := [ [ any ] ],
 4965   short := "Document me!",
 4966   ex := [  ],
 4967   see := [  ],
 4968   hash := "43bf9a",
 4969   sig := "Product(<func> l)",
 4970   sog := " -> <any>",
 4971   docsrc := "init-methods.g",
 4972   sinflat := [ func ],
 4973   souflat := [ any ],
 4974   soghash := "c5fe02",
 4975   sig4hash := "Product(func)" ),
 4976 rec(
 4977   kind := "FUNCTION",
 4978   name := "Sum",
 4979   sin := [ [ list, "l" ] ],
 4980   sou := [ [ any ] ],
 4981   short := "Return the sum of the elements of `l'.\nNote: `l' may consist of elements of different types. Generally `Sum' works on everything `+' can operate on.",
 4982   ex := [ "Sum([1..100]);", "Sum([\"a\",\"b\",\"c\"]);" ],
 4983   see := [  ],
 4984   hash := "0730f5",
 4985   sig := "Sum(<list> l)",
 4986   sog := " -> <any>",
 4987   docsrc := "init-methods.g",
 4988   sinflat := [ list ],
 4989   souflat := [ any ],
 4990   soghash := "c5fe02",
 4991   sig4hash := "Sum(list)" ),
 4992 rec(
 4993   kind := "FUNCTION",
 4994   name := "Sum",
 4995   sin := [ [ seq(), "S" ] ],
 4996   sou := [ [ any ] ],
 4997   short := "Return the sum of the elements of `s'.",
 4998   ex := [ "Sum( Sequence([1, 2, 3]) );\nSum( Sequence([1..100]) );\nSum( [1, 2, 3] );\nSum( [1..100] );" ],
 4999   see := [  ],
 5000   hash := "68305c",
 5001   sig := "Sum(<seq()> S)",
 5002   sog := " -> <any>",
 5003   docsrc := "<internal>",
 5004   sinflat := [ seq() ],
 5005   souflat := [ any ],
 5006   soghash := "da39a3",
 5007   sig4hash := "Sum(seq())" ),
 5008 rec(
 5009   kind := "FUNCTION",
 5010   name := "Sum",
 5011   sin := [ [ tup(), "t" ] ],
 5012   sou := [ [ any ] ],
 5013   short := "Return the sum of the elements of `t'.",
 5014   ex := [ "Sum(Tuple([1..100]));", "Sum(Tuple([\"a\",\"b\",\"c\"]));" ],
 5015   see := [  ],
 5016   hash := "fc8a38",
 5017   sig := "Sum(<tup()> t)",
 5018   sog := " -> <any>",
 5019   docsrc := "init-methods.g",
 5020   sinflat := [ tup() ],
 5021   souflat := [ any ],
 5022   soghash := "c5fe02",
 5023   sig4hash := "Sum(tup())" ),
 5024 rec(
 5025   kind := "FUNCTION",
 5026   name := "Sum",
 5027   sin := [ [ list, "l" ], [ func, "f" ] ],
 5028   sou := [ [ any ] ],
 5029   short := "Document me!",
 5030   ex := [  ],
 5031   see := [  ],
 5032   hash := "36bbdd",
 5033   sig := "Sum(<list> l, <func> f)",
 5034   sog := " -> <any>",
 5035   docsrc := "init-methods.g",
 5036   sinflat := [ list, func ],
 5037   souflat := [ any ],
 5038   soghash := "c5fe02",
 5039   sig4hash := "Sum(list,func)" ),
 5040 rec(
 5041   kind := "FUNCTION",
 5042   name := "Sum",
 5043   sin := [ [ func, "f" ], [ list, "l" ] ],
 5044   sou := [ [ any ] ],
 5045   short := "Document me!",
 5046   ex := [  ],
 5047   see := [  ],
 5048   hash := "ab6670",
 5049   sig := "Sum(<func> f, <list> l)",
 5050   sog := " -> <any>",
 5051   docsrc := "init-methods.g",
 5052   sinflat := [ func, list ],
 5053   souflat := [ any ],
 5054   soghash := "c5fe02",
 5055   sig4hash := "Sum(func,list)" ),
 5056 rec(
 5057   kind := "FUNCTION",
 5058   name := "Sum",
 5059   sin := [ [ func, "f" ] ],
 5060   sou := [ [ any ] ],
 5061   short := "Document me!",
 5062   ex := [  ],
 5063   see := [  ],
 5064   hash := "e60d0d",
 5065   sig := "Sum(<func> f)",
 5066   sog := " -> <any>",
 5067   docsrc := "init-methods.g",
 5068   sinflat := [ func ],
 5069   souflat := [ any ],
 5070   soghash := "c5fe02",
 5071   sig4hash := "Sum(func)" ),
 5072 rec(
 5073   kind := "FUNCTION",
 5074   name := "Iterated",
 5075   sin := [ [ list, "l" ], [ func, "f" ] ],
 5076   sou := [ [ any ] ],
 5077   short := "Document me!",
 5078   ex := [  ],
 5079   see := [  ],
 5080   hash := "650413",
 5081   sig := "Iterated(<list> l, <func> f)",
 5082   sog := " -> <any>",
 5083   docsrc := "init-methods.g",
 5084   sinflat := [ list, func ],
 5085   souflat := [ any ],
 5086   soghash := "c5fe02",
 5087   sig4hash := "Iterated(list,func)" ),
 5088 rec(
 5089   kind := "FUNCTION",
 5090   name := "Maximum",
 5091   sin := [ [ set, "s" ] ],
 5092   sou := [ [ any ] ],
 5093   short := "Determine and return the maximal element of `s'.\nNote: `s' may also be a list (nonetheless `Set(s)' must exist).",
 5094   ex := [ "Maximum([3,-3,5]);", "Maximum(['a','b']);" ],
 5095   see := [  ],
 5096   hash := "efc75e",
 5097   sig := "Maximum(<set> s)",
 5098   sog := " -> <any>",
 5099   docsrc := "init-methods.g",
 5100   sinflat := [ set ],
 5101   souflat := [ any ],
 5102   soghash := "c5fe02",
 5103   sig4hash := "Maximum(set)" ),
 5104 rec(
 5105   kind := "FUNCTION",
 5106   name := "Maximum",
 5107   sin := [ [ seq(), "S" ] ],
 5108   sou := [ [ any ] ],
 5109   short := "Determine and return the maximal element of `s'.",
 5110   ex := [ "Maximum(Sequence([1,2,3,4,5]));" ],
 5111   see := [  ],
 5112   hash := "90fb03",
 5113   sig := "Maximum(<seq()> S)",
 5114   sog := " -> <any>",
 5115   docsrc := "<internal>",
 5116   sinflat := [ seq() ],
 5117   souflat := [ any ],
 5118   soghash := "da39a3",
 5119   sig4hash := "Maximum(seq())" ),
 5120 rec(
 5121   kind := "FUNCTION",
 5122   name := "Maximum",
 5123   sin := [ [ tup(), "l" ] ],
 5124   sou := [ [ any ] ],
 5125   short := "Determine and return the maximal element in `t'.",
 5126   ex := [ "Maximum(Tuple([3,-3,5]));", "Maximum(Tuple(['a','b']));" ],
 5127   see := [  ],
 5128   hash := "d34ecf",
 5129   sig := "Maximum(<tup()> l)",
 5130   sog := " -> <any>",
 5131   docsrc := "init-methods.g",
 5132   sinflat := [ tup() ],
 5133   souflat := [ any ],
 5134   soghash := "c5fe02",
 5135   sig4hash := "Maximum(tup())" ),
 5136 rec(
 5137   kind := "FUNCTION",
 5138   name := "Minimum",
 5139   sin := [ [ set, "s" ] ],
 5140   sou := [ [ any ] ],
 5141   short := "Determine and return the minimal element of `s'.\nNote: `s' may also be a list (nonetheless `Set(s)' must exist).",
 5142   ex := [ "Minimum([3,-3,5]);", "Minimum(['a','b']);" ],
 5143   see := [  ],
 5144   hash := "96b3e7",
 5145   sig := "Minimum(<set> s)",
 5146   sog := " -> <any>",
 5147   docsrc := "init-methods.g",
 5148   sinflat := [ set ],
 5149   souflat := [ any ],
 5150   soghash := "c5fe02",
 5151   sig4hash := "Minimum(set)" ),
 5152 rec(
 5153   kind := "FUNCTION",
 5154   name := "Minimum",
 5155   sin := [ [ seq(), "S" ] ],
 5156   sou := [ [ any ] ],
 5157   short := "Determine and return the minimal element of `s'.",
 5158   ex := [ "Minimum([3.1415, 2.7183, -19]);" ],
 5159   see := [  ],
 5160   hash := "7ef2be",
 5161   sig := "Minimum(<seq()> S)",
 5162   sog := " -> <any>",
 5163   docsrc := "<internal>",
 5164   sinflat := [ seq() ],
 5165   souflat := [ any ],
 5166   soghash := "da39a3",
 5167   sig4hash := "Minimum(seq())" ),
 5168 rec(
 5169   kind := "FUNCTION",
 5170   name := "Minimum",
 5171   sin := [ [ tup(), "l" ] ],
 5172   sou := [ [ any ] ],
 5173   short := "Determine and return the minimal element in `t'.",
 5174   ex := [ "Minimum(Tuple([3,-3,5]));", "Minimum(Tuple(['a','b']));" ],
 5175   see := [  ],
 5176   hash := "72dcb5",
 5177   sig := "Minimum(<tup()> l)",
 5178   sog := " -> <any>",
 5179   docsrc := "init-methods.g",
 5180   sinflat := [ tup() ],
 5181   souflat := [ any ],
 5182   soghash := "c5fe02",
 5183   sig4hash := "Minimum(tup())" ),
 5184 rec(
 5185   kind := "FUNCTION",
 5186   name := "Remove",
 5187   sin := [ [ list, "L" ], [ elt-ord^rat, "pos" ] ],
 5188   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5189               Default := FAILURE ) ] ],
 5190   sou := [ [ list ] ],
 5191   short := "Return the list derived from removing the element at position `pos' from `L'.\nNote: `pos' must not exceed the scope of `L'.\nNote: This function returns the list created by the removal but does not affect `L'.",
 5192   ex := [ "L:=[1,,3,4];\nRemove(L,3); L;" ],
 5193   see := [ "d1d7cb" ],
 5194   hash := "1cc237",
 5195   sig := "Remove(<list> L, <elt-ord^rat> pos [, optargs])",
 5196   sog := " -> <list>",
 5197   docsrc := "init-methods.g",
 5198   sinflat := [ list, elt-ord^rat ],
 5199   souflat := [ list ],
 5200   soghash := "38b62b",
 5201   sig4hash := "Remove(list,elt-ord^rat)" ),
 5202 rec(
 5203   kind := "FUNCTION",
 5204   name := "Remove_",
 5205   sin := [ [ list, "L" ], [ elt-ord^rat, "pos" ] ],
 5206   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5207               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5208               Default := SUCCESS ) ] ],
 5209   sou := [  ],
 5210   short := "Remove the element at position `pos' in the list `L'.\nNote: `pos' must not exceed the scope of `L'.\nNote: This function works by side effect and returns VOID.",
 5211   ex := [ "L:=[1,,3,4];\nRemove_(L,3); L;" ],
 5212   see := [ "1cc237" ],
 5213   hash := "d1d7cb",
 5214   sig := "Remove_(<list> L, <elt-ord^rat> pos [, optargs])",
 5215   sog := "",
 5216   docsrc := "init-methods.g",
 5217   sinflat := [ list, elt-ord^rat ],
 5218   souflat := [  ],
 5219   soghash := "da39a3",
 5220   sig4hash := "Remove_(list,elt-ord^rat)" ),
 5221 rec(
 5222   kind := "FUNCTION",
 5223   name := "Remove",
 5224   sin := [ [ seq(), "S" ], [ elt-ord^rat, "pos" ] ],
 5225   sou := [ [ seq() ] ],
 5226   short := "Return the sequence derived from removing the element at position `pos' from `S'.\nNote: `pos' must not exceed the scope of `S'.\nNote: This function returns the sequence created by the removal but does not affect `S'.",
 5227   hash := "aeb167",
 5228   ex := [  ],
 5229   sig := "Remove(<seq()> S, <elt-ord^rat> pos)",
 5230   sog := " -> <seq()>",
 5231   docsrc := "init-methods.g",
 5232   sinflat := [ seq(), elt-ord^rat ],
 5233   souflat := [ seq() ],
 5234   soghash := "4bf3a0",
 5235   sig4hash := "Remove(seq(),elt-ord^rat)" ),
 5236 rec(
 5237   kind := "FUNCTION",
 5238   name := "Remove_",
 5239   sin := [ [ seq(), "S" ], [ elt-ord^rat, "pos" ] ],
 5240   sou := [ [  ] ],
 5241   short := "Remove the element at position `pos' in the sequence `S'.\nNote: `pos' must not exceed the scope of `S'.\nNote: This function works by side effect and returns VOID.",
 5242   hash := "98a11b",
 5243   ex := [  ],
 5244   sig := "Remove_(<seq()> S, <elt-ord^rat> pos)",
 5245   sog := "",
 5246   docsrc := "init-methods.g",
 5247   sinflat := [ seq(), elt-ord^rat ],
 5248   souflat := [  ],
 5249   soghash := "da39a3",
 5250   sig4hash := "Remove_(seq(),elt-ord^rat)" ),
 5251 rec(
 5252   kind := "FUNCTION",
 5253   name := "Add_",
 5254   sin := [ [ list, "L" ], [ any, "a" ] ],
 5255   sou := [  ],
 5256   short := "Add `a' to `L' by assigning `a' at the next position beyond the scope of `L'.\nNote: This function works by side effect and returns VOID.",
 5257   ex := [ "L:=[1,,3,4];\nAdd_(L,5); L;" ],
 5258   see := [ "ec51e2", "f55fdd" ],
 5259   hash := "ab7b5e",
 5260   sig := "Add_(<list> L, <any> a)",
 5261   sog := "",
 5262   docsrc := "init-methods.g",
 5263   sinflat := [ list, any ],
 5264   souflat := [  ],
 5265   soghash := "da39a3",
 5266   sig4hash := "Add_(list,any)" ),
 5267 rec(
 5268   kind := "FUNCTION",
 5269   name := "Add",
 5270   sin := [ [ list, "L" ], [ any, "a" ] ],
 5271   sou := [ [ list ] ],
 5272   short := "Add `a' to `L' by assigning `a' at the next position beyond the scope of `L'.\nNote: This function returns the list created by the addition but does not affect `L'.",
 5273   ex := [ "L:=[1,,3,4];\nAdd(L,5); L;" ],
 5274   see := [ "ab7b5e", "59fe3e" ],
 5275   hash := "ec51e2",
 5276   sig := "Add(<list> L, <any> a)",
 5277   sog := " -> <list>",
 5278   docsrc := "init-methods.g",
 5279   sinflat := [ list, any ],
 5280   souflat := [ list ],
 5281   soghash := "38b62b",
 5282   sig4hash := "Add(list,any)" ),
 5283 rec(
 5284   kind := "FUNCTION",
 5285   name := "Add",
 5286   sin := [ [ seq(), "Q" ], [ any, "x" ] ],
 5287   sou := [ [ seq() ] ],
 5288   short := "The sequence built by appending x to the sequence Q.",
 5289   ex := [ "L:=Sequence([1,2,3,4]);\nAdd(L,5); L;" ],
 5290   see := [ "ec51e2", "6e1a4d" ],
 5291   hash := "ca03d1",
 5292   sig := "Add(<seq()> Q, <any> x)",
 5293   sog := " -> <seq()>",
 5294   docsrc := "init-methods.g",
 5295   sinflat := [ seq(), any ],
 5296   souflat := [ seq() ],
 5297   soghash := "4bf3a0",
 5298   sig4hash := "Add(seq(),any)" ),
 5299 rec(
 5300   kind := "FUNCTION",
 5301   name := "Add_",
 5302   sin := [ [ seq(), "Q" ], [ any, "x" ] ],
 5303   sou := [ [ seq() ] ],
 5304   short := "Modify `Q' by appending x to the sequence Q.",
 5305   ex := [ "L:=Sequence([1,2,3,4]);\nAdd_(L,5); L;" ],
 5306   see := [ "ab7b5e", "8e984a" ],
 5307   hash := "b12aa7",
 5308   sig := "Add_(<seq()> Q, <any> x)",
 5309   sog := " -> <seq()>",
 5310   docsrc := "init-methods.g",
 5311   sinflat := [ seq(), any ],
 5312   souflat := [ seq() ],
 5313   soghash := "4bf3a0",
 5314   sig4hash := "Add_(seq(),any)" ),
 5315 rec(
 5316   kind := "FUNCTION",
 5317   name := "Add",
 5318   sin := [ [ string, "S" ], [ char, "c" ] ],
 5319   sou := [ [ string ] ],
 5320   short := "The string built by appending `c' to the string `S'.\nNote: This is roughly equivalent to `S+c'.",
 5321   ex := [ "S:=\"abcdef\";\nAdd(S,'z'); S;" ],
 5322   see := [ "ec51e2", "a9e9e4" ],
 5323   hash := "32de83",
 5324   sig := "Add(<string> S, <char> c)",
 5325   sog := " -> <string>",
 5326   docsrc := "init-methods.g",
 5327   sinflat := [ string, char ],
 5328   souflat := [ string ],
 5329   soghash := "ecb252",
 5330   sig4hash := "Add(string,char)" ),
 5331 rec(
 5332   kind := "FUNCTION",
 5333   name := "Add_",
 5334   sin := [ [ string, "S" ], [ char, "c" ] ],
 5335   sou := [ [ string ] ],
 5336   short := "Modify `S' by appending `c' to the string `S'.",
 5337   ex := [ "S:=\"abcdef\";\nAdd_(S,'z'); S;" ],
 5338   see := [ "ab7b5e", "f55160" ],
 5339   hash := "26ec35",
 5340   sig := "Add_(<string> S, <char> c)",
 5341   sog := " -> <string>",
 5342   docsrc := "init-methods.g",
 5343   sinflat := [ string, char ],
 5344   souflat := [ string ],
 5345   soghash := "ecb252",
 5346   sig4hash := "Add_(string,char)" ),
 5347 rec(
 5348   kind := "FUNCTION",
 5349   name := "Union",
 5350   sin := [ [ dry, "D1" ], [ list, "D2" ] ],
 5351   sou := [ [ dry ] ],
 5352   short := "Return the dry derived by the union of `D1' and `D2'.\nThe union is the dry of those elements that are elements of either dry. So `Union' adds (see DryAdd) all elements to `D1' that are in `D2'. `D2' may be a list that is not a proper dry, in which case `Dry' is silently applied to it.",
 5353   ex := [  ],
 5354   see := [  ],
 5355   hash := "637982",
 5356   sig := "Union(<dry> D1, <list> D2)",
 5357   sog := " -> <dry>",
 5358   docsrc := "init-methods.g",
 5359   sinflat := [ dry, list ],
 5360   souflat := [ dry ],
 5361   soghash := "ef926a",
 5362   sig4hash := "Union(dry,list)" ),
 5363 rec(
 5364   kind := "FUNCTION",
 5365   name := "Union",
 5366   sin := [ [ set, "S1" ], [ list, "S2" ] ],
 5367   sou := [ [ set ] ],
 5368   short := "Return the set derived by the union of `S1' and `S2'.\nThe union is the dry of those elements that are elements of either dry. So `Union' adds (see SetAdd) all elements to `S1' that are in `S2'. `S2' may be a list that is not a proper set, in which case `Set' is silently applied to it.",
 5369   ex := [  ],
 5370   see := [  ],
 5371   hash := "871abd",
 5372   sig := "Union(<set> S1, <list> S2)",
 5373   sog := " -> <set>",
 5374   docsrc := "init-methods.g",
 5375   sinflat := [ set, list ],
 5376   souflat := [ set ],
 5377   soghash := "65c10d",
 5378   sig4hash := "Union(set,list)" ),
 5379 rec(
 5380   kind := "FUNCTION",
 5381   name := "Union_",
 5382   sin := [ [ dry, "D1" ], [ list, "D2" ] ],
 5383   sou := [  ],
 5384   short := "Change `D1' so that it becomes the union of `D1' and `D2'.\nThe union is the dry of those elements that are elements of either dry. So `Union_' adds (see DryAdd) all elements to `D1' that are in `D2'. `D2' may be a list that is not a proper dry, in which case `Dry' is silently applied to it.",
 5385   ex := [  ],
 5386   see := [  ],
 5387   hash := "f2d081",
 5388   sig := "Union_(<dry> D1, <list> D2)",
 5389   sog := "",
 5390   docsrc := "init-methods.g",
 5391   sinflat := [ dry, list ],
 5392   souflat := [  ],
 5393   soghash := "da39a3",
 5394   sig4hash := "Union_(dry,list)" ),
 5395 rec(
 5396   kind := "FUNCTION",
 5397   name := "Union_",
 5398   sin := [ [ set, "S1" ], [ list, "S2" ] ],
 5399   sou := [  ],
 5400   short := "Change `S1' so that it becomes the union of `S1' and `S2'.\nThe union is the dry of those elements that are elements of either dry. So `Union_' adds (see SetAdd) all elements to `S1' that are in `S2'. `S2' may be a list that is not a proper set, in which case `Set' is silently applied to it.",
 5401   ex := [  ],
 5402   see := [  ],
 5403   hash := "1b2275",
 5404   sig := "Union_(<set> S1, <list> S2)",
 5405   sog := "",
 5406   docsrc := "init-methods.g",
 5407   sinflat := [ set, list ],
 5408   souflat := [  ],
 5409   soghash := "da39a3",
 5410   sig4hash := "Union_(set,list)" ),
 5411 rec(
 5412   kind := "FUNCTION",
 5413   name := "Intersection",
 5414   sin := [ [ dry, "D1" ], [ list, "D2" ] ],
 5415   sou := [ [ dry ] ],
 5416   short := "Return the dry derived by the intersection of the dries `D1' and `D2'.\nThe intersection is the dry of those elements that are elements in both dries. So `Intersection' removes (see `DryRemove') all elements from `D1' that are not in `D2'.\nNote: `D2' may be a list that is not a proper dry, in which case `Dry' is silently applied to it.",
 5417   hash := "ead233",
 5418   ex := [  ],
 5419   sig := "Intersection(<dry> D1, <list> D2)",
 5420   sog := " -> <dry>",
 5421   docsrc := "init-methods.g",
 5422   sinflat := [ dry, list ],
 5423   souflat := [ dry ],
 5424   soghash := "ef926a",
 5425   sig4hash := "Intersection(dry,list)" ),
 5426 rec(
 5427   kind := "FUNCTION",
 5428   name := "Intersection",
 5429   sin := [ [ set, "S1" ], [ list, "S2" ] ],
 5430   sou := [ [ set ] ],
 5431   short := "Return the set derived by the intersection of the sets `S1' and `S2'.\nThe intersection is the set of those elements that are elements in both sets. So `Intersection' removes (see `SetRemove') all elements from `S1' that are not in `S2'.\n`S2' may be a list that is not a proper set, in which case `Set' is silently applied to it.",
 5432   hash := "c601cc",
 5433   ex := [  ],
 5434   sig := "Intersection(<set> S1, <list> S2)",
 5435   sog := " -> <set>",
 5436   docsrc := "init-methods.g",
 5437   sinflat := [ set, list ],
 5438   souflat := [ set ],
 5439   soghash := "65c10d",
 5440   sig4hash := "Intersection(set,list)" ),
 5441 rec(
 5442   kind := "FUNCTION",
 5443   name := "Intersection_",
 5444   sin := [ [ dry, "D1" ], [ list, "D2" ] ],
 5445   sou := [  ],
 5446   short := "Change `D1' so that it becomes the intersection of `D1' and `D2'.\nThe intersection is the dry of those elements that are elements in both dries. So `Intersection_' removes (see `DryRemove_') all elements from `D1' which are not in `D2'.\nNote: `D2' may be a list that is not a proper dry, in which case `Dry' is silently applied to it.",
 5447   hash := "0ce1d5",
 5448   ex := [  ],
 5449   sig := "Intersection_(<dry> D1, <list> D2)",
 5450   sog := "",
 5451   docsrc := "init-methods.g",
 5452   sinflat := [ dry, list ],
 5453   souflat := [  ],
 5454   soghash := "da39a3",
 5455   sig4hash := "Intersection_(dry,list)" ),
 5456 rec(
 5457   kind := "FUNCTION",
 5458   name := "Intersection_",
 5459   sin := [ [ set, "S1" ], [ list, "S2" ] ],
 5460   sou := [  ],
 5461   short := "Change `S1' so that it becomes the intersection of `S1' and `S2'.\nThe intersection is the set of those elements that are elements in both sets. So `SetIntersection_' removes (see `SetRemove_') all elements from `S1' that are not in `S2'.\n`S2' may be a list that is not a proper set, in which case `Set' is silently applied to it.",
 5462   hash := "c025b1",
 5463   ex := [  ],
 5464   sig := "Intersection_(<set> S1, <list> S2)",
 5465   sog := "",
 5466   docsrc := "init-methods.g",
 5467   sinflat := [ set, list ],
 5468   souflat := [  ],
 5469   soghash := "da39a3",
 5470   sig4hash := "Intersection_(set,list)" ),
 5471 rec(
 5472   kind := "FUNCTION",
 5473   name := "Difference",
 5474   sin := [ [ dry, "D1" ], [ list, "D2" ] ],
 5475   sou := [ [ dry ] ],
 5476   short := "Return the dry derived by the difference of the dries `D1' and `D2'.\nThe difference is the dry of the elements that are in `D1' but not in `D2'. So `Difference' removes (see `DryRemove') all elements from `D1' that are in `D2'.\nNote: `D2' may be a list that is not a proper dry, in which case `Dry' is silently applied to it.",
 5477   hash := "8eb302",
 5478   ex := [  ],
 5479   sig := "Difference(<dry> D1, <list> D2)",
 5480   sog := " -> <dry>",
 5481   docsrc := "init-methods.g",
 5482   sinflat := [ dry, list ],
 5483   souflat := [ dry ],
 5484   soghash := "ef926a",
 5485   sig4hash := "Difference(dry,list)" ),
 5486 rec(
 5487   kind := "FUNCTION",
 5488   name := "Difference",
 5489   sin := [ [ set, "S1" ], [ list, "S2" ] ],
 5490   sou := [ [ set ] ],
 5491   short := "Return the set derived by the difference of the sets `S1' and `S2'.\nThe difference is the set of the elements that are in `S1' but not in `S2'. So `Difference' removes (see `SetRemove') all elements from `S1' that are in `S2'.\nNote: `S2' may  be a list that is not a proper set, in which case `Set' is silently applied to it.",
 5492   hash := "bb5501",
 5493   ex := [  ],
 5494   sig := "Difference(<set> S1, <list> S2)",
 5495   sog := " -> <set>",
 5496   docsrc := "init-methods.g",
 5497   sinflat := [ set, list ],
 5498   souflat := [ set ],
 5499   soghash := "65c10d",
 5500   sig4hash := "Difference(set,list)" ),
 5501 rec(
 5502   kind := "FUNCTION",
 5503   name := "Difference_",
 5504   sin := [ [ dry, "D1" ], [ list, "D2" ] ],
 5505   sou := [  ],
 5506   short := "Change `D1' so that it becomes the difference of `D1' and `D2'.\nThe difference is the dry of the elements that are in `D1' but not in `D2'. So `Difference_' removes (see `DryRemove_') all elements from `D1' that are in `D2'.\nNote: `D2' may be a list that is not a proper dry, in which case `Dry' is silently applied to it.",
 5507   hash := "2b0f66",
 5508   ex := [  ],
 5509   sig := "Difference_(<dry> D1, <list> D2)",
 5510   sog := "",
 5511   docsrc := "init-methods.g",
 5512   sinflat := [ dry, list ],
 5513   souflat := [  ],
 5514   soghash := "da39a3",
 5515   sig4hash := "Difference_(dry,list)" ),
 5516 rec(
 5517   kind := "FUNCTION",
 5518   name := "Difference_",
 5519   sin := [ [ set, "S1" ], [ list, "S2" ] ],
 5520   sou := [  ],
 5521   short := "Change `S1' so that it becomes the difference of `S1' and `S2'.\nThe difference is the set of the elements that are in `S1' but not in `S2'. So `Difference_' removes (see `SetRemove_') all elements from `S1' that are in `S2'.\nNote: `S2' may  be a list that is not a proper set, in which case `Set' is silently applied to it.",
 5522   hash := "cf988f",
 5523   ex := [  ],
 5524   sig := "Difference_(<set> S1, <list> S2)",
 5525   sog := "",
 5526   docsrc := "init-methods.g",
 5527   sinflat := [ set, list ],
 5528   souflat := [  ],
 5529   soghash := "da39a3",
 5530   sig4hash := "Difference_(set,list)" ),
 5531 rec(
 5532   kind := "FUNCTION",
 5533   name := "AlistKeys",
 5534   sin := [ [ alist, "A" ] ],
 5535   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5536               Default := FAILURE ) ] ],
 5537   sou := [ [ list, "keyl" ] ],
 5538   short := "Return a list of keys of the alist `A'.",
 5539   ex := [ "A:=Alist([\"foo\",\"someval1\"],[\"bar\",\"someval2\"]);\nAlistKeys(A);" ],
 5540   see := [ "b7306d" ],
 5541   hash := "07c92e",
 5542   sig := "AlistKeys(<alist> A [, optargs])",
 5543   sog := " -> <list> keyl",
 5544   docsrc := "init-methods.g",
 5545   sinflat := [ alist ],
 5546   souflat := [ list ],
 5547   soghash := "38b62b",
 5548   sig4hash := "AlistKeys(alist)" ),
 5549 rec(
 5550   kind := "FUNCTION",
 5551   name := "AlistValues",
 5552   sin := [ [ alist, "A" ] ],
 5553   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5554               Default := FAILURE ) ] ],
 5555   sou := [ [ list, "vall" ] ],
 5556   short := "Return a list of values of the alist `A'.",
 5557   ex := [ "A:=Alist([\"foo\",\"someval1\"],[\"bar\",\"someval2\"]);\nAlistValues(A);" ],
 5558   see := [ "07c92e" ],
 5559   hash := "b7306d",
 5560   sig := "AlistValues(<alist> A [, optargs])",
 5561   sog := " -> <list> vall",
 5562   docsrc := "init-methods.g",
 5563   sinflat := [ alist ],
 5564   souflat := [ list ],
 5565   soghash := "38b62b",
 5566   sig4hash := "AlistValues(alist)" ),
 5567 rec(
 5568   kind := "FUNCTION",
 5569   name := "Assoc",
 5570   sin := [ [ alist, "A" ], [ any, "key" ] ],
 5571   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5572               Default := FAILURE ) ] ],
 5573   sou := [ [ any, "val" ] ],
 5574   short := "Return the value associated with `key' in the alist `A'.",
 5575   ex := [ "A:=Alist([\"foo\",\"someval1\"],[\"bar\",\"someval2\"]);\nAssoc(A,\"bar\"); Assoc(A,25);" ],
 5576   see := [  ],
 5577   hash := "fa766e",
 5578   sig := "Assoc(<alist> A, <any> key [, optargs])",
 5579   sog := " -> <any> val",
 5580   docsrc := "init-methods.g",
 5581   sinflat := [ alist, any ],
 5582   souflat := [ any ],
 5583   soghash := "c5fe02",
 5584   sig4hash := "Assoc(alist,any)" ),
 5585 rec(
 5586   kind := "FUNCTION",
 5587   name := "Rassoc",
 5588   sin := [ [ alist, "A" ], [ any, "val" ] ],
 5589   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5590               Default := FAILURE ) ] ],
 5591   sou := [ [ any, "key" ] ],
 5592   short := "Return a list of keys whose associations are `val' in the alist `A'.",
 5593   ex := [ "A:=Alist([\"foo\",\"someval1\"],[\"bar\",\"someval2\"]);\nRassoc(A,\"someval1\"); Rassoc(A,25);" ],
 5594   see := [  ],
 5595   hash := "1f9485",
 5596   sig := "Rassoc(<alist> A, <any> val [, optargs])",
 5597   sog := " -> <any> key",
 5598   docsrc := "init-methods.g",
 5599   sinflat := [ alist, any ],
 5600   souflat := [ any ],
 5601   soghash := "c5fe02",
 5602   sig4hash := "Rassoc(alist,any)" ),
 5603 rec(
 5604   kind := "FUNCTION",
 5605   name := "Preimages",
 5606   sin := [ [ alist, "A" ], [ any, "val" ] ],
 5607   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5608               Default := FAILURE ) ] ],
 5609   sou := [ [ any, "key" ] ],
 5610   short := "Return a list of keys whose associations are `val' in the alist `A'.",
 5611   ex := [ "A:=Alist([\"foo\",\"someval1\"],[\"bar\",\"someval2\"]);\nPreimages(A,\"someval1\"); Preimages(A,25);" ],
 5612   see := [  ],
 5613   hash := "62d20c",
 5614   sig := "Preimages(<alist> A, <any> val [, optargs])",
 5615   sog := " -> <any> key",
 5616   docsrc := "init-methods.g",
 5617   sinflat := [ alist, any ],
 5618   souflat := [ any ],
 5619   soghash := "c5fe02",
 5620   sig4hash := "Preimages(alist,any)" ),
 5621 rec(
 5622   kind := "FUNCTION",
 5623   name := "AddAssoc",
 5624   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5625   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5626               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5627               Default := SUCCESS ) ] ],
 5628   sou := [ [ alist ] ],
 5629   short := "Associate `key' with `val' in alist `A' if `key' was not already present and return the alist derived from this association or FAILURE in case `key' already had an association in `A'.\nNote: This does not affect `A'.",
 5630   ex := [ "A:=Alist();\nAddAssoc(A,1,\"foo\");" ],
 5631   see := [ "8b4255" ],
 5632   hash := "dcca85",
 5633   sig := "AddAssoc(<alist> A, <any> key, <any> val [, optargs])",
 5634   sog := " -> <alist>",
 5635   docsrc := "init-methods.g",
 5636   sinflat := [ alist, any, any ],
 5637   souflat := [ alist ],
 5638   soghash := "4405bf",
 5639   sig4hash := "AddAssoc(alist,any,any)" ),
 5640 rec(
 5641   kind := "FUNCTION",
 5642   name := "Add",
 5643   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5644   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5645               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5646               Default := SUCCESS ) ] ],
 5647   sou := [ [ alist ] ],
 5648   short := "Associate `key' with `val' in alist `A' if `key' was not already present and return the alist derived from this association or FAILURE in case `key' already had an association in `A'.\nNote: This does not affect `A'.",
 5649   ex := [ "A:=Alist();\nAdd(A,1,\"foo\");" ],
 5650   see := [ "a0add0" ],
 5651   hash := "a0add0",
 5652   sig := "Add(<alist> A, <any> key, <any> val [, optargs])",
 5653   sog := " -> <alist>",
 5654   docsrc := "init-methods.g",
 5655   sinflat := [ alist, any, any ],
 5656   souflat := [ alist ],
 5657   soghash := "4405bf",
 5658   sig4hash := "Add(alist,any,any)" ),
 5659 rec(
 5660   kind := "FUNCTION",
 5661   name := "AddAssoc_",
 5662   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5663   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5664               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5665               Default := SUCCESS ) ] ],
 5666   sou := [  ],
 5667   short := "Associate `key' with `val' in alist `A' if `key' was not already present and return FAILURE on failure.\nNote: `A' is modified by side-effect.",
 5668   ex := [ "A:=Alist();\nAddAssoc_(A,1,\"foo\"); A;" ],
 5669   see := [ "dcca85" ],
 5670   hash := "8b4255",
 5671   sig := "AddAssoc_(<alist> A, <any> key, <any> val [, optargs])",
 5672   sog := "",
 5673   docsrc := "init-methods.g",
 5674   sinflat := [ alist, any, any ],
 5675   souflat := [  ],
 5676   soghash := "da39a3",
 5677   sig4hash := "AddAssoc_(alist,any,any)" ),
 5678 rec(
 5679   kind := "FUNCTION",
 5680   name := "Add_",
 5681   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5682   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5683               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5684               Default := SUCCESS ) ] ],
 5685   sou := [  ],
 5686   short := "Associate `key' with `val' in alist `A' if `key' was not already present and return FAILURE on failure.\nNote: `A' is modified by side-effect.",
 5687   ex := [ "A:=Alist();\nAdd_(A,1,\"foo\"); A;" ],
 5688   see := [ "a0add0" ],
 5689   hash := "b464a5",
 5690   sig := "Add_(<alist> A, <any> key, <any> val [, optargs])",
 5691   sog := "",
 5692   docsrc := "init-methods.g",
 5693   sinflat := [ alist, any, any ],
 5694   souflat := [  ],
 5695   soghash := "da39a3",
 5696   sig4hash := "Add_(alist,any,any)" ),
 5697 rec(
 5698   kind := "FUNCTION",
 5699   name := "AddAssoc",
 5700   sin := [ [ alist, "A" ], [ list, "keyval" ] ],
 5701   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5702               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5703               Default := SUCCESS ) ] ],
 5704   sou := [ [ alist ] ],
 5705   short := "Associate `key' (taken as first element of `keyval') with `val' (taken as the rest of `keyval') in alist `A' if `key' was not already present and return the alist derived from this association or FAILURE in case `key' already had an association in `A'.\nNote: This does not affect `A'.",
 5706   ex := [ "A:=Alist();\nAddAssoc(A,[2,\"bar\",\"and_baz\"]);" ],
 5707   see := [ "3109b6" ],
 5708   hash := "0c44c7",
 5709   sig := "AddAssoc(<alist> A, <list> keyval [, optargs])",
 5710   sog := " -> <alist>",
 5711   docsrc := "init-methods.g",
 5712   sinflat := [ alist, list ],
 5713   souflat := [ alist ],
 5714   soghash := "4405bf",
 5715   sig4hash := "AddAssoc(alist,list)" ),
 5716 rec(
 5717   kind := "FUNCTION",
 5718   name := "AddAssoc_",
 5719   sin := [ [ alist, "A" ], [ list, "keyval" ] ],
 5720   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5721               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5722               Default := SUCCESS ) ] ],
 5723   sou := [  ],
 5724   short := "Associate `key' (taken as first element of `keyval') with `val' (taken as the rest of `keyval') in alist `A' if `key' was not already present and return FAILURE in case of failure.\nNote: `A' is modified by side-effect.",
 5725   ex := [ "A:=Alist();\nAddAssoc_(A,[2,\"bar\",\"and_baz\"]); A;" ],
 5726   see := [ "0c44c7" ],
 5727   hash := "3109b6",
 5728   sig := "AddAssoc_(<alist> A, <list> keyval [, optargs])",
 5729   sog := "",
 5730   docsrc := "init-methods.g",
 5731   sinflat := [ alist, list ],
 5732   souflat := [  ],
 5733   soghash := "da39a3",
 5734   sig4hash := "AddAssoc_(alist,list)" ),
 5735 rec(
 5736   kind := "FUNCTION",
 5737   name := "PutAssoc",
 5738   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5739   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5740               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5741               Default := SUCCESS ) ] ],
 5742   sou := [ [ alist ] ],
 5743   short := "Associate `key' with `val' in alist `A' and return the alist derived from this association.\nNote: This does not affect `A'.",
 5744   ex := [ "A:=Alist();\nPutAssoc(A,1,\"foo\");" ],
 5745   see := [ "ebcb64" ],
 5746   hash := "79a28e",
 5747   sig := "PutAssoc(<alist> A, <any> key, <any> val [, optargs])",
 5748   sog := " -> <alist>",
 5749   docsrc := "init-methods.g",
 5750   sinflat := [ alist, any, any ],
 5751   souflat := [ alist ],
 5752   soghash := "4405bf",
 5753   sig4hash := "PutAssoc(alist,any,any)" ),
 5754 rec(
 5755   kind := "FUNCTION",
 5756   name := "Put",
 5757   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5758   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5759               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5760               Default := SUCCESS ) ] ],
 5761   sou := [ [ alist ] ],
 5762   short := "Associate `key' with `val' in alist `A' and return the alist derived from this association.\nNote: This does not affect `A'.",
 5763   ex := [ "A:=Alist();\nPut(A,1,\"foo\");" ],
 5764   see := [ "4a2939" ],
 5765   hash := "2ad5c7",
 5766   sig := "Put(<alist> A, <any> key, <any> val [, optargs])",
 5767   sog := " -> <alist>",
 5768   docsrc := "init-methods.g",
 5769   sinflat := [ alist, any, any ],
 5770   souflat := [ alist ],
 5771   soghash := "4405bf",
 5772   sig4hash := "Put(alist,any,any)" ),
 5773 rec(
 5774   kind := "FUNCTION",
 5775   name := "PutAssoc_",
 5776   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5777   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5778               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5779               Default := SUCCESS ) ] ],
 5780   sou := [  ],
 5781   short := "Associate `key' with `val' in alist `A' and return FAILURE on failure.\nNote: `A' is modified by side-effect.",
 5782   ex := [ "A:=Alist();\nPutAssoc_(A,1,\"foo\"); A;" ],
 5783   see := [ "79a28e" ],
 5784   hash := "ebcb64",
 5785   sig := "PutAssoc_(<alist> A, <any> key, <any> val [, optargs])",
 5786   sog := "",
 5787   docsrc := "init-methods.g",
 5788   sinflat := [ alist, any, any ],
 5789   souflat := [  ],
 5790   soghash := "da39a3",
 5791   sig4hash := "PutAssoc_(alist,any,any)" ),
 5792 rec(
 5793   kind := "FUNCTION",
 5794   name := "Put_",
 5795   sin := [ [ alist, "A" ], [ any, "key" ], [ any, "val" ] ],
 5796   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5797               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5798               Default := SUCCESS ) ] ],
 5799   sou := [  ],
 5800   short := "Associate `key' with `val' in alist `A' and return FAILURE on failure.\nNote: `A' is modified by side-effect.",
 5801   ex := [ "A:=Alist();\nPut_(A,1,\"foo\"); A;" ],
 5802   see := [ "2ad5c7" ],
 5803   hash := "4a2939",
 5804   sig := "Put_(<alist> A, <any> key, <any> val [, optargs])",
 5805   sog := "",
 5806   docsrc := "init-methods.g",
 5807   sinflat := [ alist, any, any ],
 5808   souflat := [  ],
 5809   soghash := "da39a3",
 5810   sig4hash := "Put_(alist,any,any)" ),
 5811 rec(
 5812   kind := "FUNCTION",
 5813   name := "PutAssoc",
 5814   sin := [ [ alist, "A" ], [ list, "keyval" ] ],
 5815   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5816               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5817               Default := SUCCESS ) ] ],
 5818   sou := [ [ alist ] ],
 5819   short := "Associate `key' (taken as first element of `keyval') with `val' (taken as second element of `keyval') in alist `A' and return the alist derived from this association.\nNote: This does not affect `A'.",
 5820   ex := [ "A:=Alist();\nPutAssoc_(A,[2,\"bar\"]);" ],
 5821   see := [ "5ec41d" ],
 5822   hash := "5ec41d",
 5823   sig := "PutAssoc(<alist> A, <list> keyval [, optargs])",
 5824   sog := " -> <alist>",
 5825   docsrc := "init-methods.g",
 5826   sinflat := [ alist, list ],
 5827   souflat := [ alist ],
 5828   soghash := "4405bf",
 5829   sig4hash := "PutAssoc(alist,list)" ),
 5830 rec(
 5831   kind := "FUNCTION",
 5832   name := "PutAssoc_",
 5833   sin := [ [ alist, "A" ], [ list, "keyval" ] ],
 5834   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5835               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5836               Default := SUCCESS ) ] ],
 5837   sou := [  ],
 5838   short := "Associate `key' (taken as first element of `keyval') with `val' (taken as second element of `keyval') in alist `A' and return FAILURE on failure.\nNote: `A' is modified by side-effect.",
 5839   ex := [ "A:=Alist();\nPutAssoc_(A,[2,\"bar\"]); A;" ],
 5840   see := [ "5ec41d" ],
 5841   hash := "90d41a",
 5842   sig := "PutAssoc_(<alist> A, <list> keyval [, optargs])",
 5843   sog := "",
 5844   docsrc := "init-methods.g",
 5845   sinflat := [ alist, list ],
 5846   souflat := [  ],
 5847   soghash := "da39a3",
 5848   sig4hash := "PutAssoc_(alist,list)" ),
 5849 rec(
 5850   kind := "FUNCTION",
 5851   name := "RemAssoc",
 5852   sin := [ [ alist, "A" ], [ any, "key" ] ],
 5853   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5854               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5855               Default := SUCCESS ) ] ],
 5856   sou := [ [ alist ] ],
 5857   short := "Remove `key' and its association in alist `A' and return the alist derived from this removal.\nNote: This does not affect `A'.",
 5858   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"]);\nRemAssoc(A,1);" ],
 5859   see := [ "88de41" ],
 5860   hash := "1c4f4b",
 5861   sig := "RemAssoc(<alist> A, <any> key [, optargs])",
 5862   sog := " -> <alist>",
 5863   docsrc := "init-methods.g",
 5864   sinflat := [ alist, any ],
 5865   souflat := [ alist ],
 5866   soghash := "4405bf",
 5867   sig4hash := "RemAssoc(alist,any)" ),
 5868 rec(
 5869   kind := "FUNCTION",
 5870   name := "Remove",
 5871   sin := [ [ alist, "A" ], [ any, "key" ] ],
 5872   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5873               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5874               Default := SUCCESS ) ] ],
 5875   sou := [ [ alist ] ],
 5876   short := "Remove `key' and its association in alist `A' and return the alist derived from this removal.\nNote: This does not affect `A'.",
 5877   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"]);\nRemAssoc(A,1);" ],
 5878   see := [ "d07f27" ],
 5879   hash := "1160f6",
 5880   sig := "Remove(<alist> A, <any> key [, optargs])",
 5881   sog := " -> <alist>",
 5882   docsrc := "init-methods.g",
 5883   sinflat := [ alist, any ],
 5884   souflat := [ alist ],
 5885   soghash := "4405bf",
 5886   sig4hash := "Remove(alist,any)" ),
 5887 rec(
 5888   kind := "FUNCTION",
 5889   name := "RemAssoc_",
 5890   sin := [ [ alist, "A" ], [ any, "key" ] ],
 5891   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5892               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5893               Default := SUCCESS ) ] ],
 5894   sou := [  ],
 5895   short := "Remove `key' and its association in alist `A' and return FAILURE on failure or SUCCESS on success.\nNote: `A' is modified by side-effect.",
 5896   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"]);\nRemAssoc_(A,1); A;" ],
 5897   see := [ "1c4f4b" ],
 5898   hash := "88de41",
 5899   sig := "RemAssoc_(<alist> A, <any> key [, optargs])",
 5900   sog := "",
 5901   docsrc := "init-methods.g",
 5902   sinflat := [ alist, any ],
 5903   souflat := [  ],
 5904   soghash := "da39a3",
 5905   sig4hash := "RemAssoc_(alist,any)" ),
 5906 rec(
 5907   kind := "FUNCTION",
 5908   name := "Remove_",
 5909   sin := [ [ alist, "A" ], [ any, "key" ] ],
 5910   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 5911               Default := FAILURE ) ], [ any, "Success", "Determines what to return in case of success.", rec(
 5912               Default := SUCCESS ) ] ],
 5913   sou := [  ],
 5914   short := "Remove `key' and its association in alist `A' and return FAILURE on failure or SUCCESS on success.\nNote: `A' is modified by side-effect.",
 5915   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"]);\nRemAssoc_(A,1); A;" ],
 5916   see := [ "1160f6" ],
 5917   hash := "d07f27",
 5918   sig := "Remove_(<alist> A, <any> key [, optargs])",
 5919   sog := "",
 5920   docsrc := "init-methods.g",
 5921   sinflat := [ alist, any ],
 5922   souflat := [  ],
 5923   soghash := "da39a3",
 5924   sig4hash := "Remove_(alist,any)" ),
 5925 rec(
 5926   kind := "FUNCTION",
 5927   name := "Alist",
 5928   sin := [ [  ] ],
 5929   sou := [ [ alist, "A" ] ],
 5930   short := "Create and return an empty association list `A'.",
 5931   ex := [ "A:=Alist();" ],
 5932   see := [ "afd6a2" ],
 5933   hash := "849310",
 5934   sig := "Alist()",
 5935   sog := " -> <alist> A",
 5936   docsrc := "init-methods.g",
 5937   sinflat := [  ],
 5938   souflat := [ alist ],
 5939   soghash := "4405bf",
 5940   sig4hash := "Alist()" ),
 5941 rec(
 5942   kind := "FUNCTION",
 5943   name := "Alist",
 5944   sin := [ [ nof(list) ] ],
 5945   sou := [ [ alist, "A" ] ],
 5946   short := "Create and return an association list `A' along with some content.\nThe arguments are two-cell lists. The alist is built by taking the first element of a list as key and the second element as associated value.",
 5947   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"]);" ],
 5948   see := [ "849310" ],
 5949   hash := "afd6a2",
 5950   sig := "Alist(<nof(list)>)",
 5951   sog := " -> <alist> A",
 5952   docsrc := "init-methods.g",
 5953   sinflat := [ nof(list) ],
 5954   souflat := [ alist ],
 5955   soghash := "4405bf",
 5956   sig4hash := "Alist(nof(list))" ),
 5957 rec(
 5958   kind := "FUNCTION",
 5959   name := "Function",
 5960   sin := [ [ alist, "A" ] ],
 5961   sou := [ [ func ] ],
 5962   short := "Create a function (not a map!) whose `domain' is the keylist of `A' and whose `co-domain' is the valuelist of `A' and return this function.",
 5963   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"],[3,\"foobar\"]);\nAF:=Function(A);\nAF(1); AF(2); AF(3); AF(4);" ],
 5964   see := [  ],
 5965   hash := "367094",
 5966   sig := "Function(<alist> A)",
 5967   sog := " -> <func>",
 5968   docsrc := "init-methods.g",
 5969   sinflat := [ alist ],
 5970   souflat := [ func ],
 5971   soghash := "99fdb3",
 5972   sig4hash := "Function(alist)" ),
 5973 rec(
 5974   kind := "FUNCTION",
 5975   name := "MapAlist",
 5976   sin := [ [ func, "f" ], [ alist, "A" ] ],
 5977   sou := [ [  ] ],
 5978   short := "Apply `f' to all entries in alist `A' and return SUCCESS.\n`f' is expected to take two arguments, the first one is bound to the key of an alist element, the second one is bound to its association.",
 5979   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"],[3,\"foobar\"]);\nf:=function(key,val)\nPrint(\"key is \",key,\", val is \",val,\"\\n\");\nend;\nMapAlist(f,A);" ],
 5980   see := [ "b49bbf" ],
 5981   hash := "c34314",
 5982   sig := "MapAlist(<func> f, <alist> A)",
 5983   sog := "",
 5984   docsrc := "init-methods.g",
 5985   sinflat := [ func, alist ],
 5986   souflat := [  ],
 5987   soghash := "da39a3",
 5988   sig4hash := "MapAlist(func,alist)" ),
 5989 rec(
 5990   kind := "FUNCTION",
 5991   name := "MapAlist",
 5992   sin := [ [ alist, "A" ], [ func, "f" ] ],
 5993   sou := [ [  ] ],
 5994   short := "Apply `f' to all entries in alist `A' and return SUCCESS.\n`f' is expected to take two arguments, the first one is bound to the key of an alist element, the second one is bound to its association.",
 5995   ex := [ "A:=Alist([1,\"foo\"],[2,\"bar\"],[3,\"foobar\"]);\nf:=function(key,val)\nPrint(\"key is \",key,\", val is \",val,\"\\n\");\nend;\nMapAlist(A,f);" ],
 5996   see := [ "b49bbf" ],
 5997   hash := "1b771b",
 5998   sig := "MapAlist(<alist> A, <func> f)",
 5999   sog := "",
 6000   docsrc := "init-methods.g",
 6001   sinflat := [ alist, func ],
 6002   souflat := [  ],
 6003   soghash := "da39a3",
 6004   sig4hash := "MapAlist(alist,func)" ),
 6005 rec(
 6006   kind := "FUNCTION",
 6007   name := "PrintString",
 6008   sin := [ [ nof(string), "S" ] ],
 6009   opt := [ [ elt-ord^rat, "Start", "Offset to indicate how many columns have already been printed in the current line", rec(
 6010               Default := "GetCurrentColumn()" ) ] ],
 6011   sou := [ [  ] ],
 6012   short := "Print a string with respect to the current term's columns and lines definition.",
 6013   ex := [  ],
 6014   see := [  ],
 6015   hash := "3196a1",
 6016   sig := "PrintString(<nof(string)> S [, optargs])",
 6017   sog := "",
 6018   docsrc := "init-methods.g",
 6019   sinflat := [ nof(string) ],
 6020   souflat := [  ],
 6021   soghash := "da39a3",
 6022   sig4hash := "PrintString(nof(string))" ),
 6023 rec(
 6024   kind := "FUNCTION",
 6025   name := "DocGenHashByString",
 6026   sin := [ [ string, "docsig" ] ],
 6027   sou := [ [ string, "dochash" ] ],
 6028   short := "Return the hash value a record with signature `docsig' would have if added to the global documentation dry.\nYou may want to use this when using the InstallDocumentation or MergeDocumentation macros in order to refer to other functions without looking up the hash value.",
 6029   ex := [ "DocGenHashByString(\"DocGenHashByString(string)\");" ],
 6030   see := [ "966a95" ],
 6031   hash := "8cb8bb",
 6032   sig := "DocGenHashByString(<string> docsig)",
 6033   sog := " -> <string> dochash",
 6034   docsrc := "init-methods.g",
 6035   sinflat := [ string ],
 6036   souflat := [ string ],
 6037   soghash := "ecb252",
 6038   sig4hash := "DocGenHashByString(string)" ),
 6039 rec(
 6040   kind := "FUNCTION",
 6041   name := "DocGenHashByRecord",
 6042   sin := [ [ record, "docrec" ] ],
 6043   sou := [ [ string, "dochash" ] ],
 6044   short := "Return the hash value a record `docrec' would have if added to the global documentation dry.\nYou may want to use this when using the InstallDocumentation or MergeDocumentation macros in order to refer to other functions without looking up the hash value.\nNote: In general there is no need to provide the whole record as argument, instead sufficient are the rec fields which are used to compute the hash sum. Currently these are `kind' and `name' and in some cases (OPERATION and FUNCTION) `sin' is also mandatory.",
 6045   ex := [ "DocGenHashByRecord(rec(kind:=\"FUNCTION\",name:=\"DocGenHashByRecord\",sin:=[[record]]));" ],
 6046   see := [ "8cb8bb" ],
 6047   hash := "966a95",
 6048   sig := "DocGenHashByRecord(<record> docrec)",
 6049   sog := " -> <string> dochash",
 6050   docsrc := "init-methods.g",
 6051   sinflat := [ record ],
 6052   souflat := [ string ],
 6053   soghash := "ecb252",
 6054   sig4hash := "DocGenHashByRecord(record)" ),
 6055 rec(
 6056   kind := "FUNCTION",
 6057   name := "CheckDocumentation",
 6058   sin := [ [ record, "r" ] ],
 6059   sou := [  ],
 6060   short := "Return true iff documentation in record 'r' tends to be correct.",
 6061   ex := [  ],
 6062   hash := "cefa10",
 6063   sig := "CheckDocumentation(<record> r)",
 6064   sog := "",
 6065   docsrc := "init-methods.g",
 6066   sinflat := [ record ],
 6067   souflat := [  ],
 6068   soghash := "da39a3",
 6069   sig4hash := "CheckDocumentation(record)" ),
 6070 rec(
 6071   kind := "FUNCTION",
 6072   name := "BlowUpDocumentation",
 6073   sin := [ [ record, "r" ] ],
 6074   sou := [  ],
 6075   short := "Blow up documentation in record 'r' by adding useful fields.",
 6076   ex := [  ],
 6077   hash := "cf9331",
 6078   sig := "BlowUpDocumentation(<record> r)",
 6079   sog := "",
 6080   docsrc := "init-methods.g",
 6081   sinflat := [ record ],
 6082   souflat := [  ],
 6083   soghash := "da39a3",
 6084   sig4hash := "BlowUpDocumentation(record)" ),
 6085 rec(
 6086   kind := "FUNCTION",
 6087   name := "InstallDocumentation",
 6088   sin := [ [ record, "r" ] ],
 6089   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 6090               Default := FAILURE ) ], [ elt-alg^boo, "ForceAdd", "Default: FALSE, indicate you want to add or replace existing documentation." ] ],
 6091   sou := [ [ elt-alg^boo, "success" ] ],
 6092   short := "Add documentation given by `r' to global documentation hash table.\nThe documentation in `r' is blown up and checked. Then it is tried to be added with a dry operation (DryReplaceOrAdd) and thus overwrites existing documentation iff the hash value computed by `r' is already in the global dry, and is appended otherwise.",
 6093   see := [ "cf9331", "cefa10" ],
 6094   ex := [  ],
 6095   hash := "c13e31",
 6096   sig := "InstallDocumentation(<record> r [, optargs])",
 6097   sog := " -> <elt-alg^boo> success",
 6098   docsrc := "init-methods.g",
 6099   sinflat := [ record ],
 6100   souflat := [ elt-alg^boo ],
 6101   soghash := "5e8dd4",
 6102   sig4hash := "InstallDocumentation(record)" ),
 6103 rec(
 6104   kind := "FUNCTION",
 6105   name := "MergeDocumentation",
 6106   sin := [ [ record, "r" ] ],
 6107   opt := [ [ any, "Fail", "Determines what to return in case of failure.", rec(
 6108               Default := FAILURE ) ], [ any, "Success", "Default: TRUE, indicate what to return in case of success" ], [ any, "Add", "Default: FALSE, add `r' to documentation dry in either case" ] ],
 6109   sou := [  ],
 6110   short := "Merge documentation given (even partially) by `r' to global documentation hash table.\n",
 6111   ex := [  ],
 6112   hash := "a3cff8",
 6113   sig := "MergeDocumentation(<record> r [, optargs])",
 6114   sog := "",
 6115   docsrc := "init-methods.g",
 6116   sinflat := [ record ],
 6117   souflat := [  ],
 6118   soghash := "da39a3",
 6119   sig4hash := "MergeDocumentation(record)" ),
 6120 rec(
 6121   kind := "FUNCTION",
 6122   name := "DocHash",
 6123   sin := [ [ string, "s" ] ],
 6124   sou := [ [ string, "hash" ] ],
 6125   short := "Return the hash value used to identify a function specified by 's'. The string 's' must be of the form \"functionname(typearg1,typearg2,...)\" or \"type\" or \"keyword\".",
 6126   ex := [ "x_s := DocHash(\"GCD(elt-ord^rat,elt-ord^rat)\"););", "x_s := DocHash(\"record\");", "x_s := DocHash(\"operations\");" ],
 6127   hash := "a283e8",
 6128   sig := "DocHash(<string> s)",
 6129   sog := " -> <string> hash",
 6130   docsrc := "init-methods.g",
 6131   sinflat := [ string ],
 6132   souflat := [ string ],
 6133   soghash := "ecb252",
 6134   sig4hash := "DocHash(string)" ),
 6135 rec(
 6136   kind := "FUNCTION",
 6137   name := "CheckArgs",
 6138   sin := [ [ list, "arglist" ], [ list, "argnames" ], [ list, "defaults" ] ],
 6139   sou := [ [ record ] ],
 6140   short := "Traverse through `arglist' and bind arguments to argument names in `argnames'. If some arguments are not provided bind them to values from `defaults'. Return the resulting record.",
 6141   see := [ "afca37", "52ee65" ],
 6142   ex := [  ],
 6143   hash := "196729",
 6144   sig := "CheckArgs(<list> arglist, <list> argnames, <list> defaults)",
 6145   sog := " -> <record>",
 6146   docsrc := "init-methods.g",
 6147   sinflat := [ list, list, list ],
 6148   souflat := [ record ],
 6149   soghash := "275a70",
 6150   sig4hash := "CheckArgs(list,list,list)" ),
 6151 rec(
 6152   kind := "KEYWORD",
 6153   name := "Optional Arguments",
 6154   short := "Many KASH3 functions take optional arguments.  These are passed to a function by passing a record as a last argument to the function. ",
 6155   see := [ "52ee65", "afca37", "196729" ],
 6156   ex := [  ],
 6157   hash := "d691ad",
 6158   sig := "Optional Arguments",
 6159   sog := "",
 6160   docsrc := "init-methods.g",
 6161   soghash := "da39a3",
 6162   sig4hash := "Optional Arguments" ),
 6163 rec(
 6164   kind := "FUNCTION",
 6165   name := "HasOptarg",
 6166   sin := [ [ list, "arglist" ] ],
 6167   sou := [ [ elt-alg^boo ] ],
 6168   short := "Return TRUE iff arglist's last argument is an optional argument record.",
 6169   see := [ "52ee65", "196729" ],
 6170   ex := [  ],
 6171   hash := "afca37",
 6172   sig := "HasOptarg(<list> arglist)",
 6173   sog := " -> <elt-alg^boo>",
 6174   docsrc := "init-methods.g",
 6175   sinflat := [ list ],
 6176   souflat := [ elt-alg^boo ],
 6177   soghash := "5e8dd4",
 6178   sig4hash := "HasOptarg(list)" ),
 6179 rec(
 6180   kind := "FUNCTION",
 6181   name := "ExtractOptarg",
 6182   sin := [ [ list, "arglist" ] ],
 6183   sou := [ [ record ] ],
 6184   short := "Return arglist's last argument if it is an optional argument, FAILURE otherwise otherwise.",
 6185   see := [ "9df99d", "afca37", "196729" ],
 6186   ex := [  ],
 6187   hash := "52ee65",
 6188   sig := "ExtractOptarg(<list> arglist)",
 6189   sog := " -> <record>",
 6190   docsrc := "init-methods.g",
 6191   sinflat := [ list ],
 6192   souflat := [ record ],
 6193   soghash := "275a70",
 6194   sig4hash := "ExtractOptarg(list)" ),
 6195 rec(
 6196   kind := "FUNCTION",
 6197   name := "ExtractOptarg_",
 6198   sin := [ [ list, "arglist" ] ],
 6199   sou := [ [ record ] ],
 6200   short := "Return and remove arglist's last argument if it is an optional argument, FAILURE otherwise.\n Note: This is the destructive version of ExtractOptarg.",
 6201   see := [ "52ee65", "afca37", "196729" ],
 6202   ex := [  ],
 6203   hash := "9df99d",
 6204   sig := "ExtractOptarg_(<list> arglist)",
 6205   sog := " -> <record>",
 6206   docsrc := "init-methods.g",
 6207   sinflat := [ list ],
 6208   souflat := [ record ],
 6209   soghash := "275a70",
 6210   sig4hash := "ExtractOptarg_(list)" ),
 6211 rec(
 6212   kind := "FUNCTION",
 6213   name := "Optarg",
 6214   sin := [ [ list, "arglist" ], [ list, "optarg_names" ], [ list, "defaults" ] ],
 6215   sou := [ [ record ] ],
 6216   short := "Process optional arguments.  Extract optional arguments record  from 'arglist'.Set missing entries (from 'optarg_names') to default values from 'defaults'.",
 6217   see := [ "52ee65", "afca37", "196729" ],
 6218   ex := [  ],
 6219   hash := "7a1f45",
 6220   sig := "Optarg(<list> arglist, <list> optarg_names, <list> defaults)",
 6221   sog := " -> <record>",
 6222   docsrc := "init-methods.g",
 6223   sinflat := [ list, list, list ],
 6224   souflat := [ record ],
 6225   soghash := "275a70",
 6226   sig4hash := "Optarg(list,list,list)" ),
 6227 rec(
 6228   kind := "FUNCTION",
 6229   name := "Read",
 6230   sin := [ [ string, "filename" ] ],
 6231   sou := [  ],
 6232   short := "Read a file 'filename' containing KASH commands.",
 6233   long := "The file 'filename' must both existing and readable.KASH looks first in the given path, then in the current directory and finally in $LIBNAME../src.",
 6234   see := [ "cc967a" ],
 6235   ex := [  ],
 6236   hash := "954a96",
 6237   sig := "Read(<string> filename)",
 6238   sog := "",
 6239   docsrc := "init-methods.g",
 6240   sinflat := [ string ],
 6241   souflat := [  ],
 6242   soghash := "da39a3",
 6243   sig4hash := "Read(string)" ),
 6244 rec(
 6245   kind := "FUNCTION",
 6246   name := "ReadLib",
 6247   sin := [ [ string, "lib" ] ],
 6248   sou := [  ],
 6249   short := "Same as `Read', but here the file should be in the KASH lib directory and it must have the extension  .g .",
 6250   see := [ "954a96" ],
 6251   ex := [  ],
 6252   hash := "cc967a",
 6253   sig := "ReadLib(<string> lib)",
 6254   sog := "",
 6255   docsrc := "init-methods.g",
 6256   sinflat := [ string ],
 6257   souflat := [  ],
 6258   soghash := "da39a3",
 6259   sig4hash := "ReadLib(string)" ),
 6260 rec(
 6261   kind := "KEYWORD",
 6262   name := "arg",
 6263   syntax := "function(arg) ... end;",
 6264   short := "Collapse arbitrary many arguments to a list of arguments and pass it to arg.",
 6265   long := "When used as (only) argument in a function's declaration this so defined function accepts any number of arguments. Arguments passed to the function at call-time are gathered into a list whose value becomes `arg' in the function body.\nNote: This will not work on abbreviated function declarations, like `arg->arg[1];'.\nNote: Also, the function keyword will not collect rests of arguments into the arg argument, that is `function(some, arg) return TRUE; end;' is a valid function which takes exactly two arguments, `arg' has no no special meaning here (yet).",
 6266   ex := [ "x_f := function(arg) return arg; end;\nx_f(1,2.3,\"hi mom\",[12,3]);\nx_f(6);" ],
 6267   hash := "04d6e2",
 6268   sig := "arg",
 6269   sog := "",
 6270   docsrc := "init-methods.g",
 6271   soghash := "da39a3",
 6272   sig4hash := "arg" ),
 6273 rec(
 6274   kind := "KEYWORD",
 6275   docsrc := "kantconst.c",
 6276   name := "Constants",
 6277   short := "For convenience some constants are predefined in KASH.  These constants cannot be overwritten.  Some constants, namely 'E' and 'PI'.  change their value with the global precision 'Precision()'.  By convention constants are written in capitals.\n\nEnter '?*.|CONSTANT' to see a list of all constants.",
 6278   ex := [  ],
 6279   hash := "0f386d",
 6280   sig := "Constants",
 6281   sog := "",
 6282   soghash := "da39a3",
 6283   sig4hash := "Constants" ),
 6284 rec(
 6285   kind := "FUNCTION",
 6286   name := "InstallConstants",
 6287   sin := [  ],
 6288   sou := [  ],
 6289   short := "Reinitialize the constants\nC := ComplexField();\nE := Exp(1);\nI := C.1;\nPI:= Pi(R);\nQ := RationalField();\nR := RealField();\nX := ZX.1;\nZ := Integers();\nZX:= PolynomialRing(Z);",
 6290   see := [ "0f386d", "4a6ac6" ],
 6291   hash := "8a7886",
 6292   ex := [  ],
 6293   sig := "InstallConstants()",
 6294   sog := "",
 6295   docsrc := "constants.g",
 6296   sinflat := [  ],
 6297   souflat := [  ],
 6298   soghash := "da39a3",
 6299   sig4hash := "InstallConstants()" ),
 6300 rec(
 6301   kind := "CONSTANT",
 6302   docsrc := "kantconst.c",
 6303   name := "Q",
 6304   sou := [ [ fld^rat ] ],
 6305   short := "The field of rational numbers.",
 6306   ex := [  ],
 6307   hash := "c3156e",
 6308   sig := "Q",
 6309   sog := " -> <fld^rat>",
 6310   souflat := [ fld^rat ],
 6311   soghash := "d77aa4",
 6312   sig4hash := "Q" ),
 6313 rec(
 6314   kind := "CONSTANT",
 6315   docsrc := "kantconst.c",
 6316   name := "Z",
 6317   sou := [ [ ord^rat ] ],
 6318   short := "The ring of rational integers.",
 6319   ex := [  ],
 6320   hash := "909f99",
 6321   sig := "Z",
 6322   sog := " -> <ord^rat>",
 6323   souflat := [ ord^rat ],
 6324   soghash := "ef1cfa",
 6325   sig4hash := "Z" ),
 6326 rec(
 6327   kind := "CONSTANT",
 6328   docsrc := "kantconst.c",
 6329   name := "ZX",
 6330   sou := [ [ alg^pol/ord^rat ] ],
 6331   short := "The ring of polynomials in X over the ring of rational integers Z.",
 6332   ex := [  ],
 6333   hash := "0f462d",
 6334   sig := "ZX",
 6335   sog := " -> <alg^pol/ord^rat>",
 6336   souflat := [ alg^pol/ord^rat ],
 6337   soghash := "6fe1a1",
 6338   sig4hash := "ZX" ),
 6339 rec(
 6340   kind := "CONSTANT",
 6341   docsrc := "kantconst.c",
 6342   name := "X",
 6343   sou := [ [ func ] ],
 6344   short := "The variable of the ring of polynomials ZX over the ring of rational integers Z.",
 6345   ex := [  ],
 6346   hash := "c032ad",
 6347   sig := "X",
 6348   sog := " -> <func>",
 6349   souflat := [ func ],
 6350   soghash := "99fdb3",
 6351   sig4hash := "X" ),
 6352 rec(
 6353   kind := "CONSTANT",
 6354   docsrc := "kantconst.c",
 6355   name := "R",
 6356   sou := [ [ fld^rea ] ],
 6357   short := "The global real field.",
 6358   ex := [  ],
 6359   hash := "065765",
 6360   sig := "R",
 6361   sog := " -> <fld^rea>",
 6362   souflat := [ fld^rea ],
 6363   soghash := "348de3",
 6364   sig4hash := "R" ),
 6365 rec(
 6366   kind := "CONSTANT",
 6367   docsrc := "kantconst.c",
 6368   name := "C",
 6369   sou := [ [ fld^com ] ],
 6370   short := "The global complex field.",
 6371   ex := [  ],
 6372   hash := "32096c",
 6373   sig := "C",
 6374   sog := " -> <fld^com>",
 6375   souflat := [ fld^com ],
 6376   soghash := "c8d5b4",
 6377   sig4hash := "C" ),
 6378 rec(
 6379   kind := "CONSTANT",
 6380   docsrc := "kantconst.c",
 6381   name := "I",
 6382   sou := [ [ elt-fld^com ] ],
 6383   short := "A complex number I with I^2=-1.",
 6384   ex := [  ],
 6385   hash := "ca73ab",
 6386   sig := "I",
 6387   sog := " -> <elt-fld^com>",
 6388   souflat := [ elt-fld^com ],
 6389   soghash := "0d772f",
 6390   sig4hash := "I" ),
 6391 rec(
 6392   kind := "CONSTANT",
 6393   docsrc := "kantconst.c",
 6394   name := "E",
 6395   sou := [ [ elt-fld^rea ] ],
 6396   short := "Eulers constant to the global precision 'Precision()'.",
 6397   ex := [  ],
 6398   hash := "e0184a",
 6399   sig := "E",
 6400   sog := " -> <elt-fld^rea>",
 6401   souflat := [ elt-fld^rea ],
 6402   soghash := "7f2490",
 6403   sig4hash := "E" ),
 6404 rec(
 6405   kind := "FUNCTION",
 6406   docsrc := "kantconst.c",
 6407   name := "Precision",
 6408   sin := [  ],
 6409   sou := [ [ elt-ord^rat, "prec" ] ],
 6410   short := "Returns the global precision for real and complex computations in the shell.",
 6411   ex := [  ],
 6412   hash := "f3f65b",
 6413   sig := "Precision()",
 6414   sog := " -> <elt-ord^rat> prec",
 6415   sinflat := [  ],
 6416   souflat := [ elt-ord^rat ],
 6417   soghash := "898213",
 6418   sig4hash := "Precision()" ),
 6419 rec(
 6420   kind := "FUNCTION",
 6421   docsrc := "kantconst.c",
 6422   name := "Precision",
 6423   sin := [ [ elt-ord^rat, "n" ] ],
 6424   sou := [ [ elt-ord^rat, "prec" ] ],
 6425   short := "Sets the global precision for real and complex computations in the shell to 'n' and returns the  new global precision. This is the smallest positive integer which is divisible by 4 and greater than or equal to Maximum(n,12).  The default precision is 20.",
 6426   ex := [  ],
 6427   hash := "4a6ac6",
 6428   sig := "Precision(<elt-ord^rat> n)",
 6429   sog := " -> <elt-ord^rat> prec",
 6430   sinflat := [ elt-ord^rat ],
 6431   souflat := [ elt-ord^rat ],
 6432   soghash := "898213",
 6433   sig4hash := "Precision(elt-ord^rat)" ),
 6434 rec(
 6435   name := "Comment",
 6436   kind := "KEYWORD",
 6437   short := "Comments in KASH3 start with '#'.  All text on a line after '#' is ignored by KASH3.",
 6438   ex := [ "# this is a comment" ],
 6439   hash := "153d7a",
 6440   sig := "Comment",
 6441   sog := "",
 6442   docsrc := "kash.g",
 6443   soghash := "da39a3",
 6444   sig4hash := "Comment" ),
 6445 rec(
 6446   kind := "FUNCTION",
 6447   name := "GAP",
 6448   sin := [  ],
 6449   sou := [  ],
 6450   short := "Initializes the GAP3 (groups algorithms and programing) emulation mode.  Not all functions are available.   KASH3 provides NO DOCUMENTATION. Please refer to the GAP3 documentation for a description of the functions.",
 6451   ex := [  ],
 6452   hash := "1b9919",
 6453   sig := "GAP()",
 6454   sog := "",
 6455   docsrc := "kash.g",
 6456   sinflat := [  ],
 6457   souflat := [  ],
 6458   soghash := "da39a3",
 6459   sig4hash := "GAP()" ),
 6460 rec(
 6461   kind := "FUNCTION",
 6462   name := "IsOdd",
 6463   sin := [ [ elt-ord^rat, "b" ] ],
 6464   sou := [ [ elt-alg^boo ] ],
 6465   short := "Return 'TRUE' if 'b' is odd",
 6466   ex := [ "IsOdd(5)" ],
 6467   see := [ "83043c" ],
 6468   hash := "14048e",
 6469   sig := "IsOdd(<elt-ord^rat> b)",
 6470   sog := " -> <elt-alg^boo>",
 6471   docsrc := "kash.g",
 6472   sinflat := [ elt-ord^rat ],
 6473   souflat := [ elt-alg^boo ],
 6474   soghash := "5e8dd4",
 6475   sig4hash := "IsOdd(elt-ord^rat)" ),
 6476 rec(
 6477   kind := "FUNCTION",
 6478   name := "BindNames_",
 6479   sin := [ [ str, "S" ], [ list, "L" ] ],
 6480   short := "Define global variables whose names are given in 'L' which contain the generators of 'S'",
 6481   ex := [ "CY := PolynomialAlgebra(C); BindNames_(CY,[\"Y\"]);" ],
 6482   see := [ "12d7db", "340989" ],
 6483   sou := [ [ any ] ],
 6484   hash := "27e1eb",
 6485   sig := "BindNames_(<str> S, <list> L)",
 6486   sog := " -> <any>",
 6487   docsrc := "kash.g",
 6488   sinflat := [ str, list ],
 6489   souflat := [ any ],
 6490   soghash := "c5fe02",
 6491   sig4hash := "BindNames_(str,list)" ),
 6492 rec(
 6493   kind := "FUNCTION",
 6494   name := "BindName_",
 6495   sin := [ [ str, "S" ], [ string, "name" ] ],
 6496   short := "Define a global variables whose name is given by 'name' which contains the (first) generator of 'S'",
 6497   ex := [ "CY := PolynomialAlgebra(C); BindName_(CY,\"Y\");" ],
 6498   see := [ "27e1eb", "340989" ],
 6499   sou := [ [ any ] ],
 6500   hash := "12d7db",
 6501   sig := "BindName_(<str> S, <string> name)",
 6502   sog := " -> <any>",
 6503   docsrc := "kash.g",
 6504   sinflat := [ str, string ],
 6505   souflat := [ any ],
 6506   soghash := "c5fe02",
 6507   sig4hash := "BindName_(str,string)" ),
 6508 rec(
 6509   kind := "FUNCTION",
 6510   name := "SetVerbose",
 6511   sin := [ [ string, "S" ], [ elt-ord^rat, "n" ] ],
 6512   short := "Set the verbose level of 'S' to 'n'.",
 6513   see := [ "adf18d", "c70f5c" ],
 6514   ex := [  ],
 6515   hash := "5974c9",
 6516   sig := "SetVerbose(<string> S, <elt-ord^rat> n)",
 6517   sog := "",
 6518   docsrc := "kash.g",
 6519   sinflat := [ string, elt-ord^rat ],
 6520   soghash := "da39a3",
 6521   sig4hash := "SetVerbose(string,elt-ord^rat)" ),
 6522 rec(
 6523   kind := "FUNCTION",
 6524   name := "GetVerbose",
 6525   sin := [ [ string, "S" ] ],
 6526   sou := [ [ elt-ord^rat, "n" ] ],
 6527   short := "Get the verbose level of 'S'.",
 6528   see := [ "adf18d", "c70f5c" ],
 6529   ex := [  ],
 6530   hash := "adf18d",
 6531   sig := "GetVerbose(<string> S)",
 6532   sog := " -> <elt-ord^rat> n",
 6533   docsrc := "kash.g",
 6534   sinflat := [ string ],
 6535   souflat := [ elt-ord^rat ],
 6536   soghash := "898213",
 6537   sig4hash := "GetVerbose(string)" ),
 6538 rec(
 6539   kind := "FUNCTION",
 6540   name := "PrintVerbose",
 6541   sin := [ [ string, "S" ], [ elt-ord^rat, "n" ], [ nof(any) ] ],
 6542   short := "If the verbose level of 'S' is greater 'n' then print information.",
 6543   see := [ "adf18d", "5974c9" ],
 6544   ex := [  ],
 6545   hash := "c70f5c",
 6546   sig := "PrintVerbose(<string> S, <elt-ord^rat> n, <nof(any)>)",
 6547   sog := "",
 6548   docsrc := "kash.g",
 6549   sinflat := [ string, elt-ord^rat, nof(any) ],
 6550   soghash := "da39a3",
 6551   sig4hash := "PrintVerbose(string,elt-ord^rat,nof(any))" ),
 6552 rec(
 6553   kind := "FUNCTION",
 6554   name := "Matrix",
 6555   sin := [ [ list, "L" ] ],
 6556   sou := [ [ elt-alg^mat ] ],
 6557   short := "Construct a matrix from the list of lists 'L'.  All list in 'L' must have the same length.  All elements in these lists must be coercible into a common coefficient ring.",
 6558   hash := "f49c4a",
 6559   ex := [  ],
 6560   sig := "Matrix(<list> L)",
 6561   sog := " -> <elt-alg^mat>",
 6562   docsrc := "matrix.g",
 6563   sinflat := [ list ],
 6564   souflat := [ elt-alg^mat ],
 6565   soghash := "8dbb64",
 6566   sig4hash := "Matrix(list)" ),
 6567 rec(
 6568   kind := "FUNCTION",
 6569   name := "Matrix",
 6570   sin := [ [ seq(seq()), "L" ] ],
 6571   sou := [ [ elt-alg^mat ] ],
 6572   short := "Construct a matrix from the sequence of sequeces 'L'.  All sequences in 'L' must have the same length.  All elements in these lists must be coercible into a common coefficient ring.",
 6573   hash := "55939c",
 6574   ex := [  ],
 6575   sig := "Matrix(<seq(seq())> L)",
 6576   sog := " -> <elt-alg^mat>",
 6577   docsrc := "matrix.g",
 6578   sinflat := [ seq(seq()) ],
 6579   souflat := [ elt-alg^mat ],
 6580   soghash := "8dbb64",
 6581   sig4hash := "Matrix(seq(seq()))" ),
 6582 rec(
 6583   name := "Maps",
 6584   kind := "KEYWORD",
 6585   short := "In KASH3 maps are functions with additional information, namely domain, codomain, and in some cases a map for computing preimages.",
 6586   see := [ "37745e", "dde0bc", "ed8fcc", "54c9fa", "881f91", "3c8afe", "90f13e", "fa446b", "d86b75" ],
 6587   ex := [  ],
 6588   hash := "80071c",
 6589   sig := "Maps",
 6590   sog := "",
 6591   docsrc := "map.g",
 6592   soghash := "da39a3",
 6593   sig4hash := "Maps" ),
 6594 rec(
 6595   name := "Composition",
 6596   kind := "FUNCTION",
 6597   sin := [ [ map(), "phi" ], [ map(), "psi" ] ],
 6598   sou := [ [ map() ] ],
 6599   short := "The composition 'phi*psi' of the maps 'phi' and 'psi'.",
 6600   ex := [ "x_add_with_inv := function(a)\n# this function returns a map that adds 'a'\nlocal phi, psi;\n  phi := function(b) return b+a; end;\n  psi := function(c) return c-a; end;\n  return Map(Z,Z,phi,psi);\nend;\n\nx_f := x_add_with_inv(5);\nx_f(2);\nx_Z7 := Quotient(Z,7);\nx_g := Composition(x_Z7.ext1,x_f);\nx_g(1);\nPreimage(Coerce(x_Z7,8),x_g);\n" ],
 6601   see := [ "37745e", "dde0bc", "ed8fcc", "54c9fa", "881f91", "3c8afe", "90f13e" ],
 6602   hash := "d86b75",
 6603   sig := "Composition(<map()> phi, <map()> psi)",
 6604   sog := " -> <map()>",
 6605   docsrc := "map.g",
 6606   sinflat := [ map(), map() ],
 6607   souflat := [ map() ],
 6608   soghash := "63931a",
 6609   sig4hash := "Composition(map(),map())" ),
 6610 rec(
 6611   name := "Map",
 6612   kind := "FUNCTION",
 6613   sin := [ [ any, "domain" ], [ any, "codomain" ], [ func, "phi" ], [ func, "psi" ] ],
 6614   sou := [ [ map() ] ],
 6615   short := "Create a map with domain 'domain' and codomain 'codomain' from the function 'phi'.  The function 'psi' is used for the computation of preimages.",
 6616   ex := [ "x_add_with_inv := function(a)\n# this function returns a map that adds 'a'\nlocal phi, psi;\n  phi := function(b) return b+a; end;\n  psi := function(c) return c-a; end;\n  return Map(Z,Z,phi,psi);\nend;\n\nx_f := x_add_with_inv(5);\nx_f(2);\nImage(3,x_f);\nPreimage(8,x_f);\nPreimage(x_f(900),x_f);" ],
 6617   see := [ "37745e", "80071c", "dde0bc", "54c9fa", "881f91", "3c8afe", "90f13e", "d86b75" ],
 6618   hash := "ed8fcc",
 6619   sig := "Map(<any> domain, <any> codomain, <func> phi, <func> psi)",
 6620   sog := " -> <map()>",
 6621   docsrc := "map.g",
 6622   sinflat := [ any, any, func, func ],
 6623   souflat := [ map() ],
 6624   soghash := "63931a",
 6625   sig4hash := "Map(any,any,func,func)" ),
 6626 rec(
 6627   name := "Map",
 6628   kind := "FUNCTION",
 6629   sin := [ [ any, "domain" ], [ any, "codomain" ], [ func, "phi" ] ],
 6630   sou := [ [ map() ] ],
 6631   short := "Create a map with domain 'domain' and codomain 'codomain' from the function 'phi'.  ",
 6632   ex := [ "x_mult := function(a)\n# this function returns a map that multiplies by 'I*a'\nlocal phi;\n  phi := function(b) return b*a*I; end;\n  return Map(R,C,phi);\nend;\n\nx_f := x_mult(5);\nx_f(2);\nImage(3.1,x_f);\nDomain(x_f);\nCodomain(x_f);" ],
 6633   see := [ "37745e", "80071c", "ed8fcc", "54c9fa", "881f91", "3c8afe", "90f13e", "d86b75" ],
 6634   hash := "dde0bc",
 6635   sig := "Map(<any> domain, <any> codomain, <func> phi)",
 6636   sog := " -> <map()>",
 6637   docsrc := "map.g",
 6638   sinflat := [ any, any, func ],
 6639   souflat := [ map() ],
 6640   soghash := "63931a",
 6641   sig4hash := "Map(any,any,func)" ),
 6642 rec(
 6643   kind := "KEYWORD",
 6644   name := "QaoS",
 6645   short := "",
 6646   see := [ "4d7a41", "d038c9" ],
 6647   ex := [  ],
 6648   hash := "f904e2",
 6649   sig := "QaoS",
 6650   sog := "",
 6651   docsrc := "qaos.k",
 6652   soghash := "da39a3",
 6653   sig4hash := "QaoS" ),
 6654 rec(
 6655   kind := "FUNCTION",
 6656   name := "QaosNumberField",
 6657   sin := [ [ string, "query" ] ],
 6658   opt := [ [ elt-ord^rat, "Limit", "Determines how many fields may be retrieved maximally", rec(
 6659               Default := 25 ) ], [ elt-ord^rat, "Offset", "Determines an offset of fields", rec(
 6660               Default := 0 ) ], [ string, "Action", "Determines which action to perform on the query string. Possible values are `query' and `count'.", rec(
 6661               Default := "query" ) ], [ list, "ColGroups", "Determines which information to return. This is a list of column group specifiers.", rec(
 6662               Default := [ "cgall" ] ) ] ],
 6663   sou := [ [ list, "L" ] ],
 6664   short := "Searches the Algebraic Objects Database in Berlin.  The query string equals the keyword search method in the web surface.\nSee `http://www.math.tu-berlin.de/cgi-bin/kant/qaos/query.scm?type=anf&action=Help' for more information about the syntax and keywords.\n\nNote: You must have `curl' (see http://curl.haxx.se) installed and properly configured in order to use QaoS from within KASH.",
 6665   ex := [  ],
 6666   hash := "4d7a41",
 6667   sig := "QaosNumberField(<string> query [, optargs])",
 6668   sog := " -> <list> L",
 6669   docsrc := "qaos.k",
 6670   sinflat := [ string ],
 6671   souflat := [ list ],
 6672   soghash := "38b62b",
 6673   sig4hash := "QaosNumberField(string)" ),
 6674 rec(
 6675   kind := "FUNCTION",
 6676   name := "QaosFunctionField",
 6677   sin := [ [ string, "query" ] ],
 6678   opt := [ [ elt-ord^rat, "Limit", "Determines how many fields may be retrieved maximally", rec(
 6679               Default := 25 ) ], [ elt-ord^rat, "Offset", "Determines an offset of fields", rec(
 6680               Default := 0 ) ], [ string, "Action", "Determines which action to perform on the query string. Possible values are `query' and `count'.", rec(
 6681               Default := "query" ) ], [ list, "ColGroups", "Determines which information to return. This is a list of column group specifiers.", rec(
 6682               Default := [ "cgall" ] ) ] ],
 6683   sou := [ [ list, "L" ] ],
 6684   short := "Searches the Algebraic Objects Database in Berlin.  The query string equals the keyword search method in the web surface.\nSee `http://www.math.tu-berlin.de/cgi-bin/kant/qaos/query.scm?type=anf&action=Help' for more information about the syntax and keywords.\n\nNote: You must have `curl' (see http://curl.haxx.se) installed and properly configured in order to use QaoS from within KASH.",
 6685   ex := [  ],
 6686   hash := "fe08ce",
 6687   sig := "QaosFunctionField(<string> query [, optargs])",
 6688   sog := " -> <list> L",
 6689   docsrc := "qaos.k",
 6690   sinflat := [ string ],
 6691   souflat := [ list ],
 6692   soghash := "38b62b",
 6693   sig4hash := "QaosFunctionField(string)" ),
 6694 rec(
 6695   kind := "FUNCTION",
 6696   name := "QaosTransitiveGroup",
 6697   sin := [ [ string, "query" ] ],
 6698   opt := [ [ elt-ord^rat, "Limit", "Determines how many groups may be retrieved maximally", rec(
 6699               Default := 25 ) ], [ elt-ord^rat, "Offset", "Determines an offset of groups", rec(
 6700               Default := 0 ) ], [ string, "Action", "Determines which action to perform on the query string. Possible values are `query' and `count'.", rec(
 6701               Default := "query" ) ], [ list, "ColGroups", "Determines which information to return. This is a list of column group specifiers.", rec(
 6702               Default := [ "cgall" ] ) ] ],
 6703   sou := [ [ list, "L" ] ],
 6704   short := "Searches the Algebraic Objects Database in Berlin.  The query string equals the keyword search method in the web surface.\nSee `http://www.math.tu-berlin.de/cgi-bin/kant/qaos/query.scm?type=trnsg&action=Help' for more information about the syntax and keywords.\n\nNote: You must have `curl' (see http://curl.haxx.se) installed and properly configured in order to use QaoS from within KASH.",
 6705   ex := [  ],
 6706   hash := "d038c9",
 6707   sig := "QaosTransitiveGroup(<string> query [, optargs])",
 6708   sog := " -> <list> L",
 6709   docsrc := "qaos.k",
 6710   sinflat := [ string ],
 6711   souflat := [ list ],
 6712   soghash := "38b62b",
 6713   sig4hash := "QaosTransitiveGroup(string)" ),
 6714 rec(
 6715   kind := "FUNCTION",
 6716   name := "QaosResult",
 6717   sin := [ [ list, "collection" ] ],
 6718   sou := [ [ list, "L" ] ],
 6719   short := "Return the actual list of objects in `collection'.",
 6720   ex := [  ],
 6721   hash := "2df183",
 6722   sig := "QaosResult(<list> collection)",
 6723   sog := " -> <list> L",
 6724   docsrc := "qaos.k",
 6725   sinflat := [ list ],
 6726   souflat := [ list ],
 6727   soghash := "38b62b",
 6728   sig4hash := "QaosResult(list)" ),
 6729 rec(
 6730   name := "Factorization",
 6731   kind := "FUNCTION",
 6732   sin := [ [ elt-alg^pol/any^loc, "Phi" ] ],
 6733   sou := [ [ list ] ],
 6734   opt := [ [ elt-alg^boo, "Certificates", "If TRUE two element certificates for the irreducibilty of factors are returned.", rec(
 6735               Default := FALSE ) ], [ elt-alg^boo, "IsSquarefree", "If TRUE the polynomial is assumed to be squarefree", rec(
 6736               Default := FALSE ) ], [ elt-alg^boo, "Ideals", "", rec(
 6737               Default := FALSE ) ], [ elt-alg^boo, "Extensions", "If TRUE the extensions generated by the irreducible factors are returned", rec(
 6738               Default := FALSE ) ] ],
 6739   short := "The factorization of a polynomial over a p-adic field or a  p-adic ring.  The algorithm used is a combinantion of the algorithms by Ford-Pauli-Roblot and by Pauli.",
 6740   hash := "306f68",
 6741   ex := [  ],
 6742   sig := "Factorization(<elt-alg^pol/any^loc> Phi [, optargs])",
 6743   sog := " -> <list>",
 6744   docsrc := "locFact.g",
 6745   sinflat := [ elt-alg^pol/any^loc ],
 6746   souflat := [ list ],
 6747   soghash := "38b62b",
 6748   sig4hash := "Factorization(elt-alg^pol/any^loc)" ),
 6749 rec(
 6750   name := "Intersection",
 6751   kind := "FUNCTION",
 6752   sin := [ [ elt-ids^int/ord^num, "A" ], [ elt-ids^int/ord^num, "B" ] ],
 6753   sou := [ [ elt-ids^int/ord^num, "C" ] ],
 6754   short := "The intersection 'C' of the ideals 'A' and 'B'. Both ideals must be in the same order.",
 6755   author := [ "Carolin Just" ],
 6756   ex := [ "o := EquationOrder(X^2+5);\nA :=256*o;\nB := 6*o;\nIntersection(A,B);" ],
 6757   hash := "16264b",
 6758   sig := "Intersection(<elt-ids^int/ord^num> A, <elt-ids^int/ord^num> B)",
 6759   sog := " -> <elt-ids^int/ord^num> C",
 6760   docsrc := "unit_group_res.g",
 6761   sinflat := [ elt-ids^int/ord^num, elt-ids^int/ord^num ],
 6762   souflat := [ elt-ids^int/ord^num ],
 6763   soghash := "607a3e",
 6764   sig4hash := "Intersection(elt-ids^int/ord^num,elt-ids^int/ord^num)" ),
 6765 rec(
 6766   name := "Intersection",
 6767   kind := "FUNCTION",
 6768   sin := [ [ ord^num, "o" ], [ elt-ids^int/ord^num, "A" ] ],
 6769   sou := [ [ elt-ids^int/ord^num, "a" ] ],
 6770   short := "The intersection 'a' of the ideal 'A' and the order 'o'. The order 'o' must be a suborder of the order of 'A'",
 6771   author := [ "Carolin Just" ],
 6772   ex := [ "o := EquationOrder(X^2-5);\nO := MaximalOrder(o);\nA :=256*O;\na := Intersection(o,A);" ],
 6773   hash := "2656fb",
 6774   sig := "Intersection(<ord^num> o, <elt-ids^int/ord^num> A)",
 6775   sog := " -> <elt-ids^int/ord^num> a",
 6776   docsrc := "unit_group_res.g",
 6777   sinflat := [ ord^num, elt-ids^int/ord^num ],
 6778   souflat := [ elt-ids^int/ord^num ],
 6779   soghash := "607a3e",
 6780   sig4hash := "Intersection(ord^num,elt-ids^int/ord^num)" ),
 6781 rec(
 6782   kind := "FUNCTION",
 6783   name := "EllipticCurve",
 6784   sin := [ [ elt-ord^rat, "q" ], [ list, "L" ] ],
 6785   sou := [ [ grp^ell ] ],
 6786   short := "Constructs an elliptic curve over the finite field with q elements. If L has length 2, the curve is defined by the equation y^2 = x^3 + L[1]*x + L[2], if L has length 5, the curve is  defined by the equation y^2 + L[1]*x*y + L[2]*y = x^3 + L[3]*x^2 + L[4]*x + L[5]. ",
 6787   ex := [ "EC:= EllipticCurve(5,[1,2]);\n" ],
 6788   hash := "9a3bee",
 6789   sig := "EllipticCurve(<elt-ord^rat> q, <list> L)",
 6790   sog := " -> <grp^ell>",
 6791   docsrc := "elliptic.g",
 6792   sinflat := [ elt-ord^rat, list ],
 6793   souflat := [ grp^ell ],
 6794   soghash := "82fd04",
 6795   sig4hash := "EllipticCurve(elt-ord^rat,list)" ),
 6796 rec(
 6797   kind := "FUNCTION",
 6798   name := "Points",
 6799   sin := [ [ grp^ell, "E" ] ],
 6800   sou := [ [ list, "L" ] ],
 6801   short := "Returns all Points of E as a list.",
 6802   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nPoints(EC);\n" ],
 6803   hash := "1d3c71",
 6804   sig := "Points(<grp^ell> E)",
 6805   sog := " -> <list> L",
 6806   docsrc := "elliptic.g",
 6807   sinflat := [ grp^ell ],
 6808   souflat := [ list ],
 6809   soghash := "38b62b",
 6810   sig4hash := "Points(grp^ell)" ),
 6811 rec(
 6812   kind := "FUNCTION",
 6813   name := "MakePoint",
 6814   sin := [ [ grp^ell, "EC" ], [ list, "L" ] ],
 6815   sou := [ [ elt-grp^ell, "P" ] ],
 6816   short := "Returns,if possible, a point on EC, defined by the coordinates given in L.",
 6817   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nMakePoint(EC,[4,0]);\n" ],
 6818   hash := "8be19d",
 6819   sig := "MakePoint(<grp^ell> EC, <list> L)",
 6820   sog := " -> <elt-grp^ell> P",
 6821   docsrc := "elliptic.g",
 6822   sinflat := [ grp^ell, list ],
 6823   souflat := [ elt-grp^ell ],
 6824   soghash := "277ec0",
 6825   sig4hash := "MakePoint(grp^ell,list)" ),
 6826 rec(
 6827   kind := "FUNCTION",
 6828   name := "MakePoints",
 6829   sin := [ [ grp^ell, "EC" ], [ elt-fld^fin, "x" ] ],
 6830   sou := [ [ elt-grp^ell, "P" ] ],
 6831   short := "Returns the points on EC with x-coordinate x.",
 6832   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nMakePoints(EC,1);\n" ],
 6833   hash := "2e50e8",
 6834   sig := "MakePoints(<grp^ell> EC, <elt-fld^fin> x)",
 6835   sog := " -> <elt-grp^ell> P",
 6836   docsrc := "elliptic.g",
 6837   sinflat := [ grp^ell, elt-fld^fin ],
 6838   souflat := [ elt-grp^ell ],
 6839   soghash := "277ec0",
 6840   sig4hash := "MakePoints(grp^ell,elt-fld^fin)" ),
 6841 rec(
 6842   kind := "FUNCTION",
 6843   name := "RandomPoint",
 6844   sin := [ [ grp^ell, "EC" ] ],
 6845   sou := [ [ elt-grp^ell, "P" ] ],
 6846   short := "Returns a random point of EC, but never the point at infinity.",
 6847   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nRandomPoint(EC);\n" ],
 6848   hash := "52a693",
 6849   sig := "RandomPoint(<grp^ell> EC)",
 6850   sog := " -> <elt-grp^ell> P",
 6851   docsrc := "elliptic.g",
 6852   sinflat := [ grp^ell ],
 6853   souflat := [ elt-grp^ell ],
 6854   soghash := "277ec0",
 6855   sig4hash := "RandomPoint(grp^ell)" ),
 6856 rec(
 6857   kind := "FUNCTION",
 6858   name := "RandomPointWithInf",
 6859   sin := [ [ grp^ell, "EC" ] ],
 6860   sou := [ [ elt-grp^ell, "P" ] ],
 6861   short := "Returns a random point of EC.",
 6862   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nRandomPointWithInf(EC);\n" ],
 6863   hash := "9e54fd",
 6864   sig := "RandomPointWithInf(<grp^ell> EC)",
 6865   sog := " -> <elt-grp^ell> P",
 6866   docsrc := "elliptic.g",
 6867   sinflat := [ grp^ell ],
 6868   souflat := [ elt-grp^ell ],
 6869   soghash := "277ec0",
 6870   sig4hash := "RandomPointWithInf(grp^ell)" ),
 6871 rec(
 6872   kind := "FUNCTION",
 6873   name := "Point",
 6874   sin := [ [ elt-pls/fld^fun, "p" ], [ elt-grp^ell, "EC" ] ],
 6875   sou := [ [ elt-grp^ell, "P" ] ],
 6876   short := "Returns the point on EC corresponding to p.",
 6877   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nRandomPoint(EC);\n" ],
 6878   hash := "17c2d1",
 6879   sig := "Point(<elt-pls/fld^fun> p, <elt-grp^ell> EC)",
 6880   sog := " -> <elt-grp^ell> P",
 6881   docsrc := "elliptic.g",
 6882   sinflat := [ elt-pls/fld^fun, elt-grp^ell ],
 6883   souflat := [ elt-grp^ell ],
 6884   soghash := "277ec0",
 6885   sig4hash := "Point(elt-pls/fld^fun,elt-grp^ell)" ),
 6886 rec(
 6887   kind := "FUNCTION",
 6888   name := "EllipticFunctionField",
 6889   sin := [ [ grp^ell, "EC" ] ],
 6890   sou := [ [ fld^fun, "F" ] ],
 6891   short := "Returns the function field of genus one corresponding to EC.",
 6892   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nRandomPoint(EC);\n" ],
 6893   hash := "3ae997",
 6894   sig := "EllipticFunctionField(<grp^ell> EC)",
 6895   sog := " -> <fld^fun> F",
 6896   docsrc := "elliptic.g",
 6897   sinflat := [ grp^ell ],
 6898   souflat := [ fld^fun ],
 6899   soghash := "d1dc27",
 6900   sig4hash := "EllipticFunctionField(grp^ell)" ),
 6901 rec(
 6902   kind := "FUNCTION",
 6903   name := "ShortWeierstrassNormalForm",
 6904   sin := [ [ grp^ell, "EC" ] ],
 6905   sou := [ [ grp^ell, "EC2" ] ],
 6906   short := "Returns the isomorphic curve EC2 defined by a polynomial of the form y^2=x^3+a*x+b.",
 6907   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nRandomPoint(EC);\n" ],
 6908   hash := "454b97",
 6909   sig := "ShortWeierstrassNormalForm(<grp^ell> EC)",
 6910   sog := " -> <grp^ell> EC2",
 6911   docsrc := "elliptic.g",
 6912   sinflat := [ grp^ell ],
 6913   souflat := [ grp^ell ],
 6914   soghash := "82fd04",
 6915   sig4hash := "ShortWeierstrassNormalForm(grp^ell)" ),
 6916 rec(
 6917   kind := "FUNCTION",
 6918   name := "jInvariant",
 6919   sin := [ [ elt-grp^ell, "EC" ] ],
 6920   sou := [ [ elt-fld^fin, "j" ] ],
 6921   short := "Returns the j-invariant of EC.",
 6922   ex := [ "EC:= EllipticCurve(5,[1,2]);;\njInvariant(EC);\n" ],
 6923   hash := "2afd97",
 6924   sig := "jInvariant(<elt-grp^ell> EC)",
 6925   sog := " -> <elt-fld^fin> j",
 6926   docsrc := "elliptic.g",
 6927   sinflat := [ elt-grp^ell ],
 6928   souflat := [ elt-fld^fin ],
 6929   soghash := "97e752",
 6930   sig4hash := "jInvariant(elt-grp^ell)" ),
 6931 rec(
 6932   kind := "FUNCTION",
 6933   name := "Subgroup",
 6934   sin := [ [ elt-grp^ell, "EC" ] ],
 6935   sou := [ [ list, "L" ] ],
 6936   short := "Returns the subgroup generated by EC.",
 6937   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= RandomPoint(EC);;\nSubgroup(P);\n" ],
 6938   hash := "06161c",
 6939   sig := "Subgroup(<elt-grp^ell> EC)",
 6940   sog := " -> <list> L",
 6941   docsrc := "elliptic.g",
 6942   sinflat := [ elt-grp^ell ],
 6943   souflat := [ list ],
 6944   soghash := "38b62b",
 6945   sig4hash := "Subgroup(elt-grp^ell)" ),
 6946 rec(
 6947   kind := "FUNCTION",
 6948   name := "DiscreteLog",
 6949   sin := [ [ elt-grp^ell, "P" ], [ elt-grp^ell, "Q" ] ],
 6950   sou := [ [ elt-ord^rat, "n" ] ],
 6951   short := "Returns, if possible, n satisfying n*P = Q.",
 6952   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= Generator(EC)[1];;\nQ:= RandomPoint(EC);;\nDiscreteLog(P,Q);\n" ],
 6953   hash := "fc2dbf",
 6954   sig := "DiscreteLog(<elt-grp^ell> P, <elt-grp^ell> Q)",
 6955   sog := " -> <elt-ord^rat> n",
 6956   docsrc := "elliptic.g",
 6957   sinflat := [ elt-grp^ell, elt-grp^ell ],
 6958   souflat := [ elt-ord^rat ],
 6959   soghash := "898213",
 6960   sig4hash := "DiscreteLog(elt-grp^ell,elt-grp^ell)" ),
 6961 rec(
 6962   kind := "FUNCTION",
 6963   name := "Discriminant",
 6964   sin := [ [ grp^ell, "EC" ] ],
 6965   sou := [ [ elt-fld^fin, "d" ] ],
 6966   short := "The discriminant of EC.",
 6967   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nDiscriminant(EC);\n" ],
 6968   hash := "3836b4",
 6969   sig := "Discriminant(<grp^ell> EC)",
 6970   sog := " -> <elt-fld^fin> d",
 6971   docsrc := "elliptic.g",
 6972   sinflat := [ grp^ell ],
 6973   souflat := [ elt-fld^fin ],
 6974   soghash := "97e752",
 6975   sig4hash := "Discriminant(grp^ell)" ),
 6976 rec(
 6977   kind := "FUNCTION",
 6978   name := "Divisor",
 6979   sin := [ [ elt-grp^ell, "P" ] ],
 6980   sou := [ [ elt-dvs/fld^fun, "D" ] ],
 6981   short := "The divisor corresponding to P.",
 6982   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= RandomPoint(EC);;\nDivisor(P);" ],
 6983   hash := "16397d",
 6984   sig := "Divisor(<elt-grp^ell> P)",
 6985   sog := " -> <elt-dvs/fld^fun> D",
 6986   docsrc := "elliptic.g",
 6987   sinflat := [ elt-grp^ell ],
 6988   souflat := [ elt-dvs/fld^fun ],
 6989   soghash := "34cafb",
 6990   sig4hash := "Divisor(elt-grp^ell)" ),
 6991 rec(
 6992   kind := "FUNCTION",
 6993   name := "BaseRing",
 6994   sin := [ [ grp^ell, "EC" ] ],
 6995   sou := [ [ fld^fin, "F" ] ],
 6996   short := "The field over which EC is defined.",
 6997   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nF:= BaseRing(EC);;\n" ],
 6998   hash := "a5a791",
 6999   sig := "BaseRing(<grp^ell> EC)",
 7000   sog := " -> <fld^fin> F",
 7001   docsrc := "elliptic.g",
 7002   sinflat := [ grp^ell ],
 7003   souflat := [ fld^fin ],
 7004   soghash := "267be8",
 7005   sig4hash := "BaseRing(grp^ell)" ),
 7006 rec(
 7007   kind := "FUNCTION",
 7008   name := "Order",
 7009   sin := [ [ elt-grp^ell, "P" ] ],
 7010   sou := [ [ elt-ord^rat, "n" ] ],
 7011   short := "The order of the point P, only works for \"small\" curves. ",
 7012   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= RandomPoint(EC);;\nOrder(P);\n" ],
 7013   see := [  ],
 7014   hash := "8ee1cd",
 7015   sig := "Order(<elt-grp^ell> P)",
 7016   sog := " -> <elt-ord^rat> n",
 7017   docsrc := "elliptic.g",
 7018   sinflat := [ elt-grp^ell ],
 7019   souflat := [ elt-ord^rat ],
 7020   soghash := "898213",
 7021   sig4hash := "Order(elt-grp^ell)" ),
 7022 rec(
 7023   kind := "FUNCTION",
 7024   name := "Generator",
 7025   sin := [ [ grp^ell, "EC" ] ],
 7026   sou := [ [ list, "L" ] ],
 7027   short := "Returns a list of generator(s) of EC, only works for \"small\" curves. ",
 7028   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nL:= Generator(EC);\n" ],
 7029   see := [  ],
 7030   hash := "4af2c5",
 7031   sig := "Generator(<grp^ell> EC)",
 7032   sog := " -> <list> L",
 7033   docsrc := "elliptic.g",
 7034   sinflat := [ grp^ell ],
 7035   souflat := [ list ],
 7036   soghash := "38b62b",
 7037   sig4hash := "Generator(grp^ell)" ),
 7038 rec(
 7039   kind := "FUNCTION",
 7040   name := "Place",
 7041   sin := [ [ elt-grp^ell, "P" ] ],
 7042   sou := [ [ elt-pls/fld^fun, "p" ] ],
 7043   short := "The place of degree one corresponding to P ",
 7044   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= RandomPoint(EC);;\nPlace(P);\n" ],
 7045   see := [  ],
 7046   hash := "2a4d61",
 7047   sig := "Place(<elt-grp^ell> P)",
 7048   sog := " -> <elt-pls/fld^fun> p",
 7049   docsrc := "elliptic.g",
 7050   sinflat := [ elt-grp^ell ],
 7051   souflat := [ elt-pls/fld^fun ],
 7052   soghash := "3691ff",
 7053   sig4hash := "Place(elt-grp^ell)" ),
 7054 rec(
 7055   kind := "FUNCTION",
 7056   name := "Size",
 7057   sin := [ [ grp^ell, "P" ] ],
 7058   sou := [ [ elt-ord^rat, "n" ] ],
 7059   short := "The number of points belonging to EC, only works for \"small\" curves. ",
 7060   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nSize(EC);\n" ],
 7061   see := [  ],
 7062   hash := "f68093",
 7063   sig := "Size(<grp^ell> P)",
 7064   sog := " -> <elt-ord^rat> n",
 7065   docsrc := "elliptic.g",
 7066   sinflat := [ grp^ell ],
 7067   souflat := [ elt-ord^rat ],
 7068   soghash := "898213",
 7069   sig4hash := "Size(grp^ell)" ),
 7070 rec(
 7071   kind := "FUNCTION",
 7072   name := "Coerce",
 7073   sin := [ [ grp^ell, "EC" ], [ elt-grp^ell, "P" ] ],
 7074   sou := [ [ elt-grp^ell, "P2" ] ],
 7075   short := "Coerces P into EC. ",
 7076   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= RandomPoint(EC);\nCoerce(EllipticCurve(5^2,[1,2]),P);" ],
 7077   see := [  ],
 7078   hash := "65cacd",
 7079   sig := "Coerce(<grp^ell> EC, <elt-grp^ell> P)",
 7080   sog := " -> <elt-grp^ell> P2",
 7081   docsrc := "elliptic.g",
 7082   sinflat := [ grp^ell, elt-grp^ell ],
 7083   souflat := [ elt-grp^ell ],
 7084   soghash := "277ec0",
 7085   sig4hash := "Coerce(grp^ell,elt-grp^ell)" ),
 7086 rec(
 7087   kind := "FUNCTION",
 7088   name := "Coerce",
 7089   sin := [ [ grp^ell, "EC" ], [ list, "L" ] ],
 7090   sou := [ [ elt-grp^ell, "P" ] ],
 7091   short := "Coerces L into EC. ",
 7092   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= RandomPoint(EC);\nCoerce(EllipticCurve(5^2,[1,2]),P);" ],
 7093   see := [  ],
 7094   hash := "be3460",
 7095   sig := "Coerce(<grp^ell> EC, <list> L)",
 7096   sog := " -> <elt-grp^ell> P",
 7097   docsrc := "elliptic.g",
 7098   sinflat := [ grp^ell, list ],
 7099   souflat := [ elt-grp^ell ],
 7100   soghash := "277ec0",
 7101   sig4hash := "Coerce(grp^ell,list)" ),
 7102 rec(
 7103   kind := "FUNCTION",
 7104   name := "Zero",
 7105   sin := [ [ grp^ell, "EC" ] ],
 7106   sou := [ [ elt-grp^ell, "P" ] ],
 7107   short := "Returns the point at infinity. ",
 7108   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= Zero(EC);\n" ],
 7109   see := [  ],
 7110   hash := "60e26c",
 7111   sig := "Zero(<grp^ell> EC)",
 7112   sog := " -> <elt-grp^ell> P",
 7113   docsrc := "elliptic.g",
 7114   sinflat := [ grp^ell ],
 7115   souflat := [ elt-grp^ell ],
 7116   soghash := "277ec0",
 7117   sig4hash := "Zero(grp^ell)" ),
 7118 rec(
 7119   kind := "FUNCTION",
 7120   name := "Parent",
 7121   sin := [ [ elt-grp^ell, "P" ] ],
 7122   sou := [ [ grp^ell, "EC" ] ],
 7123   short := "The default parent of P ",
 7124   ex := [ "EC:= EllipticCurve(5,[1,2]);;\nP:= RandomPoint(EC);;\nParent(P)=EC;\n" ],
 7125   see := [  ],
 7126   hash := "566c1e",
 7127   sig := "Parent(<elt-grp^ell> P)",
 7128   sog := " -> <grp^ell> EC",
 7129   docsrc := "elliptic.g",
 7130   sinflat := [ elt-grp^ell ],
 7131   souflat := [ grp^ell ],
 7132   soghash := "82fd04",
 7133   sig4hash := "Parent(elt-grp^ell)" ),
 7134 rec(
 7135   kind := "KEYWORD",
 7136   name := "Algebraic Structures",
 7137   short := "In this section we show how to generate matrices, modules or groups.",
 7138   see := [ "fcb739", "f8c01e", "9eede6" ],
 7139   ex := [  ],
 7140   hash := "22d77a",
 7141   sig := "Algebraic Structures",
 7142   sog := "",
 7143   docsrc := "install_doc/algstruc.g",
 7144   soghash := "da39a3",
 7145   sig4hash := "Algebraic Structures" ),
 7146 rec(
 7147   kind := "KEYWORD",
 7148   name := "Linear Algebra",
 7149   short := "",
 7150   see := [ "cff7d0" ],
 7151   ex := [  ],
 7152   hash := "fcb739",
 7153   sig := "Linear Algebra",
 7154   sog := "",
 7155   docsrc := "install_doc/algstruc.g",
 7156   soghash := "da39a3",
 7157   sig4hash := "Linear Algebra" ),
 7158 rec(
 7159   kind := "KEYWORD",
 7160   name := "Matrices",
 7161   short := "To construct a matrix first we need a ring from which are the   coefficients. For example Q,R and C are predefined for the      rational, real  and complex numbers. We can also build matrices over function or number fields. Then we need also the number of rows and columns and finitely a list consisting of the entries.We can compute the kernel N of a matrix M (as a matrix which islinear map in the kernel of M) or the Nullspace of N.",
 7162   ex := [ "k   := RationalFunctionField(FiniteField(5,2));\nP   := PolynomialAlgebra(k);\nF   := FunctionField(P.1^3 + k.1^3 + k.1 + 1);\nM   := Matrix(F, 2,2, [ F.1+k.1, 2, F.1+k.1,2]);\n", "N   := Matrix(Q, 2,3, [1,2,3,5,0,1]);\nKernelMatrix(N);\nw   := KernelMatrix(Transpose(N));\nN*Transpose(w);\nv   := Transpose(Matrix(Q, 3,1, [1,2,3]));\nSolution(N,v);\n", "T   := Matrix(Q, 2,2,[1,2,1,2]);\nKernelMatrix(T);\n" ],
 7163   hash := "cff7d0",
 7164   sig := "Matrices",
 7165   sog := "",
 7166   docsrc := "install_doc/algstruc.g",
 7167   soghash := "da39a3",
 7168   sig4hash := "Matrices" ),
 7169 rec(
 7170   kind := "KEYWORD",
 7171   name := "Abelian Groups",
 7172   short := "In KASH3 we can work with  abelian and symmetric groups. We can for example generate abelian groups and compute the direct sum. For elements of a symmetric group we can make use of cycles.",
 7173   ex := [ "G   := AbelianGroup([2,3,3]);\nH   := AbelianGroup([5,3,3,7]);\nGH  := DirectSum(H,G);\nFG1 := FreeAbelianGroup(3);\nFG2 := FreeAbelianGroup(5);\nG1G2:= DirectSum(FG1,FG2);\n" ],
 7174   hash := "f8c01e",
 7175   sig := "Abelian Groups",
 7176   sog := "",
 7177   docsrc := "install_doc/algstruc.g",
 7178   soghash := "da39a3",
 7179   sig4hash := "Abelian Groups" ),
 7180 rec(
 7181   kind := "KEYWORD",
 7182   name := "Modules and Lattices",
 7183   short := "In KASH3 we can construct for example modules in number fields over orders. Lattices are represented as matrices. We can compute the Gram matrix and a LLL-reduced basis of a lattice.",
 7184   ex := [ "o2 := MaximalOrder(X^2-2);\nPo2:= PolynomialAlgebra(o2);\nO  := EquationOrder(Po2.1^3-3);\nM  := Module(O);\nN  := Matrix(Q,3,3,[1/2,3,2,3,0,1,2,9/2,2]);\nG  := GramMatrix(N);LLL(N);" ],
 7185   hash := "9eede6",
 7186   sig := "Modules and Lattices",
 7187   sog := "",
 7188   docsrc := "install_doc/algstruc.g",
 7189   soghash := "da39a3",
 7190   sig4hash := "Modules and Lattices" ),
 7191 rec(
 7192   kind := "KEYWORD",
 7193   name := "Preface",
 7194   short := "This is the current release of KANT, the KANT SHell. The quasi-acronym KANT stands for Computational Algebraic Number Theory with a slight twist hinting at its German origin.  ",
 7195   see := [ "79fde2", "90ccd6", "76ce42", "bdc1fd", "a420ab" ],
 7196   ex := [  ],
 7197   hash := "707dde",
 7198   sig := "Preface",
 7199   sog := "",
 7200   docsrc := "install_doc/intro.g",
 7201   soghash := "da39a3",
 7202   sig4hash := "Preface" ),
 7203 rec(
 7204   kind := "KEYWORD",
 7205   name := "Functionality",
 7206   short := "KANT is a program library for computations in algebraic number fields, algebraic function fields and local fields.  In the number field case, algebraic integers are considered to be elements of a specified order of an appropriate field F.  The available algorithms provide the user with the means to compute many invariants of F. It is possible to solve tasks like calculating the solutions of Diophantine equations related to F.  Furthermore subfields of F can be generated and F can be embedded into an overfield.  The potential of moving elements between different fields (orders) is a significant feature of our system. In the function field case, for example, genus computations and the construction of Riemann-Roch spaces are available. ",
 7207   ex := [  ],
 7208   hash := "79fde2",
 7209   sig := "Functionality",
 7210   sog := "",
 7211   docsrc := "install_doc/intro.g",
 7212   soghash := "da39a3",
 7213   sig4hash := "Functionality" ),
 7214 rec(
 7215   kind := "KEYWORD",
 7216   name := "History",
 7217   short := "KANT was developed at the University of Duesseldorf from 1987 until 1993 and at Technische Universitaet Berlin afterwards.  During these years the performance of existing algorithms and their implementations grew dramatically. While calculations in number fields of degree 4 and greater were nearly impossible before 1970 and number fields of degree more than 10 were beyond reach until 1990, it is now possible to compute in number fields of degree well over 20, and -- in special cases -- even beyond 1000. This also characterizes one of the principles of KANT, namely to support computations in number fields of arbitrary degree rather than fixing the degree and pushing the size of the discriminant to the limit. ",
 7218   ex := [  ],
 7219   hash := "90ccd6",
 7220   sig := "History",
 7221   sog := "",
 7222   docsrc := "install_doc/intro.g",
 7223   soghash := "da39a3",
 7224   sig4hash := "History" ),
 7225 rec(
 7226   kind := "KEYWORD",
 7227   name := "KANT",
 7228   short := "KANT consists of a C--library of thousands of functions for doing arithmetic in number fields, function fields, and local fields.  Of course, the necessary auxiliaries from linear algebra over rings, especially lattices, are also included. The set of these functions is based on the core of the computer algebra system MAGMA from which we adopt our storage management, base arithmetic, arithmetic for finite fields, polynomial arithmetic and a variety of other tools.  ",
 7229   ex := [  ],
 7230   hash := "76ce42",
 7231   sig := "KANT",
 7232   sog := "",
 7233   docsrc := "install_doc/intro.g",
 7234   soghash := "da39a3",
 7235   sig4hash := "KANT" ),
 7236 rec(
 7237   kind := "KEYWORD",
 7238   name := "Shell",
 7239   short := "To make KANT easier to use we developed a shell called KASH. This shell is based on that of the group theory package GAP3 and the handling is similar to that of MAPLE.  We put great effort into enabling the user to handle the number theoretical objects in the very same way as one would do using pencil and paper. For example, there is just one command Factorization for the factorization of elements from a factorial monoid like rational integers in Z, polynomials over a field, or ideals from a Dedekind ring.",
 7240   ex := [  ],
 7241   hash := "bdc1fd",
 7242   sig := "Shell",
 7243   sog := "",
 7244   docsrc := "install_doc/intro.g",
 7245   soghash := "da39a3",
 7246   sig4hash := "Shell" ),
 7247 rec(
 7248   kind := "KEYWORD",
 7249   name := "Programming Language",
 7250   short := "KASH3 uses the GAP3 shell as a user interface.  The programming language of GAP3 is an imperative language with some functional and some object oriented features.  In KASH3 additional features like Methods, Maps, and Extendable Objects are available.  The following describes the imperative control structures of the GAP3/KASH3 programming language.\n\nBy convention the names of KASH3 functions, which change the arguments (in the GAP3/KASH3 programming language all complex data structures are passed to functions by reference), end in '_'.",
 7251   see := [ "958f57", "6517f8", "c0ac48", "43eef9", "c218e3", "63143b", "04d6e2" ],
 7252   ex := [  ],
 7253   hash := "749950",
 7254   sig := "Programming Language",
 7255   sog := "",
 7256   docsrc := "install_doc/intro.g",
 7257   soghash := "da39a3",
 7258   sig4hash := "Programming Language" ),
 7259 rec(
 7260   kind := "KEYWORD",
 7261   name := "Inside KASH3",
 7262   short := "KASH3 contains several advanced features that facilitate extending its functionality.  Some of these come from the GAP3 programming language, in particular the overloading of operators using records.  Extendable objects are also build on records.  They allow storing additional  information in objects on the shell level.  Together with the type system this also allows inheritance of functionality to objects of new types.  The type system also makes it possible to overload functions ('InstallMethods').  Overloading and the type system are tied in with the help system.",
 7263   see := [ "93b9e2", "74e8bb", "d691ad", "80071c", "9e9cf3", "7e4ac6" ],
 7264   ex := [  ],
 7265   hash := "e854e6",
 7266   sig := "Inside KASH3",
 7267   sog := "",
 7268   docsrc := "install_doc/intro.g",
 7269   soghash := "da39a3",
 7270   sig4hash := "Inside KASH3" ),
 7271 rec(
 7272   kind := "KEYWORD",
 7273   name := "Generic Functions",
 7274   short := "Some functions are implemented for a variety of structures. A few of them are not documented for all possible signatures. You find the most important of those listed below.",
 7275   see := [ "8f26c3", "b27abc", "21391a", "9b3d76", "47a76e", "bb3c97", "cc360c", "3fac1b" ],
 7276   ex := [  ],
 7277   hash := "83082f",
 7278   sig := "Generic Functions",
 7279   sog := "",
 7280   docsrc := "install_doc/intro.g",
 7281   soghash := "da39a3",
 7282   sig4hash := "Generic Functions" ),
 7283 rec(
 7284   kind := "KEYWORD",
 7285   name := "Methods",
 7286   short := "Methods allow overloading of functions. A method is installed by calling 'InstallMethod' with a documentation record and a function.  The documentation record specifies the name and the signature under which the given function will be called.",
 7287   see := [ "cfb542" ],
 7288   ex := [  ],
 7289   hash := "7e4ac6",
 7290   sig := "Methods",
 7291   sog := "",
 7292   docsrc := "install_doc/intro.g",
 7293   soghash := "da39a3",
 7294   sig4hash := "Methods" ),
 7295 rec(
 7296   kind := "KEYWORD",
 7297   name := "Introduction to KASH3",
 7298   short := "",
 7299   see := [ "707dde", "010b85", "a26b37", "08ba89", "e854e6", "4c47dd" ],
 7300   ex := [  ],
 7301   hash := "79731e",
 7302   sig := "Introduction to KASH3",
 7303   sog := "",
 7304   docsrc := "install_doc/intro.g",
 7305   soghash := "da39a3",
 7306   sig4hash := "Introduction to KASH3" ),
 7307 rec(
 7308   kind := "KEYWORD",
 7309   name := "Getting Started",
 7310   short := "The following gives a short introduction to KASH3.  We explain the basic types supported by KASH3 and how to effectively use them. As the main points of the KASH3 shell are given in conjunction with the type specific information, special attention should be paid to the examples.",
 7311   see := [ "b520c7", "058bfd", "2582ff", "842b64", "a1fdaa", "58ab0e", "8d5179", "6e06f6", "57c950", "0d5fda", "b5fb63", "538a8c", "c92634", "cff7d0" ],
 7312   ex := [  ],
 7313   hash := "010b85",
 7314   sig := "Getting Started",
 7315   sog := "",
 7316   docsrc := "install_doc/start.g",
 7317   soghash := "da39a3",
 7318   sig4hash := "Getting Started" ),
 7319 rec(
 7320   kind := "KEYWORD",
 7321   name := "Starting and Leaving",
 7322   short := "If KASH3 is correctly installed, then you start KASH3 by simply typing 'kash3' at the prompt of your operating system. If you are successful in starting KASH3, the KASH3 banner should appear, at which time a command or function call may be entered.  To exit KASH3 type 'quit;' at the prompt (the semicolon is necessary!). ",
 7323   ex := [ "quit;" ],
 7324   hash := "b520c7",
 7325   sig := "Starting and Leaving",
 7326   sog := "",
 7327   docsrc := "install_doc/start.g",
 7328   soghash := "da39a3",
 7329   sig4hash := "Starting and Leaving" ),
 7330 rec(
 7331   kind := "KEYWORD",
 7332   name := "First Steps",
 7333   short := "A simple calculation with KASH3 is as easy as one can imagine.  You type the problem just after the prompt, terminate it with a semicolon and then pass the problem to the program with the 'return' key. For example, to multiply the difference between 9 and 7 by the sum of 5 and 6, that is to calculate '(9 - 7)*(5 + 6)', you type exactly this last sequence of symbols followed by ';' and 'return'. If you omitted the semicolon at the end of the line but had already typed 'return', then KASH3 has read everything you typed, but does not know that the command is complete.  The program is waiting for further input and indicates this with a partial prompt. This little problem is solved by simply typing the missing semicolon on the next line of input.  Then the result is printed and the normal prompt returns. Whenever you see this partial prompt and you cannot decide what KASH3 is still waiting for, then you have to type semicolons until the normal prompt returns.",
 7334   ex := [ "(9 - 7) * (5 + 6);" ],
 7335   hash := "058bfd",
 7336   sig := "First Steps",
 7337   sog := "",
 7338   docsrc := "install_doc/start.g",
 7339   soghash := "da39a3",
 7340   sig4hash := "First Steps" ),
 7341 rec(
 7342   kind := "KEYWORD",
 7343   name := "Inline Help",
 7344   short := "For inline help, '?' is a valuable tool.  A single question mark followed by the name of a function or type or statement or keyword causes the description of the identifier found in the reference manual to appear on the screen.  If a list of all functions beginning with a particular string is desired, use '?^' followed by the string to match.  If no match is found, the response 'No matches. Maybe try ?*<string>.' will be displayed.  '?*' followed by something searches for all of its occurences in the documentation. \n\nA query can also be started by ending a line with '?' and its modifier instead of starting it with '?'. In both cases the function 'Help' with the entered line (without the ?) as a parameter.",
 7345   ex := [  ],
 7346   hash := "2582ff",
 7347   sig := "Inline Help",
 7348   sog := "",
 7349   docsrc := "install_doc/start.g",
 7350   soghash := "da39a3",
 7351   sig4hash := "Inline Help" ),
 7352 rec(
 7353   kind := "KEYWORD",
 7354   name := "Operations",
 7355   short := "In an expression like '(9 - 7) * (5 + 6)' the constants '5', '6', '7', and '9' are being composed by the operators  '+', '*' and '-' to result in a new value. \n\nThere are three kinds of operators in KASH3, arithmetical operators, comparison operators, and logical operators.KASH3  knows a  precedence  between operators that may be overridden by parentheses. \n\nYou have already seen that it is possible to form the sums, differences, and products. The remaining arithmetical operators are exponentiation '^' and 'mod'.\n\nA comparison result is a boolean value. Integers, rationals and real numbers are comparable via '=', '<', '<=', '>=', '>' and '<>'; algebraic elements, ideals, matrices and complex numbers can be compared via '=' and '<>'.  Membership of an element in a structure can be tested eith 'in'.\n\nThe boolean values 'TRUE' and 'FALSE' can be manipulated via logical operators, i.e., the unary operator 'not' and the binary operators 'and' and 'or'.",
 7356   ex := [ "12345/25;", "7^69;" ],
 7357   hash := "a1fdaa",
 7358   sig := "Operations",
 7359   sog := "",
 7360   docsrc := "install_doc/start.g",
 7361   soghash := "da39a3",
 7362   sig4hash := "Operations" ),
 7363 rec(
 7364   kind := "KEYWORD",
 7365   name := "Variables and Assignments",
 7366   short := "Values may be assigned to variables.  A variable enables you to refer to an object via a name.  The assignment operator is ':='. Do not confuse the assignment operator ':=' with the single equality sign '=' which in KASH3 is only used for the test of equality.\nAfter an  assignment, the assigned value is echoed on the next  line. The printing of the value of  a statement  may be in every case prevented by typing a double semicolon. \nAfter the assignment, the variable evaluates to that value if evaluated. Thus it is possible to refer to that value by the name of the variable in any situation. \nA variable name may be sequences of letters and digits containing at least one letter.  For example 'abc' and 'a1b2' are valid names. Since KASH3 distinguishes upper and lower case, 'a' and 'A' are different  names.  Keywords such as 'quit' must not be used as names.",
 7367   ex := [ "a:=32233; A:=76; a+A;" ],
 7368   hash := "58ab0e",
 7369   sig := "Variables and Assignments",
 7370   sog := "",
 7371   docsrc := "install_doc/start.g",
 7372   soghash := "da39a3",
 7373   sig4hash := "Variables and Assignments" ),
 7374 rec(
 7375   kind := "KEYWORD",
 7376   name := "Integers and Rationals",
 7377   short := "KASH3 integers are entered as a sequence of digits optionally preceded by a '+' sign for positive integers or a '-' sign for negative integers. In KASH3, the size of integers is only limited by the amount of available memory. The binary operations '+', '-', '*', '/' allow combinations of arguments from the integers, the rationals, and real and complex fields; automatic coercion is applied where necessary. \n\nSince integers are naturally embedded in the field of real numbers, all real functions are applicable to integers.\nRationals can be created by simply typing in the fraction using the symbol '/' to denote the division bar. The value is not converted to decimal form, however the reduced form of the fraction is found. Similarly all real functions are applicable to rationals.",
 7378   ex := [ "4/6;" ],
 7379   hash := "8d5179",
 7380   sig := "Integers and Rationals",
 7381   sog := "",
 7382   docsrc := "install_doc/start.g",
 7383   soghash := "da39a3",
 7384   sig4hash := "Integers and Rationals" ),
 7385 rec(
 7386   kind := "KEYWORD",
 7387   name := "Reals and Complex",
 7388   short := "Real numbers can only be stored in the computer effectively in the form of approximations. KASH3 provides a number of facilities for calculating with such approximations to (at least) a given, but arbitrary, precision.  Real numbers have a default precision of 20. One can change the precision to arbitrary 'n' (See example below!).\nKASH3 provides the following real functions; refer to the reference manual for detailed descriptions and examples. \nIn KASH3, complex numbers have the same precision as real numbers. This precision can be modified by calling the 'Precision' function (see example). A complex number can be designated using the function Element, which requires two real arguments (See example).\nMost real functions can be applied to complex numbers. Additionally, KASH3 provides the several complex functions.",
 7389   ex := [ "Precision();   # the default precision of the real and complex numbers", "R;             # the default real field", "Precision(40); # set the default precision of real and complex numbers to 40", "C;             # the default complex field", "z := 1+2*I;    # a complex number,\nz*z;           " ],
 7390   hash := "6e06f6",
 7391   sig := "Reals and Complex",
 7392   sog := "",
 7393   docsrc := "install_doc/start.g",
 7394   soghash := "da39a3",
 7395   sig4hash := "Reals and Complex" ),
 7396 rec(
 7397   kind := "KEYWORD",
 7398   name := "Lists",
 7399   short := "A 'list' is a collection of objects separated by commas and enclosed in brackets.",
 7400   ex := [ "primes:= [2, 3, 5, 7, 11, 13, 17, 19];  # a list containing 8 elements\nAppend_(primes, [23, 29]); # append two numbers to the list\nprimes[5]; # the 5th element in the list\nprimes[9] := 77; # set the 9th list entry to 77\n", "L := [1,2,TRUE,3/4, X^2+2]; # a list of elements of different types" ],
 7401   see := [ "ec51e2", "ab7b5e", "f55fdd", "59fe3e" ],
 7402   hash := "57c950",
 7403   sig := "Lists",
 7404   sog := "",
 7405   docsrc := "install_doc/start.g",
 7406   soghash := "da39a3",
 7407   sig4hash := "Lists" ),
 7408 rec(
 7409   kind := "KEYWORD",
 7410   name := "Ranges",
 7411   short := "A range is a finite sequence of integers which is another special kind of list.  A range is described by its minimum (the first entry), its second entry and its maximum, separated by a comma resp. two dots and enclosed in brackets.  In the usual case of an ascending list of consecutive integers the second entry may be omitted. ",
 7412   ex := [ "L := [1..100]; # list of all positive integers less than or equal to 100", "L := [2,4..100]; # list of all even integers between 2 and 100" ],
 7413   hash := "0d5fda",
 7414   sig := "Ranges",
 7415   sog := "",
 7416   docsrc := "install_doc/start.g",
 7417   soghash := "da39a3",
 7418   sig4hash := "Ranges" ),
 7419 rec(
 7420   kind := "KEYWORD",
 7421   name := "Sequences",
 7422   short := "A sequence is a list containing elements from the same 'universe'. Writing different types in a sequence is not allowed.",
 7423   ex := [ "Sequence([1,5,7]); # List of integers 1,5 and 7", "Sequence([1,Q]); # not a sequence" ],
 7424   hash := "b5fb63",
 7425   sig := "Sequences",
 7426   sog := "",
 7427   docsrc := "install_doc/start.g",
 7428   soghash := "da39a3",
 7429   sig4hash := "Sequences" ),
 7430 rec(
 7431   kind := "KEYWORD",
 7432   name := "Tuples",
 7433   short := "A tuple is a list containing any elements.  A tuple is an element of a Cartesian product. The types of the elements of the factors of this product may be specified. Once a tuple is created, insertions are possible only if the type of the new element is the same as the type of the element that will be replaced.",
 7434   ex := [ "x_a:=Tuple([1,3.2,\"text\"]);\nType(x_a);\nParent(x_a);" ],
 7435   hash := "538a8c",
 7436   sig := "Tuples",
 7437   sog := "",
 7438   docsrc := "install_doc/start.g",
 7439   soghash := "da39a3",
 7440   sig4hash := "Tuples" ),
 7441 rec(
 7442   kind := "KEYWORD",
 7443   name := "Generators",
 7444   short := "The generators of many of the structures can be accessed with the '.' operator.  In most cases the respective elements are also printed in this representation.",
 7445   ex := [ "x_a := FreeAbelianGroup(3);\nElement(x_a,[1,2,3]);\nx_a.2;" ],
 7446   hash := "a3e705",
 7447   sig := "Generators",
 7448   sog := "",
 7449   docsrc := "install_doc/start.g",
 7450   soghash := "da39a3",
 7451   sig4hash := "Generators" ),
 7452 rec(
 7453   kind := "KEYWORD",
 7454   name := "Polynomials",
 7455   short := "At the moment, KASH3 can only handle univariate polynomials. The polynomial ring 'ZX' over the integers and its indeterminate 'X=ZX.1' are predefined constants.  Use the 'Evaluation' routine to calculate the value of a polynomial when the variable 'X' is substituted by certain values.  To create the polynomial algebra 'S[x]' with coefficients from a designated ring 'S', the routine 'PolynomialAlgebra' should be used. This routine requires one argument, namely the coefficient ring of the polynomial algebra.\n Recall that 'Q' is the predefined constant for the ring .\nNote that KASH3 always declares the variable by 'P.1', if 'P' is the name of your polynomial algebra.",
 7456   ex := [ "f := X^3 + X + 1; # a polynomial over Z\nf+f;\nf*f;\n Evaluate(f,10); # Evaluation of f at 10", "Qx := PolynomialAlgebra(Q); # Univariate Polynomial Ring over Rational Field\nQx.1^5+7/3; # A polynomial over Q" ],
 7457   hash := "c92634",
 7458   sig := "Polynomials",
 7459   sog := "",
 7460   docsrc := "install_doc/start.g",
 7461   soghash := "da39a3",
 7462   sig4hash := "Polynomials" ),
 7463 rec(
 7464   kind := "KEYWORD",
 7465   name := "Introduction to Number Fields",
 7466   short := "This section describes the central part of KASH3.  After learning how to do simple arithmetic in algebraic number fields using KASH3, you will be able to compute the main invariants of algebraic number fields.",
 7467   see := [ "a26b37", "ab46c5", "afac3c", "ead637", "65d8e9" ],
 7468   ex := [  ],
 7469   hash := "ed35c2",
 7470   sig := "Introduction to Number Fields",
 7471   sog := "",
 7472   docsrc := "install_doc/number_field.g",
 7473   soghash := "da39a3",
 7474   sig4hash := "Introduction to Number Fields" ),
 7475 rec(
 7476   kind := "KEYWORD",
 7477   name := "Number Fields",
 7478   short := "We call 'alpha in C' an algebraic integer if there exists a monic irreducible polynomial 'f(x) in Z[x]' with 'f(alpha) = 0'. An algebraic number field 'F' is a finite extension of the field of rationals 'Q'. There always exists an algebraic integer 'rho in C' such that 'F = Q(rho)'. The set of algebraic integers in 'F' forms a ring which is denoted by 'O = O_F'. An order 'o' in 'F' is a unital subring of 'O' which, as a 'Z-module', is finitely generated and of rank '[F:Q]'. Of course, 'O' is an order which we call the maximal order of 'F' (see Orders of Number Fields for details).  In KASH3, any computations in an algebraic number field 'F' are performed with respect to a certain order in 'F'.",
 7479   ex := [ "f := X^5 + 4*X^4 - 56*X^2 -16*X + 192;\n# we want to do arithmetic in the field F = Q(rho),\n# where 'rho' is a root of irreducible polynomial f\no := EquationOrder(f);\n # Define the ring Z[x]/(f(x))" ],
 7480   see := [ "8bd6eb", "f49308", "1cd502" ],
 7481   hash := "a26b37",
 7482   sig := "Number Fields",
 7483   sog := "",
 7484   docsrc := "install_doc/number_field.g",
 7485   soghash := "da39a3",
 7486   sig4hash := "Number Fields" ),
 7487 rec(
 7488   kind := "KEYWORD",
 7489   name := "Orders of Number Fields",
 7490   short := "KASH3 makes it easy to compute in arbitrary orders of number fields.  Given the minimal polynomial 'f' of an algebraic integer 'rho' one obtains the equation order 'Z[rho]' easily as 'Z[x]/(rho)'. In order to compute a maximal order 'O' of the number field 'F=Q(rho)', one has  to compute an integral bases of 'F'. Maximal orders are  not given by polynomials but a transformation matrix, which transforms a power basis '(1,rho,...,rho^4)' to a basis '(w_1,...,w_5)' of the maximal order.  The 'MaximalOrder' function computes an integral basis '(w_1,...,w_5)'. Using the 'Element' function one can enter algebraic numbers with respect to this basis.",
 7491   ex := [ "f := X^5 + 4*X^4 - 56*X^2 -16*X + 192;\no := EquationOrder(f);\nO := MaximalOrder(o); # maximal order of 'o'\nw1 := Element(O,[1,0,0,0,0]);\nw2 := Element(O,[0,1,0,0,0]);\nw3 := Element(O,[0,0,1,0,0]);\nw4 := Element(O,[0,0,0,1,0]);\nw5 := Element(O,[0,0,0,0,1]);\n" ],
 7492   hash := "ab46c5",
 7493   sig := "Orders of Number Fields",
 7494   sog := "",
 7495   docsrc := "install_doc/number_field.g",
 7496   soghash := "da39a3",
 7497   sig4hash := "Orders of Number Fields" ),
 7498 rec(
 7499   kind := "KEYWORD",
 7500   name := "Unit Groups",
 7501   short := "KASH3 provides several functions dealing with the units of an order. In order to compute a system of fundamental units the 'UnitGroup' function should be used.  It returns the unit group as a finitely generated abelian group and a map from this abelian group to the order.The function 'TorsionUnitGroup' returns the torsion subgroup of the unit group",
 7502   ex := [ "f := X^5 + 4*X^4 - 56*X^2 -16*X + 192;o := EquationOrder(f);\nO := MaximalOrder(o);\nU := UnitGroup(O);\nApply(x->U.ext1(x),List(Generators(U))); " ],
 7503   hash := "afac3c",
 7504   sig := "Unit Groups",
 7505   sog := "",
 7506   docsrc := "install_doc/number_field.g",
 7507   soghash := "da39a3",
 7508   sig4hash := "Unit Groups" ),
 7509 rec(
 7510   kind := "KEYWORD",
 7511   name := "Ideals",
 7512   short := "In KASH3 an ideal is an object which is, like an algebraic number, defined over a certain order. There are many ways to create an ideal in KASH3. The most basic one is to use the function 'Ideal'. The sum and the difference of two ideals are the smallest ideals which contain both operands. The product of two ideals is the ideal formed by all products of an element of the first ideal with an element of the second one. KASH3 can also handle fractional ideals (a fractional ideal is an integral ideal divided by a certain non--zero integer). This feature allows ideals to be inverted if the underlying order is the maximal one (remember that in a Dedekind ring the fractional ideals form a group under multiplication).",
 7513   ex := [  ],
 7514   hash := "ead637",
 7515   sig := "Ideals",
 7516   sog := "",
 7517   docsrc := "install_doc/number_field.g",
 7518   soghash := "da39a3",
 7519   sig4hash := "Ideals" ),
 7520 rec(
 7521   kind := "KEYWORD",
 7522   name := "Class Groups",
 7523   short := "The task of computing the ideal class group is solved by invoking the 'ClassGroup' function.  As a result an abelian group 'G' that the class group is isomorphic to,  extended the by the map from 'G' into the set of Ideals in 'O'. Using the 'ClassGroupCyclicFactorGenerators' routine one can obtain a list of ideals representing generators of the cyclic factors of ideal class group. Notice  that you must first compute the class group before you can use the 'ClassGroupCyclicFactorGenerators' routine.\n The Minkowski bound is used to compute a class group in KASH3. This bound always guarantees correct results. However, when the field discriminant is 'large', the Minkowski bound causes very time consuming computations requiring a large amount of memory.  You can pass a smaller bound to the 'OrderClassGroup' function calling it with optional arguments.",
 7524   ex := [ "f := X^5 + 4*X^4 - 56*X^2 -16*X + 192;\no := EquationOrder(f);\nO := MaximalOrder(o);\nCl := ClassGroup(O);\n" ],
 7525   hash := "65d8e9",
 7526   sig := "Class Groups",
 7527   sog := "",
 7528   docsrc := "install_doc/number_field.g",
 7529   soghash := "da39a3",
 7530   sig4hash := "Class Groups" ),
 7531 rec(
 7532   kind := "KEYWORD",
 7533   name := "Global Function Fields",
 7534   short := "In this section the basic steps necessary for the creation of an algebraic function field and for doing simple operations are explained. The concepts are quite similar to the algebraic number field case, so you may also have a look at the first sections dealing with algebraic number fields.",
 7535   see := [ "08ba89", "54eb9f", "51a70b" ],
 7536   ex := [  ],
 7537   hash := "9b982b",
 7538   sig := "Global Function Fields",
 7539   sog := "",
 7540   docsrc := "install_doc/function_field.g",
 7541   soghash := "da39a3",
 7542   sig4hash := "Global Function Fields" ),
 7543 rec(
 7544   kind := "KEYWORD",
 7545   name := "Function Fields",
 7546   short := "In KASH3, creation of an algebraic  function field begins with choosing a bivariate polynomial 'f' over 'k', which is separable and monic in the second variable, such that 'f(T,y) = 0'. For this there have to be defined the field 'k', the polynomial rings 'k[T]' and 'k[T][y]', respectively (see example). It is afterwards  possible to define an algebraic function field. We test first whether the bivariate polynomial is irreducible and separable in the second variable. Then as a first application, one can compute the genus of the function field by calling 'Genus' function.",
 7547   ex := [ "k := FiniteField(25);\nkT := RationalFunctionField(k);\nkTy := PolynomialAlgebra(kT);\nT := kT.1;; y := kTy.1;;\nf := y^3 + T^4 + 1;\nK := FunctionField(f);\nGenus(K);" ],
 7548   hash := "08ba89",
 7549   sig := "Function Fields",
 7550   sog := "",
 7551   docsrc := "install_doc/function_field.g",
 7552   soghash := "da39a3",
 7553   sig4hash := "Function Fields" ),
 7554 rec(
 7555   kind := "KEYWORD",
 7556   name := "Finite and Infinite Maximal Orders",
 7557   short := "According to their coefficient rings 'k[T]' or 'O at infinity'  orders are called finite or infinite. By an equation order (or coordinate ring) over 'k[T]' we mean the quotient ring 'k[T][y] / f(T,y)k[T][y]'. Equation orders over 'O at infinity' are defined analogously for suitable, field generating polynomials (See examples for different orders).\nOne can define elements of orders by calling 'Element'. Since the orders have bases, it is enough to specify coefficients of linear combinations of the basis elements (see example). Afterwards one can perform the operations with these elements as usual.\nUsually one wants to work with the maximal orders since only these are Dedekind rings. For convenience there is a function which expects the defining polynomial and which first checks for irreducibility and separability and defines then the algebraic function field 'F' and the maximal orders 'o' and 'oi' (see example below).",
 7558   ex := [ "ff := FiniteField(5);\nfx := FunctionField(ff);\nfxy := PolynomialAlgebra(fx);\nF := FunctionField(fxy.1^3+fx.1^4+1);\no:=MaximalOrderFinite(F);\noi:=MaximalOrderInfinite(F);\na:=Element(o,[0,1,0]); b:=Element(oi,[0,1/fx.1,1/fx.1^2+1]);\na^3+fx.1^4+1;\na+b;\nCoerce(o,a);" ],
 7559   hash := "54eb9f",
 7560   sig := "Finite and Infinite Maximal Orders",
 7561   sog := "",
 7562   docsrc := "install_doc/function_field.g",
 7563   soghash := "da39a3",
 7564   sig4hash := "Finite and Infinite Maximal Orders" ),
 7565 rec(
 7566   kind := "KEYWORD",
 7567   name := "Ideals and Divisors",
 7568   short := "There are two representations for ideals, first by two generating elements and second by a module basis over the coefficient ring of the order. Multiplicative arithmetic is supported and you may also take the sum of two ideals, which is the same as to compute the gcd of these ideals.",
 7569   ex := [  ],
 7570   hash := "51a70b",
 7571   sig := "Ideals and Divisors",
 7572   sog := "",
 7573   docsrc := "install_doc/function_field.g",
 7574   soghash := "da39a3",
 7575   sig4hash := "Ideals and Divisors" ),
 7576 rec(
 7577   kind := "KEYWORD",
 7578   name := "Outside KASH3",
 7579   short := "KASH3 supports sophisticated access function to the world outside of KASH.  We will discuss input/output functions to access the file system and the system environment as well as functions to access the QaoS databases.\nFurthermore, for historical reasons we provide a so called GAP compatibility mode.",
 7580   see := [ "6ce6c5", "bc0792", "61074f", "7d5323" ],
 7581   ex := [  ],
 7582   hash := "4c47dd",
 7583   sig := "Outside KASH3",
 7584   sog := "",
 7585   docsrc := "install_doc/gapstuff.g",
 7586   soghash := "da39a3",
 7587   sig4hash := "Outside KASH3" ),
 7588 rec(
 7589   kind := "KEYWORD",
 7590   name := "Files",
 7591   short := "Basically KASH is aware of both writing to files and reading from files.  While the former may be used to output arbitrary data formats, the latter is restricted to files with valid KASH syntax.\nIndeed, the primary intention for output to files is logging.  In constrast, reading files (thusly, evaluating their contents) is primarily suitable for storing user function definitions or even variable bindings permanently.",
 7592   see := [ "954a96", "cc967a", "594a6f", "b720bf", "6c53a7", "d039f9" ],
 7593   ex := [  ],
 7594   hash := "6ce6c5",
 7595   sig := "Files",
 7596   sog := "",
 7597   docsrc := "install_doc/gapstuff.g",
 7598   soghash := "da39a3",
 7599   sig4hash := "Files" ),
 7600 rec(
 7601   kind := "KEYWORD",
 7602   name := "System",
 7603   short := "KASH offers access to the system environment, read the underlying shell, from within a running session.\nNote: Having bound the Exec() and Pipe() functions _IS A SECURITY RISK_! Everybody who has access to your KASH session is also able to run commands in the name of your uid.\nYou may consider unbinding the function definitions globally.",
 7604   see := [ "8e4ba1", "e6f248", "bb8323" ],
 7605   ex := [  ],
 7606   hash := "bc0792",
 7607   sig := "System",
 7608   sog := "",
 7609   docsrc := "install_doc/gapstuff.g",
 7610   soghash := "da39a3",
 7611   sig4hash := "System" ),
 7612 rec(
 7613   kind := "KEYWORD",
 7614   name := "Database",
 7615   short := "KASH can read various algebraic objects from the QaoS databases in Berlin.  You can establish criteria and query for meeting objects.\nNote: The system KASH runs on must have access to the WWW and you must have cURL installed and configured properly.",
 7616   see := [ "4d7a41", "d038c9" ],
 7617   ex := [  ],
 7618   hash := "61074f",
 7619   sig := "Database",
 7620   sog := "",
 7621   docsrc := "install_doc/gapstuff.g",
 7622   soghash := "da39a3",
 7623   sig4hash := "Database" ),
 7624 rec(
 7625   kind := "KEYWORD",
 7626   name := "GAP compatibility mode",
 7627   short := "KASH can operate in a so called GAP compatibilty mode.  This provides additional group theoretic functions and objects as in GAP3.\nYou can enter the GAP emulation mode with the command `GAP();'.  Leaving the GAP mode is not possible until the end of your session.\nNote: Also, since GAP does not follow our type system, many of the usual GAP functions might not succeed or even work!",
 7628   see := [ "fd2d29", "bd102f", "7cc48c", "7acb1d", "2d83c5" ],
 7629   ex := [  ],
 7630   hash := "7d5323",
 7631   sig := "GAP compatibility mode",
 7632   sog := "",
 7633   docsrc := "install_doc/gapstuff.g",
 7634   soghash := "da39a3",
 7635   sig4hash := "GAP compatibility mode" ),
 7636 rec(
 7637   kind := "KEYWORD",
 7638   name := "Creating GAP groups/objects",
 7639   short := "The main constructor function for GAP objects (read groups) is `Group()'.  There are other several built-in ``templates'' for groups which we assume are known from GAP.",
 7640   ex := [ "GAP();\nGroup((1,2),(3,4));CyclicGroup(4);" ],
 7641   hash := "fd2d29",
 7642   sig := "Creating GAP groups/objects",
 7643   sog := "",
 7644   docsrc := "install_doc/gapstuff.g",
 7645   soghash := "da39a3",
 7646   sig4hash := "Creating GAP groups/objects" ),
 7647 rec(
 7648   kind := "KEYWORD",
 7649   name := "Accessing GAP groups/objects",
 7650   short := "Some of the usual GAP accessor functions are available.\n`Generators', `Elements', `Normalizer', `Centralizer', `Stabilizer', `Centre'.",
 7651   ex := [  ],
 7652   hash := "bd102f",
 7653   sig := "Accessing GAP groups/objects",
 7654   sog := "",
 7655   docsrc := "install_doc/gapstuff.g",
 7656   soghash := "da39a3",
 7657   sig4hash := "Accessing GAP groups/objects" ),
 7658 rec(
 7659   kind := "KEYWORD",
 7660   name := "Properties of GAP groups/objects",
 7661   short := "Some of the usual GAP predicates are available.\n`IsAbelian', `IsSolvable', `IsCyclic', ...",
 7662   ex := [  ],
 7663   hash := "7cc48c",
 7664   sig := "Properties of GAP groups/objects",
 7665   sog := "",
 7666   docsrc := "install_doc/gapstuff.g",
 7667   soghash := "da39a3",
 7668   sig4hash := "Properties of GAP groups/objects" ),
 7669 rec(
 7670   kind := "KEYWORD",
 7671   name := "Converting GAP groups/objects to KASH3",
 7672   short := "Unfortuneately, (automated) conversion of arbitrary groups is not possible.\nFor the special case of Abelian groups, use the usual constructors, such as 'AbelianGroup', or 'FreeAbelianGroup'.\nThis might change in the future.",
 7673   ex := [  ],
 7674   hash := "7acb1d",
 7675   sig := "Converting GAP groups/objects to KASH3",
 7676   sog := "",
 7677   docsrc := "install_doc/gapstuff.g",
 7678   soghash := "da39a3",
 7679   sig4hash := "Converting GAP groups/objects to KASH3" ),
 7680 rec(
 7681   kind := "KEYWORD",
 7682   name := "Known failures in GAP compat mode",
 7683   short := "Some of the GAP functions are known to fail due to different type systems.  This is a (incomplete) list thereof:\nElementaryAbelianGroup(<elt-ord^rat>)\n",
 7684   ex := [  ],
 7685   hash := "2d83c5",
 7686   sig := "Known failures in GAP compat mode",
 7687   sog := "",
 7688   docsrc := "install_doc/gapstuff.g",
 7689   soghash := "da39a3",
 7690   sig4hash := "Known failures in GAP compat mode" ),
 7691 rec(
 7692   kind := "FUNCTION",
 7693   sin := [ [ fld^fin, "F" ], [ fld^fin, "S" ] ],
 7694   sou := [ [ elt-fld^fin ] ],
 7695   name := "Generator",
 7696   short := "Given a finite field F and a subfield S of F, return the (algebra) generator of F over S.",
 7697   ex := [ "x_F := FiniteField(25);\nx_S := FiniteField(5);\nGenerator(x_F, x_S);" ],
 7698   hash := "1352b4",
 7699   sig := "Generator(<fld^fin> F, <fld^fin> S)",
 7700   sog := " -> <elt-fld^fin>",
 7701   docsrc := "<internal>",
 7702   sinflat := [ fld^fin, fld^fin ],
 7703   souflat := [ elt-fld^fin ],
 7704   soghash := "da39a3",
 7705   sig4hash := "Generator(fld^fin,fld^fin)" ),
 7706 rec(
 7707   kind := "FUNCTION",
 7708   sin := [ [ fld^fin, "F" ] ],
 7709   sou := [ [ elt-fld^fin ] ],
 7710   name := "Generator",
 7711   short := "Given a finite field F, return the (algebra) generator of F over its ground field.",
 7712   ex := [ "x_F := FiniteField(25);\nGenerator(x_F);" ],
 7713   hash := "1a564a",
 7714   sig := "Generator(<fld^fin> F)",
 7715   sog := " -> <elt-fld^fin>",
 7716   docsrc := "<internal>",
 7717   sinflat := [ fld^fin ],
 7718   souflat := [ elt-fld^fin ],
 7719   soghash := "da39a3",
 7720   sig4hash := "Generator(fld^fin)" ),
 7721 rec(
 7722   kind := "FUNCTION",
 7723   sin := [ [ res^rat, "R" ] ],
 7724   sou := [ [ elt-res^rat ] ],
 7725   name := "Generator",
 7726   short := "The generator of R.",
 7727   ex := [ "x_R := ResidueClassRing(2^23);\nGenerator(x_R);" ],
 7728   hash := "61057a",
 7729   sig := "Generator(<res^rat> R)",
 7730   sog := " -> <elt-res^rat>",
 7731   docsrc := "<internal>",
 7732   sinflat := [ res^rat ],
 7733   souflat := [ elt-res^rat ],
 7734   soghash := "da39a3",
 7735   sig4hash := "Generator(res^rat)" ),
 7736 rec(
 7737   kind := "FUNCTION",
 7738   sin := [ [ ord^rat, "R" ] ],
 7739   sou := [ [ elt-ord^rat ] ],
 7740   name := "Generator",
 7741   short := "The generator of R.",
 7742   ex := [ "x_Z := IntegerRing();\nGenerator(x_Z);" ],
 7743   hash := "cc954c",
 7744   sig := "Generator(<ord^rat> R)",
 7745   sog := " -> <elt-ord^rat>",
 7746   docsrc := "<internal>",
 7747   sinflat := [ ord^rat ],
 7748   souflat := [ elt-ord^rat ],
 7749   soghash := "da39a3",
 7750   sig4hash := "Generator(ord^rat)" ),
 7751 rec(
 7752   kind := "FUNCTION",
 7753   sin := [ [ alg^pol, "R" ] ],
 7754   sou := [ [ elt-alg^pol ] ],
 7755   name := "Generator",
 7756   short := "The generator of R.",
 7757   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nGenerator(x_R);" ],
 7758   hash := "716b03",
 7759   sig := "Generator(<alg^pol> R)",
 7760   sog := " -> <elt-alg^pol>",
 7761   docsrc := "<internal>",
 7762   sinflat := [ alg^pol ],
 7763   souflat := [ elt-alg^pol ],
 7764   soghash := "da39a3",
 7765   sig4hash := "Generator(alg^pol)" ),
 7766 rec(
 7767   kind := "FUNCTION",
 7768   sin := [ [ seq(elt-alg^boo), "x" ], [ seq(elt-alg^boo), "y" ] ],
 7769   sou := [ [ seq() ] ],
 7770   name := "And",
 7771   short := "The pointwise logical AND of the elements of x and y.",
 7772   ex := [ "And( [ TRUE, TRUE, FALSE ], [ TRUE, FALSE, FALSE ] );" ],
 7773   hash := "33ff40",
 7774   sig := "And(<seq(elt-alg^boo)> x, <seq(elt-alg^boo)> y)",
 7775   sog := " -> <seq()>",
 7776   docsrc := "<internal>",
 7777   sinflat := [ seq(elt-alg^boo), seq(elt-alg^boo) ],
 7778   souflat := [ seq() ],
 7779   soghash := "da39a3",
 7780   sig4hash := "And(seq(elt-alg^boo),seq(elt-alg^boo))" ),
 7781 rec(
 7782   kind := "FUNCTION",
 7783   sin := [ [ seq(), "x" ], [ seq(elt-alg^boo), "y" ] ],
 7784   name := "And_",
 7785   short := "The pointwise logical AND of the elements of x and y.",
 7786   ex := [ "x_L := [ TRUE, TRUE, FALSE ];\nAnd_( x_L, [ TRUE, FALSE, FALSE ] );\nx_L;" ],
 7787   hash := "a9e585",
 7788   sig := "And_(<seq()> x, <seq(elt-alg^boo)> y)",
 7789   sog := "",
 7790   docsrc := "<internal>",
 7791   sinflat := [ seq(), seq(elt-alg^boo) ],
 7792   soghash := "da39a3",
 7793   sig4hash := "And_(seq(),seq(elt-alg^boo))" ),
 7794 rec(
 7795   kind := "FUNCTION",
 7796   sin := [ [ elt-fld^fra, "a" ] ],
 7797   sou := [ [ elt-fld^rea ] ],
 7798   name := "T2Norm",
 7799   short := "Returns the T_2-norm of a.",
 7800   ex := [  ],
 7801   hash := "82f7c4",
 7802   sig := "T2Norm(<elt-fld^fra> a)",
 7803   sog := " -> <elt-fld^rea>",
 7804   docsrc := "<internal>",
 7805   sinflat := [ elt-fld^fra ],
 7806   souflat := [ elt-fld^rea ],
 7807   soghash := "7f2490",
 7808   sig4hash := "T2Norm(elt-fld^fra)" ),
 7809 rec(
 7810   kind := "FUNCTION",
 7811   sin := [ [ elt-ord^num, "a" ] ],
 7812   sou := [ [ elt-fld^rea ] ],
 7813   name := "T2Norm",
 7814   short := "Returns the T_2-norm of a.",
 7815   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_O := EquationOrder(x_x^2 - 18);\nx_a := Generator(x_O, 2);\nT2Norm(x_a);" ],
 7816   hash := "dfa314",
 7817   sig := "T2Norm(<elt-ord^num> a)",
 7818   sog := " -> <elt-fld^rea>",
 7819   docsrc := "<internal>",
 7820   sinflat := [ elt-ord^num ],
 7821   souflat := [ elt-fld^rea ],
 7822   soghash := "da39a3",
 7823   sig4hash := "T2Norm(elt-ord^num)" ),
 7824 rec(
 7825   kind := "FUNCTION",
 7826   sin := [ [ any, "M" ], [ any, "x" ] ],
 7827   sou := [ [ any ] ],
 7828   name := "Coerce",
 7829   short := "Coerce x into M.",
 7830   ex := [ "x_Z := IntegerRing();\nx_R := PolynomialAlgebra( x_Z );\nx_a := Coerce( x_R, Zero(x_Z) );\nType(x_a);\nx_b := Coerce( x_Z, x_a );\nType(x_b);" ],
 7831   hash := "8f26c3",
 7832   sig := "Coerce(<any> M, <any> x)",
 7833   sog := " -> <any>",
 7834   docsrc := "<internal>",
 7835   sinflat := [ any, any ],
 7836   souflat := [ any ],
 7837   soghash := "da39a3",
 7838   sig4hash := "Coerce(any,any)" ),
 7839 rec(
 7840   kind := "FUNCTION",
 7841   sin := [ [ fld^fra, "F" ], [ elt-ids^fra/ord^num, "I" ] ],
 7842   sou := [ [ elt-ids^fra/ord^num ] ],
 7843   name := "CoerceIdeal",
 7844   short := "Return the ideal I as an ideal of F or O.",
 7845   ex := [  ],
 7846   hash := "55e26b",
 7847   sig := "CoerceIdeal(<fld^fra> F, <elt-ids^fra/ord^num> I)",
 7848   sog := " -> <elt-ids^fra/ord^num>",
 7849   docsrc := "<internal>",
 7850   sinflat := [ fld^fra, elt-ids^fra/ord^num ],
 7851   souflat := [ elt-ids^fra/ord^num ],
 7852   soghash := "ca011c",
 7853   sig4hash := "CoerceIdeal(fld^fra,elt-ids^fra/ord^num)" ),
 7854 rec(
 7855   kind := "FUNCTION",
 7856   sin := [ [ ord^num, "O" ], [ elt-ids^fra/ord^num, "I" ] ],
 7857   sou := [ [ elt-ids^int/ord^num ] ],
 7858   name := "CoerceIdeal",
 7859   short := "Return the ideal I as an ideal of F or O.",
 7860   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_O := MaximalOrder(x_x^2 - 18);\nx_a := Element(x_O, [0,1] );\nx_I := Factorization( 3*x_O )[1][1];\nx_Ox := PolynomialAlgebra( x_O );\nx_x := Generator(x_Ox, 1);\nx_OO := MaximalOrder( x_x^3 - 27*x_a );\nx_II := CoerceIdeal(x_OO, x_I);" ],
 7861   hash := "6f0af0",
 7862   sig := "CoerceIdeal(<ord^num> O, <elt-ids^fra/ord^num> I)",
 7863   sog := " -> <elt-ids^int/ord^num>",
 7864   docsrc := "<internal>",
 7865   sinflat := [ ord^num, elt-ids^fra/ord^num ],
 7866   souflat := [ elt-ids^int/ord^num ],
 7867   soghash := "da39a3",
 7868   sig4hash := "CoerceIdeal(ord^num,elt-ids^fra/ord^num)" ),
 7869 rec(
 7870   kind := "FUNCTION",
 7871   sin := [ [ ord^fun, "O" ], [ elt-ids^int/ord^fun, "I" ] ],
 7872   sou := [ [ elt-ids^int/ord^fun ] ],
 7873   name := "CoerceIdeal",
 7874   short := "Return the ideal I as an ideal of F or O.",
 7875   ex := [ "x_k := FiniteField(5);\nx_kx := PolynomialAlgebra(x_k);\nx_kxy := PolynomialAlgebra(x_kx);\nx_x := Generator(x_kx, 1);\nx_y := Generator(x_kxy, 1);\nx_F := FunctionField(x_y^2 - x_x^3 + 1);\nx_O := MaximalOrderFinite(x_F);\nx_a := Element(x_O, [0,1] );\nx_I := Factorization( x_x*x_O )[1][1];\nx_Fz := PolynomialAlgebra( x_F );\nx_z := Generator(x_Fz, 1);\nx_G := FunctionField(x_z^3 - x_a);\nx_OO := MaximalOrderFinite(x_G);\nx_II := CoerceIdeal(x_OO, x_I);" ],
 7876   hash := "71e03d",
 7877   sig := "CoerceIdeal(<ord^fun> O, <elt-ids^int/ord^fun> I)",
 7878   sog := " -> <elt-ids^int/ord^fun>",
 7879   docsrc := "<internal>",
 7880   sinflat := [ ord^fun, elt-ids^int/ord^fun ],
 7881   souflat := [ elt-ids^int/ord^fun ],
 7882   soghash := "da39a3",
 7883   sig4hash := "CoerceIdeal(ord^fun,elt-ids^int/ord^fun)" ),
 7884 rec(
 7885   kind := "FUNCTION",
 7886   sin := [ [ seq(), "S" ] ],
 7887   sou := [ [ elt-ord^rat ] ],
 7888   name := "Size",
 7889   short := "The length of the sequence Q.",
 7890   ex := [ "Size([]);\nSize([3]);\nSize([1,2,3]);\nSize([1..10]);" ],
 7891   hash := "c16201",
 7892   sig := "Size(<seq()> S)",
 7893   sog := " -> <elt-ord^rat>",
 7894   docsrc := "<internal>",
 7895   sinflat := [ seq() ],
 7896   souflat := [ elt-ord^rat ],
 7897   soghash := "da39a3",
 7898   sig4hash := "Size(seq())" ),
 7899 rec(
 7900   kind := "FUNCTION",
 7901   sin := [ [ alg^mat, "A" ] ],
 7902   sou := [ [ elt-ord^rat ] ],
 7903   name := "Size",
 7904   short := "The cardinality of ring R (if finite).",
 7905   ex := [ "x_R := MatrixAlgebra( FiniteField(5), 3);\nSize(x_R);" ],
 7906   hash := "aa88e2",
 7907   sig := "Size(<alg^mat> A)",
 7908   sog := " -> <elt-ord^rat>",
 7909   docsrc := "<internal>",
 7910   sinflat := [ alg^mat ],
 7911   souflat := [ elt-ord^rat ],
 7912   soghash := "da39a3",
 7913   sig4hash := "Size(alg^mat)" ),
 7914 rec(
 7915   kind := "FUNCTION",
 7916   sin := [ [ rng, "R" ] ],
 7917   sou := [ [ elt-ord^rat ] ],
 7918   name := "Size",
 7919   short := "The cardinality of ring R (if finite).",
 7920   ex := [ "x_R := FiniteField(5);\nSize(x_R);\nx_R := IntegerRing();\nSize(x_R);" ],
 7921   hash := "ee3f72",
 7922   sig := "Size(<rng> R)",
 7923   sog := " -> <elt-ord^rat>",
 7924   docsrc := "<internal>",
 7925   sinflat := [ rng ],
 7926   souflat := [ elt-ord^rat ],
 7927   soghash := "da39a3",
 7928   sig4hash := "Size(rng)" ),
 7929 rec(
 7930   kind := "FUNCTION",
 7931   sin := [ [ tup(), "T" ] ],
 7932   sou := [ [ elt-ord^rat ] ],
 7933   name := "Size",
 7934   short := "The length (number of components) of T.",
 7935   ex := [ "x_t := Tuple( [ 1, FiniteField(5), Pi(RealField()) ] );\nSize(x_t);" ],
 7936   hash := "93f01f",
 7937   sig := "Size(<tup()> T)",
 7938   sog := " -> <elt-ord^rat>",
 7939   docsrc := "<internal>",
 7940   sinflat := [ tup() ],
 7941   souflat := [ elt-ord^rat ],
 7942   soghash := "da39a3",
 7943   sig4hash := "Size(tup())" ),
 7944 rec(
 7945   kind := "FUNCTION",
 7946   sin := [ [ map(), "T" ] ],
 7947   sou := [ [ elt-ord^rat ] ],
 7948   name := "Size",
 7949   short := "The number of rows in the coset table T.",
 7950   ex := [  ],
 7951   hash := "4e3050",
 7952   sig := "Size(<map()> T)",
 7953   sog := " -> <elt-ord^rat>",
 7954   docsrc := "<internal>",
 7955   sinflat := [ map() ],
 7956   souflat := [ elt-ord^rat ],
 7957   soghash := "898213",
 7958   sig4hash := "Size(map())" ),
 7959 rec(
 7960   kind := "FUNCTION",
 7961   sin := [ [ str, "C" ] ],
 7962   sou := [ [ elt-ord^rat ] ],
 7963   name := "Size",
 7964   short := "The cardinality of C.",
 7965   ex := [ "x_z5 := pAdicRing(5,30);\nx_r5 := Quotient(x_z5, 5^10);\nSize( x_r5 );" ],
 7966   hash := "51e100",
 7967   sig := "Size(<str> C)",
 7968   sog := " -> <elt-ord^rat>",
 7969   docsrc := "<internal>",
 7970   sinflat := [ str ],
 7971   souflat := [ elt-ord^rat ],
 7972   soghash := "da39a3",
 7973   sig4hash := "Size(str)" ),
 7974 rec(
 7975   kind := "FUNCTION",
 7976   sin := [ [ fld^fin, "R" ] ],
 7977   sou := [ [ elt-ord^rat ] ],
 7978   name := "Size",
 7979   short := "The cardinality of R.",
 7980   ex := [ "Size( FiniteField( 2 ) );" ],
 7981   hash := "96758c",
 7982   sig := "Size(<fld^fin> R)",
 7983   sog := " -> <elt-ord^rat>",
 7984   docsrc := "<internal>",
 7985   sinflat := [ fld^fin ],
 7986   souflat := [ elt-ord^rat ],
 7987   soghash := "da39a3",
 7988   sig4hash := "Size(fld^fin)" ),
 7989 rec(
 7990   kind := "FUNCTION",
 7991   sin := [ [ res^rat, "R" ] ],
 7992   sou := [ [ elt-ord^rat ] ],
 7993   name := "Size",
 7994   short := "The cardinality of R.",
 7995   ex := [ "x_R := ResidueClassRing(2^23);\nSize( x_R );" ],
 7996   hash := "46626e",
 7997   sig := "Size(<res^rat> R)",
 7998   sog := " -> <elt-ord^rat>",
 7999   docsrc := "<internal>",
 8000   sinflat := [ res^rat ],
 8001   souflat := [ elt-ord^rat ],
 8002   soghash := "da39a3",
 8003   sig4hash := "Size(res^rat)" ),
 8004 rec(
 8005   kind := "FUNCTION",
 8006   sin := [ [ res^pad, "R" ] ],
 8007   sou := [ [ elt-ord^rat ] ],
 8008   name := "Size",
 8009   short := "The cardinality of R.",
 8010   ex := [ "x_z5 := pAdicRing(5,30);\nx_r5 := Quotient(x_z5, 5^10);\nSize( x_r5 );" ],
 8011   hash := "ea70c0",
 8012   sig := "Size(<res^pad> R)",
 8013   sog := " -> <elt-ord^rat>",
 8014   docsrc := "<internal>",
 8015   sinflat := [ res^pad ],
 8016   souflat := [ elt-ord^rat ],
 8017   soghash := "da39a3",
 8018   sig4hash := "Size(res^pad)" ),
 8019 rec(
 8020   kind := "FUNCTION",
 8021   sin := [ [ grp^abl, "G" ] ],
 8022   sou := [ [ elt-ord^rat ] ],
 8023   name := "Size",
 8024   short := "The cardinality of M (if finite).",
 8025   ex := [ "x_G := AbelianGroup( [2,5] );\nSize( x_G );" ],
 8026   hash := "ee0a32",
 8027   sig := "Size(<grp^abl> G)",
 8028   sog := " -> <elt-ord^rat>",
 8029   docsrc := "<internal>",
 8030   sinflat := [ grp^abl ],
 8031   souflat := [ elt-ord^rat ],
 8032   soghash := "da39a3",
 8033   sig4hash := "Size(grp^abl)" ),
 8034 rec(
 8035   kind := "FUNCTION",
 8036   sin := [ [ mdl^vec, "M" ] ],
 8037   sou := [ [ elt-ord^rat ] ],
 8038   name := "Size",
 8039   short := "The cardinality of M (if finite).",
 8040   ex := [ "x_V := VectorSpace( FiniteField( 5 ), 3 );\nSize( x_V );" ],
 8041   hash := "de2e6c",
 8042   sig := "Size(<mdl^vec> M)",
 8043   sog := " -> <elt-ord^rat>",
 8044   docsrc := "<internal>",
 8045   sinflat := [ mdl^vec ],
 8046   souflat := [ elt-ord^rat ],
 8047   soghash := "da39a3",
 8048   sig4hash := "Size(mdl^vec)" ),
 8049 rec(
 8050   kind := "FUNCTION",
 8051   sin := [ [ mdl^mat, "M" ] ],
 8052   sou := [ [ elt-ord^rat ] ],
 8053   name := "Size",
 8054   short := "The cardinality of M (if finite).",
 8055   ex := [ "" ],
 8056   hash := "bd482b",
 8057   sig := "Size(<mdl^mat> M)",
 8058   sog := " -> <elt-ord^rat>",
 8059   docsrc := "<internal>",
 8060   sinflat := [ mdl^mat ],
 8061   souflat := [ elt-ord^rat ],
 8062   soghash := "da39a3",
 8063   sig4hash := "Size(mdl^mat)" ),
 8064 rec(
 8065   kind := "FUNCTION",
 8066   sin := [ [ mdl, "M" ] ],
 8067   sou := [ [ elt-ord^rat ] ],
 8068   name := "Size",
 8069   short := "The cardinality of M (if finite).",
 8070   ex := [  ],
 8071   hash := "2ee348",
 8072   sig := "Size(<mdl> M)",
 8073   sog := " -> <elt-ord^rat>",
 8074   docsrc := "<internal>",
 8075   sinflat := [ mdl ],
 8076   souflat := [ elt-ord^rat ],
 8077   soghash := "da39a3",
 8078   sig4hash := "Size(mdl)" ),
 8079 rec(
 8080   kind := "FUNCTION",
 8081   sin := [ [ alg^boo, "M" ] ],
 8082   sou := [ [ elt-ord^rat ] ],
 8083   name := "Size",
 8084   short := "The cardinality of M (if finite).",
 8085   ex := [ "Size( Booleans() );" ],
 8086   hash := "cf4269",
 8087   sig := "Size(<alg^boo> M)",
 8088   sog := " -> <elt-ord^rat>",
 8089   docsrc := "<internal>",
 8090   sinflat := [ alg^boo ],
 8091   souflat := [ elt-ord^rat ],
 8092   soghash := "da39a3",
 8093   sig4hash := "Size(alg^boo)" ),
 8094 rec(
 8095   kind := "FUNCTION",
 8096   sin := [ [ seq(elt-alg^boo), "S" ] ],
 8097   sou := [ [ elt-alg^boo ] ],
 8098   name := "And",
 8099   ex := [ "And( Sequence( [TRUE, TRUE, TRUE ] ) );\nAnd( [TRUE, TRUE, TRUE] );" ],
 8100   hash := "120c98",
 8101   sig := "And(<seq(elt-alg^boo)> S)",
 8102   sog := " -> <elt-alg^boo>",
 8103   docsrc := "<internal>",
 8104   sinflat := [ seq(elt-alg^boo) ],
 8105   souflat := [ elt-alg^boo ],
 8106   soghash := "da39a3",
 8107   sig4hash := "And(seq(elt-alg^boo))" ),
 8108 rec(
 8109   kind := "FUNCTION",
 8110   sin := [ [ seq(seq()), "S" ] ],
 8111   sou := [ [ seq() ] ],
 8112   name := "Concatenation",
 8113   short := "The concatenation of all elements of S.",
 8114   ex := [ "x_L := Concatenation( Sequence( [ Sequence( [1,2] ), Sequence( [2,3] ) ] ) );\nType(x_L);\nx_L := Concatenation( [ [1,2], [2,3] ] );\nType(x_L);" ],
 8115   hash := "86383f",
 8116   sig := "Concatenation(<seq(seq())> S)",
 8117   sog := " -> <seq()>",
 8118   docsrc := "<internal>",
 8119   sinflat := [ seq(seq()) ],
 8120   souflat := [ seq() ],
 8121   soghash := "da39a3",
 8122   sig4hash := "Concatenation(seq(seq()))" ),
 8123 rec(
 8124   kind := "FUNCTION",
 8125   sin := [ [ seq(string), "S" ] ],
 8126   sou := [ [ string ] ],
 8127   name := "Concatenation",
 8128   short := "The concatenation of all elements of S.",
 8129   ex := [ "Concatenation( Sequence( [ \"Good\", \" \", \"Morning!\" ] ) );\nConcatenation( [ \"Good\", \" \", \"Morning!\" ] );" ],
 8130   hash := "5b5c8d",
 8131   sig := "Concatenation(<seq(string)> S)",
 8132   sog := " -> <string>",
 8133   docsrc := "<internal>",
 8134   sinflat := [ seq(string) ],
 8135   souflat := [ string ],
 8136   soghash := "da39a3",
 8137   sig4hash := "Concatenation(seq(string))" ),
 8138 rec(
 8139   kind := "FUNCTION",
 8140   sin := [ [ seq(elt-alg^boo), "S" ] ],
 8141   sou := [ [ elt-alg^boo ] ],
 8142   name := "Or",
 8143   ex := [ "Or( Sequence( [ TRUE, FALSE, FALSE ] ) );\nOr( [ TRUE, FALSE, FALSE ] );" ],
 8144   hash := "1f60ed",
 8145   sig := "Or(<seq(elt-alg^boo)> S)",
 8146   sog := " -> <elt-alg^boo>",
 8147   docsrc := "<internal>",
 8148   sinflat := [ seq(elt-alg^boo) ],
 8149   souflat := [ elt-alg^boo ],
 8150   soghash := "da39a3",
 8151   sig4hash := "Or(seq(elt-alg^boo))" ),
 8152 rec(
 8153   kind := "OPERATION",
 8154   sin := [ [ elt-ord^rat, "x" ], [ elt-ord^rat, "y" ] ],
 8155   sou := [ [ elt-ord^rat ] ],
 8156   name := "*",
 8157   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8158   ex := [  ],
 8159   hash := "5d2a18",
 8160   sig := "<elt-ord^rat> x * <elt-ord^rat> y",
 8161   sog := " -> <elt-ord^rat>",
 8162   docsrc := "<internal>",
 8163   sinflat := [ elt-ord^rat, elt-ord^rat ],
 8164   souflat := [ elt-ord^rat ],
 8165   soghash := "898213",
 8166   sig4hash := "*(elt-ord^rat,elt-ord^rat)" ),
 8167 rec(
 8168   kind := "OPERATION",
 8169   sin := [ [ elt-fld^rat, "x" ], [ elt-fld^rat, "y" ] ],
 8170   sou := [ [ elt-fld^rat ] ],
 8171   name := "*",
 8172   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8173   ex := [  ],
 8174   hash := "97f2d4",
 8175   sig := "<elt-fld^rat> x * <elt-fld^rat> y",
 8176   sog := " -> <elt-fld^rat>",
 8177   docsrc := "<internal>",
 8178   sinflat := [ elt-fld^rat, elt-fld^rat ],
 8179   souflat := [ elt-fld^rat ],
 8180   soghash := "89f5fc",
 8181   sig4hash := "*(elt-fld^rat,elt-fld^rat)" ),
 8182 rec(
 8183   kind := "OPERATION",
 8184   sin := [ [ elt-mdl^vec, "v" ], [ elt-alg^mat, "X" ] ],
 8185   sou := [ [ elt-mdl^vec ] ],
 8186   name := "*",
 8187   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8188   ex := [  ],
 8189   hash := "6708e8",
 8190   sig := "<elt-mdl^vec> v * <elt-alg^mat> X",
 8191   sog := " -> <elt-mdl^vec>",
 8192   docsrc := "<internal>",
 8193   sinflat := [ elt-mdl^vec, elt-alg^mat ],
 8194   souflat := [ elt-mdl^vec ],
 8195   soghash := "b46581",
 8196   sig4hash := "*(elt-mdl^vec,elt-alg^mat)" ),
 8197 rec(
 8198   kind := "OPERATION",
 8199   sin := [ [ string, "x" ], [ string, "y" ] ],
 8200   sou := [ [ string ] ],
 8201   name := "*",
 8202   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8203   ex := [  ],
 8204   hash := "8d5ec6",
 8205   sig := "<string> x * <string> y",
 8206   sog := " -> <string>",
 8207   docsrc := "<internal>",
 8208   sinflat := [ string, string ],
 8209   souflat := [ string ],
 8210   soghash := "ecb252",
 8211   sig4hash := "*(string,string)" ),
 8212 rec(
 8213   kind := "OPERATION",
 8214   sin := [ [ elt-fld^rea, "x" ], [ elt-fld^rea, "y" ] ],
 8215   sou := [ [ elt-fld^rea ] ],
 8216   name := "*",
 8217   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8218   ex := [  ],
 8219   hash := "a6ea5b",
 8220   sig := "<elt-fld^rea> x * <elt-fld^rea> y",
 8221   sog := " -> <elt-fld^rea>",
 8222   docsrc := "<internal>",
 8223   sinflat := [ elt-fld^rea, elt-fld^rea ],
 8224   souflat := [ elt-fld^rea ],
 8225   soghash := "7f2490",
 8226   sig4hash := "*(elt-fld^rea,elt-fld^rea)" ),
 8227 rec(
 8228   kind := "OPERATION",
 8229   sin := [ [ elt-fld^com, "x" ], [ elt-fld^com, "y" ] ],
 8230   sou := [ [ elt-fld^com ] ],
 8231   name := "*",
 8232   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8233   ex := [  ],
 8234   hash := "f2b426",
 8235   sig := "<elt-fld^com> x * <elt-fld^com> y",
 8236   sog := " -> <elt-fld^com>",
 8237   docsrc := "<internal>",
 8238   sinflat := [ elt-fld^com, elt-fld^com ],
 8239   souflat := [ elt-fld^com ],
 8240   soghash := "0d772f",
 8241   sig4hash := "*(elt-fld^com,elt-fld^com)" ),
 8242 rec(
 8243   kind := "OPERATION",
 8244   sin := [ [ elt-fld^fin, "x" ], [ elt-fld^fin, "y" ] ],
 8245   sou := [ [ elt-fld^fin ] ],
 8246   name := "*",
 8247   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8248   ex := [  ],
 8249   hash := "a946db",
 8250   sig := "<elt-fld^fin> x * <elt-fld^fin> y",
 8251   sog := " -> <elt-fld^fin>",
 8252   docsrc := "<internal>",
 8253   sinflat := [ elt-fld^fin, elt-fld^fin ],
 8254   souflat := [ elt-fld^fin ],
 8255   soghash := "97e752",
 8256   sig4hash := "*(elt-fld^fin,elt-fld^fin)" ),
 8257 rec(
 8258   kind := "OPERATION",
 8259   sin := [ [ elt-alg^mat, "x" ], [ elt-alg^mat, "y" ] ],
 8260   sou := [ [ elt-alg^mat ] ],
 8261   name := "*",
 8262   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8263   ex := [  ],
 8264   hash := "1a92f7",
 8265   sig := "<elt-alg^mat> x * <elt-alg^mat> y",
 8266   sog := " -> <elt-alg^mat>",
 8267   docsrc := "<internal>",
 8268   sinflat := [ elt-alg^mat, elt-alg^mat ],
 8269   souflat := [ elt-alg^mat ],
 8270   soghash := "8dbb64",
 8271   sig4hash := "*(elt-alg^mat,elt-alg^mat)" ),
 8272 rec(
 8273   kind := "OPERATION",
 8274   sin := [ [ elt-alg^pol, "x" ], [ elt-alg^pol, "y" ] ],
 8275   sou := [ [ elt-alg^pol ] ],
 8276   name := "*",
 8277   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8278   ex := [  ],
 8279   hash := "6b513a",
 8280   sig := "<elt-alg^pol> x * <elt-alg^pol> y",
 8281   sog := " -> <elt-alg^pol>",
 8282   docsrc := "<internal>",
 8283   sinflat := [ elt-alg^pol, elt-alg^pol ],
 8284   souflat := [ elt-alg^pol ],
 8285   soghash := "ba7338",
 8286   sig4hash := "*(elt-alg^pol,elt-alg^pol)" ),
 8287 rec(
 8288   kind := "OPERATION",
 8289   sin := [ [ elt-fld^pol, "x" ], [ elt-fld^pol, "y" ] ],
 8290   sou := [ [ elt-fld^pol ] ],
 8291   name := "*",
 8292   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8293   ex := [  ],
 8294   hash := "fdca38",
 8295   sig := "<elt-fld^pol> x * <elt-fld^pol> y",
 8296   sog := " -> <elt-fld^pol>",
 8297   docsrc := "<internal>",
 8298   sinflat := [ elt-fld^pol, elt-fld^pol ],
 8299   souflat := [ elt-fld^pol ],
 8300   soghash := "540d59",
 8301   sig4hash := "*(elt-fld^pol,elt-fld^pol)" ),
 8302 rec(
 8303   kind := "OPERATION",
 8304   sin := [ [ elt-rng, "x" ], [ elt-rng, "y" ] ],
 8305   sou := [ [ elt-rng ] ],
 8306   name := "*",
 8307   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8308   ex := [  ],
 8309   hash := "548853",
 8310   sig := "<elt-rng> x * <elt-rng> y",
 8311   sog := " -> <elt-rng>",
 8312   docsrc := "<internal>",
 8313   sinflat := [ elt-rng, elt-rng ],
 8314   souflat := [ elt-rng ],
 8315   soghash := "7ef0ef",
 8316   sig4hash := "*(elt-rng,elt-rng)" ),
 8317 rec(
 8318   kind := "OPERATION",
 8319   sin := [ [ elt-res^pol, "x" ], [ elt-res^pol, "y" ] ],
 8320   sou := [ [ elt-res^pol ] ],
 8321   name := "*",
 8322   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8323   ex := [  ],
 8324   hash := "5345a1",
 8325   sig := "<elt-res^pol> x * <elt-res^pol> y",
 8326   sog := " -> <elt-res^pol>",
 8327   docsrc := "<internal>",
 8328   sinflat := [ elt-res^pol, elt-res^pol ],
 8329   souflat := [ elt-res^pol ],
 8330   soghash := "8ffe0c",
 8331   sig4hash := "*(elt-res^pol,elt-res^pol)" ),
 8332 rec(
 8333   kind := "OPERATION",
 8334   sin := [ [ elt-mdl^mat, "x" ], [ elt-mdl^mat, "y" ] ],
 8335   sou := [ [ elt-mdl^mat ] ],
 8336   name := "*",
 8337   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8338   ex := [  ],
 8339   hash := "e292e9",
 8340   sig := "<elt-mdl^mat> x * <elt-mdl^mat> y",
 8341   sog := " -> <elt-mdl^mat>",
 8342   docsrc := "<internal>",
 8343   sinflat := [ elt-mdl^mat, elt-mdl^mat ],
 8344   souflat := [ elt-mdl^mat ],
 8345   soghash := "5284ac",
 8346   sig4hash := "*(elt-mdl^mat,elt-mdl^mat)" ),
 8347 rec(
 8348   kind := "OPERATION",
 8349   sin := [ [ elt-alg^mat, "x" ], [ elt-mdl^mat, "y" ] ],
 8350   sou := [ [ elt-mdl^mat ] ],
 8351   name := "*",
 8352   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8353   ex := [  ],
 8354   hash := "b38c0e",
 8355   sig := "<elt-alg^mat> x * <elt-mdl^mat> y",
 8356   sog := " -> <elt-mdl^mat>",
 8357   docsrc := "<internal>",
 8358   sinflat := [ elt-alg^mat, elt-mdl^mat ],
 8359   souflat := [ elt-mdl^mat ],
 8360   soghash := "5284ac",
 8361   sig4hash := "*(elt-alg^mat,elt-mdl^mat)" ),
 8362 rec(
 8363   kind := "OPERATION",
 8364   sin := [ [ elt-mdl^mat, "x" ], [ elt-alg^mat, "y" ] ],
 8365   sou := [ [ elt-mdl^mat ] ],
 8366   name := "*",
 8367   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8368   ex := [  ],
 8369   hash := "f03e60",
 8370   sig := "<elt-mdl^mat> x * <elt-alg^mat> y",
 8371   sog := " -> <elt-mdl^mat>",
 8372   docsrc := "<internal>",
 8373   sinflat := [ elt-mdl^mat, elt-alg^mat ],
 8374   souflat := [ elt-mdl^mat ],
 8375   soghash := "5284ac",
 8376   sig4hash := "*(elt-mdl^mat,elt-alg^mat)" ),
 8377 rec(
 8378   kind := "OPERATION",
 8379   sin := [ [ elt-res^rat, "x" ], [ elt-res^rat, "y" ] ],
 8380   sou := [ [ elt-res^rat ] ],
 8381   name := "*",
 8382   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8383   ex := [  ],
 8384   hash := "1b536b",
 8385   sig := "<elt-res^rat> x * <elt-res^rat> y",
 8386   sog := " -> <elt-res^rat>",
 8387   docsrc := "<internal>",
 8388   sinflat := [ elt-res^rat, elt-res^rat ],
 8389   souflat := [ elt-res^rat ],
 8390   soghash := "7a2c2e",
 8391   sig4hash := "*(elt-res^rat,elt-res^rat)" ),
 8392 rec(
 8393   kind := "OPERATION",
 8394   sin := [ [ elt-res^pad, "x" ], [ elt-res^pad, "y" ] ],
 8395   sou := [ [ elt-res^pad ] ],
 8396   name := "*",
 8397   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8398   ex := [  ],
 8399   hash := "94b4b7",
 8400   sig := "<elt-res^pad> x * <elt-res^pad> y",
 8401   sog := " -> <elt-res^pad>",
 8402   docsrc := "<internal>",
 8403   sinflat := [ elt-res^pad, elt-res^pad ],
 8404   souflat := [ elt-res^pad ],
 8405   soghash := "0061b4",
 8406   sig4hash := "*(elt-res^pad,elt-res^pad)" ),
 8407 rec(
 8408   kind := "OPERATION",
 8409   sin := [ [ elt-ord^pad, "x" ], [ elt-ord^pad, "y" ] ],
 8410   sou := [ [ elt-ord^pad ] ],
 8411   name := "*",
 8412   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8413   ex := [  ],
 8414   hash := "296081",
 8415   sig := "<elt-ord^pad> x * <elt-ord^pad> y",
 8416   sog := " -> <elt-ord^pad>",
 8417   docsrc := "<internal>",
 8418   sinflat := [ elt-ord^pad, elt-ord^pad ],
 8419   souflat := [ elt-ord^pad ],
 8420   soghash := "9ee81d",
 8421   sig4hash := "*(elt-ord^pad,elt-ord^pad)" ),
 8422 rec(
 8423   kind := "OPERATION",
 8424   sin := [ [ elt-fld^pad, "x" ], [ elt-fld^pad, "y" ] ],
 8425   sou := [ [ elt-fld^pad ] ],
 8426   name := "*",
 8427   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8428   ex := [  ],
 8429   hash := "e28cd6",
 8430   sig := "<elt-fld^pad> x * <elt-fld^pad> y",
 8431   sog := " -> <elt-fld^pad>",
 8432   docsrc := "<internal>",
 8433   sinflat := [ elt-fld^pad, elt-fld^pad ],
 8434   souflat := [ elt-fld^pad ],
 8435   soghash := "8c3f71",
 8436   sig4hash := "*(elt-fld^pad,elt-fld^pad)" ),
 8437 rec(
 8438   kind := "OPERATION",
 8439   sin := [ [ elt-fld^fra, "x" ], [ elt-fld^fra, "y" ] ],
 8440   sou := [ [ elt-fld^fra ] ],
 8441   name := "*",
 8442   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8443   ex := [  ],
 8444   hash := "c6d89b",
 8445   sig := "<elt-fld^fra> x * <elt-fld^fra> y",
 8446   sog := " -> <elt-fld^fra>",
 8447   docsrc := "<internal>",
 8448   sinflat := [ elt-fld^fra, elt-fld^fra ],
 8449   souflat := [ elt-fld^fra ],
 8450   soghash := "74ef48",
 8451   sig4hash := "*(elt-fld^fra,elt-fld^fra)" ),
 8452 rec(
 8453   kind := "OPERATION",
 8454   sin := [ [ elt-ord^num, "x" ], [ elt-ord^num, "y" ] ],
 8455   sou := [ [ elt-ord^num ] ],
 8456   name := "*",
 8457   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8458   ex := [  ],
 8459   hash := "1322a4",
 8460   sig := "<elt-ord^num> x * <elt-ord^num> y",
 8461   sog := " -> <elt-ord^num>",
 8462   docsrc := "<internal>",
 8463   sinflat := [ elt-ord^num, elt-ord^num ],
 8464   souflat := [ elt-ord^num ],
 8465   soghash := "6b03f8",
 8466   sig4hash := "*(elt-ord^num,elt-ord^num)" ),
 8467 rec(
 8468   kind := "OPERATION",
 8469   sin := [ [ elt-res^num, "x" ], [ elt-res^num, "y" ] ],
 8470   sou := [ [ elt-res^num ] ],
 8471   name := "*",
 8472   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8473   ex := [  ],
 8474   hash := "e63d5b",
 8475   sig := "<elt-res^num> x * <elt-res^num> y",
 8476   sog := " -> <elt-res^num>",
 8477   docsrc := "<internal>",
 8478   sinflat := [ elt-res^num, elt-res^num ],
 8479   souflat := [ elt-res^num ],
 8480   soghash := "a87f47",
 8481   sig4hash := "*(elt-res^num,elt-res^num)" ),
 8482 rec(
 8483   kind := "OPERATION",
 8484   sin := [ [ elt-ids^fra/ord^num, "x" ], [ elt-ids^fra/ord^num, "y" ] ],
 8485   sou := [ [ elt-ids^fra/ord^num ] ],
 8486   name := "*",
 8487   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8488   ex := [  ],
 8489   hash := "edab48",
 8490   sig := "<elt-ids^fra/ord^num> x * <elt-ids^fra/ord^num> y",
 8491   sog := " -> <elt-ids^fra/ord^num>",
 8492   docsrc := "<internal>",
 8493   sinflat := [ elt-ids^fra/ord^num, elt-ids^fra/ord^num ],
 8494   souflat := [ elt-ids^fra/ord^num ],
 8495   soghash := "ca011c",
 8496   sig4hash := "*(elt-ids^fra/ord^num,elt-ids^fra/ord^num)" ),
 8497 rec(
 8498   kind := "OPERATION",
 8499   sin := [ [ elt-ids^int/ord^fun, "x" ], [ elt-ids^int/ord^fun, "y" ] ],
 8500   sou := [ [ elt-ids^int/ord^fun ] ],
 8501   name := "*",
 8502   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8503   ex := [  ],
 8504   hash := "dbaff7",
 8505   sig := "<elt-ids^int/ord^fun> x * <elt-ids^int/ord^fun> y",
 8506   sog := " -> <elt-ids^int/ord^fun>",
 8507   docsrc := "<internal>",
 8508   sinflat := [ elt-ids^int/ord^fun, elt-ids^int/ord^fun ],
 8509   souflat := [ elt-ids^int/ord^fun ],
 8510   soghash := "918914",
 8511   sig4hash := "*(elt-ids^int/ord^fun,elt-ids^int/ord^fun)" ),
 8512 rec(
 8513   kind := "OPERATION",
 8514   sin := [ [ elt-rng^ser, "x" ], [ elt-rng^ser, "y" ] ],
 8515   sou := [ [ elt-rng^ser ] ],
 8516   name := "*",
 8517   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8518   ex := [  ],
 8519   hash := "1362af",
 8520   sig := "<elt-rng^ser> x * <elt-rng^ser> y",
 8521   sog := " -> <elt-rng^ser>",
 8522   docsrc := "<internal>",
 8523   sinflat := [ elt-rng^ser, elt-rng^ser ],
 8524   souflat := [ elt-rng^ser ],
 8525   soghash := "28734d",
 8526   sig4hash := "*(elt-rng^ser,elt-rng^ser)" ),
 8527 rec(
 8528   kind := "OPERATION",
 8529   sin := [ [ res^rat, "x" ], [ res^rat, "y" ] ],
 8530   sou := [ [ res^rat ] ],
 8531   name := "*",
 8532   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8533   ex := [  ],
 8534   hash := "7d6800",
 8535   sig := "<res^rat> x * <res^rat> y",
 8536   sog := " -> <res^rat>",
 8537   docsrc := "<internal>",
 8538   sinflat := [ res^rat, res^rat ],
 8539   souflat := [ res^rat ],
 8540   soghash := "a3bb08",
 8541   sig4hash := "*(res^rat,res^rat)" ),
 8542 rec(
 8543   kind := "OPERATION",
 8544   sin := [ [ ord^rat, "x" ], [ ord^rat, "y" ] ],
 8545   sou := [ [ ord^rat ] ],
 8546   name := "*",
 8547   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8548   ex := [  ],
 8549   hash := "a8d39a",
 8550   sig := "<ord^rat> x * <ord^rat> y",
 8551   sog := " -> <ord^rat>",
 8552   docsrc := "<internal>",
 8553   sinflat := [ ord^rat, ord^rat ],
 8554   souflat := [ ord^rat ],
 8555   soghash := "ef1cfa",
 8556   sig4hash := "*(ord^rat,ord^rat)" ),
 8557 rec(
 8558   kind := "OPERATION",
 8559   sin := [ [ alg^pol, "x" ], [ alg^pol, "y" ] ],
 8560   sou := [ [ alg^pol ] ],
 8561   name := "*",
 8562   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8563   ex := [  ],
 8564   hash := "567a74",
 8565   sig := "<alg^pol> x * <alg^pol> y",
 8566   sog := " -> <alg^pol>",
 8567   docsrc := "<internal>",
 8568   sinflat := [ alg^pol, alg^pol ],
 8569   souflat := [ alg^pol ],
 8570   soghash := "75868e",
 8571   sig4hash := "*(alg^pol,alg^pol)" ),
 8572 rec(
 8573   kind := "OPERATION",
 8574   sin := [ [ elt-fld^fun, "x" ], [ elt-fld^fun, "y" ] ],
 8575   sou := [ [ elt-fld^fun ] ],
 8576   name := "*",
 8577   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8578   ex := [  ],
 8579   hash := "675095",
 8580   sig := "<elt-fld^fun> x * <elt-fld^fun> y",
 8581   sog := " -> <elt-fld^fun>",
 8582   docsrc := "<internal>",
 8583   sinflat := [ elt-fld^fun, elt-fld^fun ],
 8584   souflat := [ elt-fld^fun ],
 8585   soghash := "23d8b4",
 8586   sig4hash := "*(elt-fld^fun,elt-fld^fun)" ),
 8587 rec(
 8588   kind := "OPERATION",
 8589   sin := [ [ elt-ord^fun, "x" ], [ elt-ord^fun, "y" ] ],
 8590   sou := [ [ elt-ord^fun ] ],
 8591   name := "*",
 8592   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8593   ex := [  ],
 8594   hash := "a5b5a6",
 8595   sig := "<elt-ord^fun> x * <elt-ord^fun> y",
 8596   sog := " -> <elt-ord^fun>",
 8597   docsrc := "<internal>",
 8598   sinflat := [ elt-ord^fun, elt-ord^fun ],
 8599   souflat := [ elt-ord^fun ],
 8600   soghash := "0fe368",
 8601   sig4hash := "*(elt-ord^fun,elt-ord^fun)" ),
 8602 rec(
 8603   kind := "OPERATION",
 8604   sin := [ [ elt-dif/fld^fun, "x" ], [ elt-rng, "y" ] ],
 8605   sou := [ [ elt-dif/fld^fun ] ],
 8606   name := "*",
 8607   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8608   ex := [  ],
 8609   hash := "3b4186",
 8610   sig := "<elt-dif/fld^fun> x * <elt-rng> y",
 8611   sog := " -> <elt-dif/fld^fun>",
 8612   docsrc := "<internal>",
 8613   sinflat := [ elt-dif/fld^fun, elt-rng ],
 8614   souflat := [ elt-dif/fld^fun ],
 8615   soghash := "fb8974",
 8616   sig4hash := "*(elt-dif/fld^fun,elt-rng)" ),
 8617 rec(
 8618   kind := "OPERATION",
 8619   sin := [ [ elt-rng, "x" ], [ elt-dif/fld^fun, "y" ] ],
 8620   sou := [ [ elt-dif/fld^fun ] ],
 8621   name := "*",
 8622   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8623   ex := [  ],
 8624   hash := "cd7ab2",
 8625   sig := "<elt-rng> x * <elt-dif/fld^fun> y",
 8626   sog := " -> <elt-dif/fld^fun>",
 8627   docsrc := "<internal>",
 8628   sinflat := [ elt-rng, elt-dif/fld^fun ],
 8629   souflat := [ elt-dif/fld^fun ],
 8630   soghash := "fb8974",
 8631   sig4hash := "*(elt-rng,elt-dif/fld^fun)" ),
 8632 rec(
 8633   kind := "OPERATION",
 8634   sin := [ [ elt-ord^inf, "x" ], [ any, "y" ] ],
 8635   sou := [ [ elt-ord^inf ] ],
 8636   name := "*",
 8637   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8638   ex := [  ],
 8639   hash := "39cdfc",
 8640   sig := "<elt-ord^inf> x * <any> y",
 8641   sog := " -> <elt-ord^inf>",
 8642   docsrc := "<internal>",
 8643   sinflat := [ elt-ord^inf, any ],
 8644   souflat := [ elt-ord^inf ],
 8645   soghash := "08787a",
 8646   sig4hash := "*(elt-ord^inf,any)" ),
 8647 rec(
 8648   kind := "OPERATION",
 8649   sin := [ [ any, "x" ], [ elt-ord^inf, "y" ] ],
 8650   sou := [ [ elt-ord^inf ] ],
 8651   name := "*",
 8652   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8653   ex := [  ],
 8654   hash := "1eaf4c",
 8655   sig := "<any> x * <elt-ord^inf> y",
 8656   sog := " -> <elt-ord^inf>",
 8657   docsrc := "<internal>",
 8658   sinflat := [ any, elt-ord^inf ],
 8659   souflat := [ elt-ord^inf ],
 8660   soghash := "08787a",
 8661   sig4hash := "*(any,elt-ord^inf)" ),
 8662 rec(
 8663   kind := "OPERATION",
 8664   sin := [ [ elt-ord^inf, "x" ], [ elt-ord^inf, "y" ] ],
 8665   sou := [ [ elt-ord^inf ] ],
 8666   name := "*",
 8667   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8668   ex := [  ],
 8669   hash := "c5c1d4",
 8670   sig := "<elt-ord^inf> x * <elt-ord^inf> y",
 8671   sog := " -> <elt-ord^inf>",
 8672   docsrc := "<internal>",
 8673   sinflat := [ elt-ord^inf, elt-ord^inf ],
 8674   souflat := [ elt-ord^inf ],
 8675   soghash := "08787a",
 8676   sig4hash := "*(elt-ord^inf,elt-ord^inf)" ),
 8677 rec(
 8678   kind := "OPERATION",
 8679   sin := [ [ elt-mdl^vec, "v" ], [ elt-mdl^mat, "X" ] ],
 8680   sou := [ [ elt-mdl^vec ] ],
 8681   name := "*",
 8682   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8683   ex := [  ],
 8684   hash := "088b6b",
 8685   sig := "<elt-mdl^vec> v * <elt-mdl^mat> X",
 8686   sog := " -> <elt-mdl^vec>",
 8687   docsrc := "<internal>",
 8688   sinflat := [ elt-mdl^vec, elt-mdl^mat ],
 8689   souflat := [ elt-mdl^vec ],
 8690   soghash := "b46581",
 8691   sig4hash := "*(elt-mdl^vec,elt-mdl^mat)" ),
 8692 rec(
 8693   kind := "OPERATION",
 8694   sin := [ [ elt-mdl, "v" ], [ elt-mdl^mat, "X" ] ],
 8695   sou := [ [ elt-mdl ] ],
 8696   name := "*",
 8697   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8698   ex := [  ],
 8699   hash := "99775d",
 8700   sig := "<elt-mdl> v * <elt-mdl^mat> X",
 8701   sog := " -> <elt-mdl>",
 8702   docsrc := "<internal>",
 8703   sinflat := [ elt-mdl, elt-mdl^mat ],
 8704   souflat := [ elt-mdl ],
 8705   soghash := "97b5cd",
 8706   sig4hash := "*(elt-mdl,elt-mdl^mat)" ),
 8707 rec(
 8708   kind := "OPERATION",
 8709   sin := [ [ elt-mdl, "v" ], [ elt-alg^mat, "X" ] ],
 8710   sou := [ [ elt-mdl ] ],
 8711   name := "*",
 8712   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8713   ex := [  ],
 8714   hash := "e98dea",
 8715   sig := "<elt-mdl> v * <elt-alg^mat> X",
 8716   sog := " -> <elt-mdl>",
 8717   docsrc := "<internal>",
 8718   sinflat := [ elt-mdl, elt-alg^mat ],
 8719   souflat := [ elt-mdl ],
 8720   soghash := "97b5cd",
 8721   sig4hash := "*(elt-mdl,elt-alg^mat)" ),
 8722 rec(
 8723   kind := "OPERATION",
 8724   sin := [ [ mdl^vec, "M" ], [ elt-alg^mat, "X" ] ],
 8725   sou := [ [ mdl^vec ] ],
 8726   name := "*",
 8727   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8728   ex := [  ],
 8729   hash := "579958",
 8730   sig := "<mdl^vec> M * <elt-alg^mat> X",
 8731   sog := " -> <mdl^vec>",
 8732   docsrc := "<internal>",
 8733   sinflat := [ mdl^vec, elt-alg^mat ],
 8734   souflat := [ mdl^vec ],
 8735   soghash := "886ffa",
 8736   sig4hash := "*(mdl^vec,elt-alg^mat)" ),
 8737 rec(
 8738   kind := "OPERATION",
 8739   sin := [ [ mdl^vec, "M" ], [ elt-mdl^mat, "X" ] ],
 8740   sou := [ [ mdl^vec ] ],
 8741   name := "*",
 8742   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8743   ex := [  ],
 8744   hash := "a3fe4c",
 8745   sig := "<mdl^vec> M * <elt-mdl^mat> X",
 8746   sog := " -> <mdl^vec>",
 8747   docsrc := "<internal>",
 8748   sinflat := [ mdl^vec, elt-mdl^mat ],
 8749   souflat := [ mdl^vec ],
 8750   soghash := "886ffa",
 8751   sig4hash := "*(mdl^vec,elt-mdl^mat)" ),
 8752 rec(
 8753   kind := "OPERATION",
 8754   sin := [ [ seq(), "A" ], [ seq(), "B" ] ],
 8755   sou := [ [ seq() ] ],
 8756   name := "*",
 8757   short := "The product of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 8758   ex := [  ],
 8759   hash := "b9714c",
 8760   sig := "<seq()> A * <seq()> B",
 8761   sog := " -> <seq()>",
 8762   docsrc := "<internal>",
 8763   sinflat := [ seq(), seq() ],
 8764   souflat := [ seq() ],
 8765   soghash := "4bf3a0",
 8766   sig4hash := "*(seq(),seq())" ),
 8767 rec(
 8768   kind := "OPERATION",
 8769   sin := [ [ elt-grp^abl, "x" ], [ elt-ord^rat, "p" ] ],
 8770   sou := [ [ elt-grp^abl ] ],
 8771   name := "*",
 8772   short := "The scalar product p * x (i.e., the power x^p in additive notation).",
 8773   ex := [  ],
 8774   hash := "1b29b5",
 8775   sig := "<elt-grp^abl> x * <elt-ord^rat> p",
 8776   sog := " -> <elt-grp^abl>",
 8777   docsrc := "<internal>",
 8778   sinflat := [ elt-grp^abl, elt-ord^rat ],
 8779   souflat := [ elt-grp^abl ],
 8780   soghash := "b42d93",
 8781   sig4hash := "*(elt-grp^abl,elt-ord^rat)" ),
 8782 rec(
 8783   kind := "OPERATION",
 8784   sin := [ [ elt-ord^rat, "p" ], [ elt-grp^abl, "x" ] ],
 8785   sou := [ [ elt-grp^abl ] ],
 8786   name := "*",
 8787   short := "The scalar product p * x (i.e., the power x^p in additive notation).",
 8788   ex := [  ],
 8789   hash := "8646f9",
 8790   sig := "<elt-ord^rat> p * <elt-grp^abl> x",
 8791   sog := " -> <elt-grp^abl>",
 8792   docsrc := "<internal>",
 8793   sinflat := [ elt-ord^rat, elt-grp^abl ],
 8794   souflat := [ elt-grp^abl ],
 8795   soghash := "b42d93",
 8796   sig4hash := "*(elt-ord^rat,elt-grp^abl)" ),
 8797 rec(
 8798   kind := "OPERATION",
 8799   sin := [ [ elt-mdl^mat, "X" ], [ elt-rng, "c" ] ],
 8800   sou := [ [ elt-mdl^mat ] ],
 8801   name := "*",
 8802   short := "Product of X and the scalar c",
 8803   ex := [  ],
 8804   hash := "135a15",
 8805   sig := "<elt-mdl^mat> X * <elt-rng> c",
 8806   sog := " -> <elt-mdl^mat>",
 8807   docsrc := "<internal>",
 8808   sinflat := [ elt-mdl^mat, elt-rng ],
 8809   souflat := [ elt-mdl^mat ],
 8810   soghash := "5284ac",
 8811   sig4hash := "*(elt-mdl^mat,elt-rng)" ),
 8812 rec(
 8813   kind := "OPERATION",
 8814   sin := [ [ elt-rng, "c" ], [ elt-mdl^mat, "X" ] ],
 8815   sou := [ [ elt-mdl^mat ] ],
 8816   name := "*",
 8817   short := "Product of X and the scalar c",
 8818   ex := [  ],
 8819   hash := "7e460e",
 8820   sig := "<elt-rng> c * <elt-mdl^mat> X",
 8821   sog := " -> <elt-mdl^mat>",
 8822   docsrc := "<internal>",
 8823   sinflat := [ elt-rng, elt-mdl^mat ],
 8824   souflat := [ elt-mdl^mat ],
 8825   soghash := "5284ac",
 8826   sig4hash := "*(elt-rng,elt-mdl^mat)" ),
 8827 rec(
 8828   kind := "OPERATION",
 8829   sin := [ [ elt-mdl^vec, "u" ], [ elt-rng, "c" ] ],
 8830   sou := [ [ elt-mdl^vec ] ],
 8831   name := "*",
 8832   short := "Product of u and the scalar c.",
 8833   ex := [  ],
 8834   hash := "103b26",
 8835   sig := "<elt-mdl^vec> u * <elt-rng> c",
 8836   sog := " -> <elt-mdl^vec>",
 8837   docsrc := "<internal>",
 8838   sinflat := [ elt-mdl^vec, elt-rng ],
 8839   souflat := [ elt-mdl^vec ],
 8840   soghash := "b46581",
 8841   sig4hash := "*(elt-mdl^vec,elt-rng)" ),
 8842 rec(
 8843   kind := "OPERATION",
 8844   sin := [ [ elt-rng, "c" ], [ elt-mdl^vec, "u" ] ],
 8845   sou := [ [ elt-mdl^vec ] ],
 8846   name := "*",
 8847   short := "Product of u and the scalar c.",
 8848   ex := [  ],
 8849   hash := "268863",
 8850   sig := "<elt-rng> c * <elt-mdl^vec> u",
 8851   sog := " -> <elt-mdl^vec>",
 8852   docsrc := "<internal>",
 8853   sinflat := [ elt-rng, elt-mdl^vec ],
 8854   souflat := [ elt-mdl^vec ],
 8855   soghash := "b46581",
 8856   sig4hash := "*(elt-rng,elt-mdl^vec)" ),
 8857 rec(
 8858   kind := "OPERATION",
 8859   sin := [ [ elt-mdl, "u" ], [ elt-rng, "c" ] ],
 8860   sou := [ [ elt-mdl ] ],
 8861   name := "*",
 8862   short := "Product of u and the scalar c.",
 8863   ex := [  ],
 8864   hash := "c00cab",
 8865   sig := "<elt-mdl> u * <elt-rng> c",
 8866   sog := " -> <elt-mdl>",
 8867   docsrc := "<internal>",
 8868   sinflat := [ elt-mdl, elt-rng ],
 8869   souflat := [ elt-mdl ],
 8870   soghash := "97b5cd",
 8871   sig4hash := "*(elt-mdl,elt-rng)" ),
 8872 rec(
 8873   kind := "OPERATION",
 8874   sin := [ [ elt-rng, "c" ], [ elt-mdl, "u" ] ],
 8875   sou := [ [ elt-mdl ] ],
 8876   name := "*",
 8877   short := "Product of u and the scalar c.",
 8878   ex := [  ],
 8879   hash := "7646a5",
 8880   sig := "<elt-rng> c * <elt-mdl> u",
 8881   sog := " -> <elt-mdl>",
 8882   docsrc := "<internal>",
 8883   sinflat := [ elt-rng, elt-mdl ],
 8884   souflat := [ elt-mdl ],
 8885   soghash := "97b5cd",
 8886   sig4hash := "*(elt-rng,elt-mdl)" ),
 8887 rec(
 8888   kind := "OPERATION",
 8889   sin := [ [ elt-rng, "c" ], [ elt-mdl^ded, "u" ] ],
 8890   sou := [ [ elt-mdl^ded ] ],
 8891   name := "*",
 8892   short := "Product of u and the scalar c.",
 8893   ex := [  ],
 8894   hash := "86055e",
 8895   sig := "<elt-rng> c * <elt-mdl^ded> u",
 8896   sog := " -> <elt-mdl^ded>",
 8897   docsrc := "<internal>",
 8898   sinflat := [ elt-rng, elt-mdl^ded ],
 8899   souflat := [ elt-mdl^ded ],
 8900   soghash := "2fccf1",
 8901   sig4hash := "*(elt-rng,elt-mdl^ded)" ),
 8902 rec(
 8903   kind := "OPERATION",
 8904   sin := [ [ elt-mdl^ded, "u" ], [ elt-rng, "c" ] ],
 8905   sou := [ [ elt-mdl^ded ] ],
 8906   name := "*",
 8907   short := "Product of u and the scalar c.",
 8908   ex := [  ],
 8909   hash := "062463",
 8910   sig := "<elt-mdl^ded> u * <elt-rng> c",
 8911   sog := " -> <elt-mdl^ded>",
 8912   docsrc := "<internal>",
 8913   sinflat := [ elt-mdl^ded, elt-rng ],
 8914   souflat := [ elt-mdl^ded ],
 8915   soghash := "2fccf1",
 8916   sig4hash := "*(elt-mdl^ded,elt-rng)" ),
 8917 rec(
 8918   kind := "OPERATION",
 8919   sin := [ [ map(), "f" ], [ map(), "g" ] ],
 8920   sou := [ [ map() ] ],
 8921   name := "*",
 8922   short := "The composition of maps f and g.",
 8923   ex := [  ],
 8924   hash := "8bab25",
 8925   sig := "<map()> f * <map()> g",
 8926   sog := " -> <map()>",
 8927   docsrc := "<internal>",
 8928   sinflat := [ map(), map() ],
 8929   souflat := [ map() ],
 8930   soghash := "63931a",
 8931   sig4hash := "*(map(),map())" ),
 8932 rec(
 8933   kind := "OPERATION",
 8934   sin := [ [ ord^num, "O" ], [ elt-rng, "e" ] ],
 8935   sou := [ [ elt-ids^fra/ord^num ] ],
 8936   name := "*",
 8937   short := "The ideal e*O.",
 8938   ex := [  ],
 8939   hash := "6bcd2e",
 8940   sig := "<ord^num> O * <elt-rng> e",
 8941   sog := " -> <elt-ids^fra/ord^num>",
 8942   docsrc := "<internal>",
 8943   sinflat := [ ord^num, elt-rng ],
 8944   souflat := [ elt-ids^fra/ord^num ],
 8945   soghash := "ca011c",
 8946   sig4hash := "*(ord^num,elt-rng)" ),
 8947 rec(
 8948   kind := "OPERATION",
 8949   sin := [ [ elt-rng, "e" ], [ ord^num, "O" ] ],
 8950   sou := [ [ elt-ids^fra/ord^num ] ],
 8951   name := "*",
 8952   short := "The ideal e*O.",
 8953   ex := [  ],
 8954   hash := "9d9291",
 8955   sig := "<elt-rng> e * <ord^num> O",
 8956   sog := " -> <elt-ids^fra/ord^num>",
 8957   docsrc := "<internal>",
 8958   sinflat := [ elt-rng, ord^num ],
 8959   souflat := [ elt-ids^fra/ord^num ],
 8960   soghash := "ca011c",
 8961   sig4hash := "*(elt-rng,ord^num)" ),
 8962 rec(
 8963   kind := "OPERATION",
 8964   sin := [ [ ord^fun, "O" ], [ elt-rng, "e" ] ],
 8965   sou := [ [ elt-ids^int/ord^fun ] ],
 8966   name := "*",
 8967   short := "The ideal e*O.",
 8968   ex := [  ],
 8969   hash := "a3f4c7",
 8970   sig := "<ord^fun> O * <elt-rng> e",
 8971   sog := " -> <elt-ids^int/ord^fun>",
 8972   docsrc := "<internal>",
 8973   sinflat := [ ord^fun, elt-rng ],
 8974   souflat := [ elt-ids^int/ord^fun ],
 8975   soghash := "918914",
 8976   sig4hash := "*(ord^fun,elt-rng)" ),
 8977 rec(
 8978   kind := "OPERATION",
 8979   sin := [ [ elt-rng, "e" ], [ ord^fun, "O" ] ],
 8980   sou := [ [ elt-ids^int/ord^fun ] ],
 8981   name := "*",
 8982   short := "The ideal e*O.",
 8983   ex := [  ],
 8984   hash := "b39c6c",
 8985   sig := "<elt-rng> e * <ord^fun> O",
 8986   sog := " -> <elt-ids^int/ord^fun>",
 8987   docsrc := "<internal>",
 8988   sinflat := [ elt-rng, ord^fun ],
 8989   souflat := [ elt-ids^int/ord^fun ],
 8990   soghash := "918914",
 8991   sig4hash := "*(elt-rng,ord^fun)" ),
 8992 rec(
 8993   kind := "OPERATION",
 8994   sin := [ [ elt-rng, "c" ], [ elt-ids^fra/ord^num, "I" ] ],
 8995   sou := [ [ elt-ids^fra/ord^num ] ],
 8996   name := "*",
 8997   short := "Product of the ideal I and the scalar c.",
 8998   ex := [  ],
 8999   hash := "c2fce0",
 9000   sig := "<elt-rng> c * <elt-ids^fra/ord^num> I",
 9001   sog := " -> <elt-ids^fra/ord^num>",
 9002   docsrc := "<internal>",
 9003   sinflat := [ elt-rng, elt-ids^fra/ord^num ],
 9004   souflat := [ elt-ids^fra/ord^num ],
 9005   soghash := "ca011c",
 9006   sig4hash := "*(elt-rng,elt-ids^fra/ord^num)" ),
 9007 rec(
 9008   kind := "OPERATION",
 9009   sin := [ [ elt-ids^fra/ord^num, "I" ], [ elt-rng, "c" ] ],
 9010   sou := [ [ elt-ids^fra/ord^num ] ],
 9011   name := "*",
 9012   short := "Product of the ideal I and the scalar c.",
 9013   ex := [  ],
 9014   hash := "e5b910",
 9015   sig := "<elt-ids^fra/ord^num> I * <elt-rng> c",
 9016   sog := " -> <elt-ids^fra/ord^num>",
 9017   docsrc := "<internal>",
 9018   sinflat := [ elt-ids^fra/ord^num, elt-rng ],
 9019   souflat := [ elt-ids^fra/ord^num ],
 9020   soghash := "ca011c",
 9021   sig4hash := "*(elt-ids^fra/ord^num,elt-rng)" ),
 9022 rec(
 9023   kind := "OPERATION",
 9024   sin := [ [ elt-rng, "c" ], [ elt-ids^int/ord^fun, "I" ] ],
 9025   sou := [ [ elt-ids^int/ord^fun ] ],
 9026   name := "*",
 9027   short := "Product of the ideal I and the scalar c.",
 9028   ex := [  ],
 9029   hash := "187ae4",
 9030   sig := "<elt-rng> c * <elt-ids^int/ord^fun> I",
 9031   sog := " -> <elt-ids^int/ord^fun>",
 9032   docsrc := "<internal>",
 9033   sinflat := [ elt-rng, elt-ids^int/ord^fun ],
 9034   souflat := [ elt-ids^int/ord^fun ],
 9035   soghash := "918914",
 9036   sig4hash := "*(elt-rng,elt-ids^int/ord^fun)" ),
 9037 rec(
 9038   kind := "OPERATION",
 9039   sin := [ [ elt-ids^int/ord^fun, "I" ], [ elt-rng, "c" ] ],
 9040   sou := [ [ elt-ids^int/ord^fun ] ],
 9041   name := "*",
 9042   short := "Product of the ideal I and the scalar c.",
 9043   ex := [  ],
 9044   hash := "42f968",
 9045   sig := "<elt-ids^int/ord^fun> I * <elt-rng> c",
 9046   sog := " -> <elt-ids^int/ord^fun>",
 9047   docsrc := "<internal>",
 9048   sinflat := [ elt-ids^int/ord^fun, elt-rng ],
 9049   souflat := [ elt-ids^int/ord^fun ],
 9050   soghash := "918914",
 9051   sig4hash := "*(elt-ids^int/ord^fun,elt-rng)" ),
 9052 rec(
 9053   kind := "OPERATION",
 9054   sin := [ [ elt-ord^rat, "x" ], [ elt-dvs/fld^fun, "D" ] ],
 9055   sou := [ [ elt-ord^rat ] ],
 9056   name := "*",
 9057   short := "The product of the integer x and the divisor D or place P.",
 9058   ex := [  ],
 9059   hash := "2dd4da",
 9060   sig := "<elt-ord^rat> x * <elt-dvs/fld^fun> D",
 9061   sog := " -> <elt-ord^rat>",
 9062   docsrc := "<internal>",
 9063   sinflat := [ elt-ord^rat, elt-dvs/fld^fun ],
 9064   souflat := [ elt-ord^rat ],
 9065   soghash := "898213",
 9066   sig4hash := "*(elt-ord^rat,elt-dvs/fld^fun)" ),
 9067 rec(
 9068   kind := "OPERATION",
 9069   sin := [ [ elt-ord^rat, "x" ], [ elt-pls/fld^fun, "P" ] ],
 9070   sou := [ [ elt-dvs/fld^fun ] ],
 9071   name := "*",
 9072   short := "The product of the integer x and the divisor D or place P.",
 9073   ex := [  ],
 9074   hash := "141812",
 9075   sig := "<elt-ord^rat> x * <elt-pls/fld^fun> P",
 9076   sog := " -> <elt-dvs/fld^fun>",
 9077   docsrc := "<internal>",
 9078   sinflat := [ elt-ord^rat, elt-pls/fld^fun ],
 9079   souflat := [ elt-dvs/fld^fun ],
 9080   soghash := "34cafb",
 9081   sig4hash := "*(elt-ord^rat,elt-pls/fld^fun)" ),
 9082 rec(
 9083   kind := "OPERATION",
 9084   sin := [ [ elt-ids^int/ord^num, "I" ], [ elt-mdl^ded, "u" ] ],
 9085   sou := [ [ mdl^ded ] ],
 9086   name := "*",
 9087   short := "the module I*u.",
 9088   ex := [  ],
 9089   hash := "6869ff",
 9090   sig := "<elt-ids^int/ord^num> I * <elt-mdl^ded> u",
 9091   sog := " -> <mdl^ded>",
 9092   docsrc := "<internal>",
 9093   sinflat := [ elt-ids^int/ord^num, elt-mdl^ded ],
 9094   souflat := [ mdl^ded ],
 9095   soghash := "5ba52c",
 9096   sig4hash := "*(elt-ids^int/ord^num,elt-mdl^ded)" ),
 9097 rec(
 9098   kind := "OPERATION",
 9099   sin := [ [ elt-mdl^ded, "u" ], [ elt-ids^int/ord^num, "I" ] ],
 9100   sou := [ [ mdl^ded ] ],
 9101   name := "*",
 9102   short := "the module I*u.",
 9103   ex := [  ],
 9104   hash := "e0443c",
 9105   sig := "<elt-mdl^ded> u * <elt-ids^int/ord^num> I",
 9106   sog := " -> <mdl^ded>",
 9107   docsrc := "<internal>",
 9108   sinflat := [ elt-mdl^ded, elt-ids^int/ord^num ],
 9109   souflat := [ mdl^ded ],
 9110   soghash := "5ba52c",
 9111   sig4hash := "*(elt-mdl^ded,elt-ids^int/ord^num)" ),
 9112 rec(
 9113   kind := "OPERATION",
 9114   sin := [ [ elt-ids^int/ord^fun, "I" ], [ elt-mdl^ded, "u" ] ],
 9115   sou := [ [ mdl^ded ] ],
 9116   name := "*",
 9117   short := "the module I*u.",
 9118   ex := [  ],
 9119   hash := "1a0a18",
 9120   sig := "<elt-ids^int/ord^fun> I * <elt-mdl^ded> u",
 9121   sog := " -> <mdl^ded>",
 9122   docsrc := "<internal>",
 9123   sinflat := [ elt-ids^int/ord^fun, elt-mdl^ded ],
 9124   souflat := [ mdl^ded ],
 9125   soghash := "5ba52c",
 9126   sig4hash := "*(elt-ids^int/ord^fun,elt-mdl^ded)" ),
 9127 rec(
 9128   kind := "OPERATION",
 9129   sin := [ [ elt-mdl^ded, "u" ], [ elt-ids^int/ord^fun, "I" ] ],
 9130   sou := [ [ mdl^ded ] ],
 9131   name := "*",
 9132   short := "the module I*u.",
 9133   ex := [  ],
 9134   hash := "ee8c2e",
 9135   sig := "<elt-mdl^ded> u * <elt-ids^int/ord^fun> I",
 9136   sog := " -> <mdl^ded>",
 9137   docsrc := "<internal>",
 9138   sinflat := [ elt-mdl^ded, elt-ids^int/ord^fun ],
 9139   souflat := [ mdl^ded ],
 9140   soghash := "5ba52c",
 9141   sig4hash := "*(elt-mdl^ded,elt-ids^int/ord^fun)" ),
 9142 rec(
 9143   kind := "OPERATION",
 9144   sin := [ [ mdl^ded, "M" ], [ elt-ids^int/ord^num, "I" ] ],
 9145   sou := [ [ mdl^ded ] ],
 9146   name := "*",
 9147   short := "the module I*M.",
 9148   ex := [  ],
 9149   hash := "ce5458",
 9150   sig := "<mdl^ded> M * <elt-ids^int/ord^num> I",
 9151   sog := " -> <mdl^ded>",
 9152   docsrc := "<internal>",
 9153   sinflat := [ mdl^ded, elt-ids^int/ord^num ],
 9154   souflat := [ mdl^ded ],
 9155   soghash := "5ba52c",
 9156   sig4hash := "*(mdl^ded,elt-ids^int/ord^num)" ),
 9157 rec(
 9158   kind := "OPERATION",
 9159   sin := [ [ elt-ids^int/ord^num, "I" ], [ mdl^ded, "M" ] ],
 9160   sou := [ [ mdl^ded ] ],
 9161   name := "*",
 9162   short := "the module I*M.",
 9163   ex := [  ],
 9164   hash := "487c0f",
 9165   sig := "<elt-ids^int/ord^num> I * <mdl^ded> M",
 9166   sog := " -> <mdl^ded>",
 9167   docsrc := "<internal>",
 9168   sinflat := [ elt-ids^int/ord^num, mdl^ded ],
 9169   souflat := [ mdl^ded ],
 9170   soghash := "5ba52c",
 9171   sig4hash := "*(elt-ids^int/ord^num,mdl^ded)" ),
 9172 rec(
 9173   kind := "OPERATION",
 9174   sin := [ [ mdl^ded, "M" ], [ elt-ids^int/ord^fun, "I" ] ],
 9175   sou := [ [ mdl^ded ] ],
 9176   name := "*",
 9177   short := "the module I*M.",
 9178   ex := [  ],
 9179   hash := "a8a50b",
 9180   sig := "<mdl^ded> M * <elt-ids^int/ord^fun> I",
 9181   sog := " -> <mdl^ded>",
 9182   docsrc := "<internal>",
 9183   sinflat := [ mdl^ded, elt-ids^int/ord^fun ],
 9184   souflat := [ mdl^ded ],
 9185   soghash := "5ba52c",
 9186   sig4hash := "*(mdl^ded,elt-ids^int/ord^fun)" ),
 9187 rec(
 9188   kind := "OPERATION",
 9189   sin := [ [ elt-ids^int/ord^fun, "I" ], [ mdl^ded, "M" ] ],
 9190   sou := [ [ mdl^ded ] ],
 9191   name := "*",
 9192   short := "the module I*M.",
 9193   ex := [  ],
 9194   hash := "63c9db",
 9195   sig := "<elt-ids^int/ord^fun> I * <mdl^ded> M",
 9196   sog := " -> <mdl^ded>",
 9197   docsrc := "<internal>",
 9198   sinflat := [ elt-ids^int/ord^fun, mdl^ded ],
 9199   souflat := [ mdl^ded ],
 9200   soghash := "5ba52c",
 9201   sig4hash := "*(elt-ids^int/ord^fun,mdl^ded)" ),
 9202 rec(
 9203   kind := "OPERATION",
 9204   sin := [ [ elt-rng, "a" ], [ mdl^ded, "M" ] ],
 9205   sou := [ [ mdl^ded ] ],
 9206   name := "*",
 9207   short := "the module a*M.",
 9208   ex := [  ],
 9209   hash := "3943fc",
 9210   sig := "<elt-rng> a * <mdl^ded> M",
 9211   sog := " -> <mdl^ded>",
 9212   docsrc := "<internal>",
 9213   sinflat := [ elt-rng, mdl^ded ],
 9214   souflat := [ mdl^ded ],
 9215   soghash := "5ba52c",
 9216   sig4hash := "*(elt-rng,mdl^ded)" ),
 9217 rec(
 9218   kind := "OPERATION",
 9219   sin := [ [ mdl^ded, "M" ], [ elt-rng, "a" ] ],
 9220   sou := [ [ mdl^ded ] ],
 9221   name := "*",
 9222   short := "the module a*M.",
 9223   ex := [  ],
 9224   hash := "c5f8b8",
 9225   sig := "<mdl^ded> M * <elt-rng> a",
 9226   sog := " -> <mdl^ded>",
 9227   docsrc := "<internal>",
 9228   sinflat := [ mdl^ded, elt-rng ],
 9229   souflat := [ mdl^ded ],
 9230   soghash := "5ba52c",
 9231   sig4hash := "*(mdl^ded,elt-rng)" ),
 9232 rec(
 9233   kind := "OPERATION",
 9234   sin := [ [ elt-dvs/fld^num, "d" ], [ elt-ord^rat, "k" ] ],
 9235   sou := [ [ elt-dvs/fld^num ] ],
 9236   name := "*",
 9237   short := "k lots of the divisor d of a number field.",
 9238   ex := [  ],
 9239   hash := "60328f",
 9240   sig := "<elt-dvs/fld^num> d * <elt-ord^rat> k",
 9241   sog := " -> <elt-dvs/fld^num>",
 9242   docsrc := "<internal>",
 9243   sinflat := [ elt-dvs/fld^num, elt-ord^rat ],
 9244   souflat := [ elt-dvs/fld^num ],
 9245   soghash := "87f535",
 9246   sig4hash := "*(elt-dvs/fld^num,elt-ord^rat)" ),
 9247 rec(
 9248   kind := "OPERATION",
 9249   sin := [ [ elt-ord^rat, "k" ], [ elt-dvs/fld^num, "d" ] ],
 9250   sou := [ [ elt-dvs/fld^num ] ],
 9251   name := "*",
 9252   short := "k lots of the divisor d of a number field.",
 9253   ex := [  ],
 9254   hash := "8dd900",
 9255   sig := "<elt-ord^rat> k * <elt-dvs/fld^num> d",
 9256   sog := " -> <elt-dvs/fld^num>",
 9257   docsrc := "<internal>",
 9258   sinflat := [ elt-ord^rat, elt-dvs/fld^num ],
 9259   souflat := [ elt-dvs/fld^num ],
 9260   soghash := "87f535",
 9261   sig4hash := "*(elt-ord^rat,elt-dvs/fld^num)" ),
 9262 rec(
 9263   kind := "OPERATION",
 9264   sin := [ [ elt-pls/fld^num, "p" ], [ elt-ord^rat, "k" ] ],
 9265   sou := [ [ elt-dvs/fld^num ] ],
 9266   name := "*",
 9267   short := "k lots of the divisor d of a number field.",
 9268   ex := [  ],
 9269   hash := "09db15",
 9270   sig := "<elt-pls/fld^num> p * <elt-ord^rat> k",
 9271   sog := " -> <elt-dvs/fld^num>",
 9272   docsrc := "<internal>",
 9273   sinflat := [ elt-pls/fld^num, elt-ord^rat ],
 9274   souflat := [ elt-dvs/fld^num ],
 9275   soghash := "87f535",
 9276   sig4hash := "*(elt-pls/fld^num,elt-ord^rat)" ),
 9277 rec(
 9278   kind := "OPERATION",
 9279   sin := [ [ elt-ord^rat, "k" ], [ elt-pls/fld^num, "p" ] ],
 9280   sou := [ [ elt-dvs/fld^num ] ],
 9281   name := "*",
 9282   short := "k lots of the divisor d of a number field.",
 9283   ex := [  ],
 9284   hash := "03e031",
 9285   sig := "<elt-ord^rat> k * <elt-pls/fld^num> p",
 9286   sog := " -> <elt-dvs/fld^num>",
 9287   docsrc := "<internal>",
 9288   sinflat := [ elt-ord^rat, elt-pls/fld^num ],
 9289   souflat := [ elt-dvs/fld^num ],
 9290   soghash := "87f535",
 9291   sig4hash := "*(elt-ord^rat,elt-pls/fld^num)" ),
 9292 rec(
 9293   kind := "OPERATION",
 9294   sin := [ [ elt-mdl^vec, "x" ], [ elt-mdl^vec, "y" ] ],
 9295   sou := [ [ elt-mdl^vec ] ],
 9296   name := "*",
 9297   short := "The componentwise product of x and y.",
 9298   ex := [  ],
 9299   hash := "dea687",
 9300   sig := "<elt-mdl^vec> x * <elt-mdl^vec> y",
 9301   sog := " -> <elt-mdl^vec>",
 9302   docsrc := "<internal>",
 9303   sinflat := [ elt-mdl^vec, elt-mdl^vec ],
 9304   souflat := [ elt-mdl^vec ],
 9305   soghash := "b46581",
 9306   sig4hash := "*(elt-mdl^vec,elt-mdl^vec)" ),
 9307 rec(
 9308   kind := "OPERATION",
 9309   sin := [ [ elt-ord^rat, "x" ], [ elt-ord^rat, "y" ] ],
 9310   sou := [ [ elt-ord^rat ] ],
 9311   name := "+",
 9312   short := "Sum of x and y.",
 9313   ex := [  ],
 9314   hash := "6a788f",
 9315   sig := "<elt-ord^rat> x + <elt-ord^rat> y",
 9316   sog := " -> <elt-ord^rat>",
 9317   docsrc := "<internal>",
 9318   sinflat := [ elt-ord^rat, elt-ord^rat ],
 9319   souflat := [ elt-ord^rat ],
 9320   soghash := "898213",
 9321   sig4hash := "+(elt-ord^rat,elt-ord^rat)" ),
 9322 rec(
 9323   kind := "OPERATION",
 9324   sin := [ [ elt-fld^rat, "x" ], [ elt-fld^rat, "y" ] ],
 9325   sou := [ [ elt-fld^rat ] ],
 9326   name := "+",
 9327   short := "Sum of x and y.",
 9328   ex := [  ],
 9329   hash := "885945",
 9330   sig := "<elt-fld^rat> x + <elt-fld^rat> y",
 9331   sog := " -> <elt-fld^rat>",
 9332   docsrc := "<internal>",
 9333   sinflat := [ elt-fld^rat, elt-fld^rat ],
 9334   souflat := [ elt-fld^rat ],
 9335   soghash := "89f5fc",
 9336   sig4hash := "+(elt-fld^rat,elt-fld^rat)" ),
 9337 rec(
 9338   kind := "OPERATION",
 9339   sin := [ [ elt-alg^pol, "x" ], [ elt-alg^pol, "y" ] ],
 9340   sou := [ [ elt-alg^pol ] ],
 9341   name := "+",
 9342   short := "Sum of x and y.",
 9343   ex := [  ],
 9344   hash := "a9c98d",
 9345   sig := "<elt-alg^pol> x + <elt-alg^pol> y",
 9346   sog := " -> <elt-alg^pol>",
 9347   docsrc := "<internal>",
 9348   sinflat := [ elt-alg^pol, elt-alg^pol ],
 9349   souflat := [ elt-alg^pol ],
 9350   soghash := "ba7338",
 9351   sig4hash := "+(elt-alg^pol,elt-alg^pol)" ),
 9352 rec(
 9353   kind := "OPERATION",
 9354   sin := [ [ elt-fld^pol, "x" ], [ elt-fld^pol, "y" ] ],
 9355   sou := [ [ elt-fld^pol ] ],
 9356   name := "+",
 9357   short := "Sum of x and y.",
 9358   ex := [  ],
 9359   hash := "006396",
 9360   sig := "<elt-fld^pol> x + <elt-fld^pol> y",
 9361   sog := " -> <elt-fld^pol>",
 9362   docsrc := "<internal>",
 9363   sinflat := [ elt-fld^pol, elt-fld^pol ],
 9364   souflat := [ elt-fld^pol ],
 9365   soghash := "540d59",
 9366   sig4hash := "+(elt-fld^pol,elt-fld^pol)" ),
 9367 rec(
 9368   kind := "OPERATION",
 9369   sin := [ [ elt-rng, "x" ], [ elt-rng, "y" ] ],
 9370   sou := [ [ elt-rng ] ],
 9371   name := "+",
 9372   short := "Sum of x and y.",
 9373   ex := [  ],
 9374   hash := "5e69c1",
 9375   sig := "<elt-rng> x + <elt-rng> y",
 9376   sog := " -> <elt-rng>",
 9377   docsrc := "<internal>",
 9378   sinflat := [ elt-rng, elt-rng ],
 9379   souflat := [ elt-rng ],
 9380   soghash := "7ef0ef",
 9381   sig4hash := "+(elt-rng,elt-rng)" ),
 9382 rec(
 9383   kind := "OPERATION",
 9384   sin := [ [ elt-res^pol, "x" ], [ elt-res^pol, "y" ] ],
 9385   sou := [ [ elt-res^pol ] ],
 9386   name := "+",
 9387   short := "Sum of x and y.",
 9388   ex := [  ],
 9389   hash := "90cf6e",
 9390   sig := "<elt-res^pol> x + <elt-res^pol> y",
 9391   sog := " -> <elt-res^pol>",
 9392   docsrc := "<internal>",
 9393   sinflat := [ elt-res^pol, elt-res^pol ],
 9394   souflat := [ elt-res^pol ],
 9395   soghash := "8ffe0c",
 9396   sig4hash := "+(elt-res^pol,elt-res^pol)" ),
 9397 rec(
 9398   kind := "OPERATION",
 9399   sin := [ [ elt-alg^mat, "x" ], [ elt-alg^mat, "y" ] ],
 9400   sou := [ [ elt-alg^mat ] ],
 9401   name := "+",
 9402   short := "Sum of x and y.",
 9403   ex := [  ],
 9404   hash := "14eea5",
 9405   sig := "<elt-alg^mat> x + <elt-alg^mat> y",
 9406   sog := " -> <elt-alg^mat>",
 9407   docsrc := "<internal>",
 9408   sinflat := [ elt-alg^mat, elt-alg^mat ],
 9409   souflat := [ elt-alg^mat ],
 9410   soghash := "8dbb64",
 9411   sig4hash := "+(elt-alg^mat,elt-alg^mat)" ),
 9412 rec(
 9413   kind := "OPERATION",
 9414   sin := [ [ elt-mdl^vec, "x" ], [ elt-mdl^vec, "y" ] ],
 9415   sou := [ [ elt-mdl^vec ] ],
 9416   name := "+",
 9417   short := "Sum of x and y.",
 9418   ex := [  ],
 9419   hash := "fdb426",
 9420   sig := "<elt-mdl^vec> x + <elt-mdl^vec> y",
 9421   sog := " -> <elt-mdl^vec>",
 9422   docsrc := "<internal>",
 9423   sinflat := [ elt-mdl^vec, elt-mdl^vec ],
 9424   souflat := [ elt-mdl^vec ],
 9425   soghash := "b46581",
 9426   sig4hash := "+(elt-mdl^vec,elt-mdl^vec)" ),
 9427 rec(
 9428   kind := "OPERATION",
 9429   sin := [ [ elt-mdl^mat, "x" ], [ elt-mdl^mat, "y" ] ],
 9430   sou := [ [ elt-mdl^mat ] ],
 9431   name := "+",
 9432   short := "Sum of x and y.",
 9433   ex := [  ],
 9434   hash := "d1103e",
 9435   sig := "<elt-mdl^mat> x + <elt-mdl^mat> y",
 9436   sog := " -> <elt-mdl^mat>",
 9437   docsrc := "<internal>",
 9438   sinflat := [ elt-mdl^mat, elt-mdl^mat ],
 9439   souflat := [ elt-mdl^mat ],
 9440   soghash := "5284ac",
 9441   sig4hash := "+(elt-mdl^mat,elt-mdl^mat)" ),
 9442 rec(
 9443   kind := "OPERATION",
 9444   sin := [ [ elt-mdl, "x" ], [ elt-mdl, "y" ] ],
 9445   sou := [ [ elt-mdl ] ],
 9446   name := "+",
 9447   short := "Sum of x and y.",
 9448   ex := [  ],
 9449   hash := "e8fd95",
 9450   sig := "<elt-mdl> x + <elt-mdl> y",
 9451   sog := " -> <elt-mdl>",
 9452   docsrc := "<internal>",
 9453   sinflat := [ elt-mdl, elt-mdl ],
 9454   souflat := [ elt-mdl ],
 9455   soghash := "97b5cd",
 9456   sig4hash := "+(elt-mdl,elt-mdl)" ),
 9457 rec(
 9458   kind := "OPERATION",
 9459   sin := [ [ elt-fld^rea, "x" ], [ elt-fld^rea, "y" ] ],
 9460   sou := [ [ elt-fld^rea ] ],
 9461   name := "+",
 9462   short := "Sum of x and y.",
 9463   ex := [  ],
 9464   hash := "bbfd6e",
 9465   sig := "<elt-fld^rea> x + <elt-fld^rea> y",
 9466   sog := " -> <elt-fld^rea>",
 9467   docsrc := "<internal>",
 9468   sinflat := [ elt-fld^rea, elt-fld^rea ],
 9469   souflat := [ elt-fld^rea ],
 9470   soghash := "7f2490",
 9471   sig4hash := "+(elt-fld^rea,elt-fld^rea)" ),
 9472 rec(
 9473   kind := "OPERATION",
 9474   sin := [ [ elt-fld^com, "x" ], [ elt-fld^com, "y" ] ],
 9475   sou := [ [ elt-fld^com ] ],
 9476   name := "+",
 9477   short := "Sum of x and y.",
 9478   ex := [  ],
 9479   hash := "9aa461",
 9480   sig := "<elt-fld^com> x + <elt-fld^com> y",
 9481   sog := " -> <elt-fld^com>",
 9482   docsrc := "<internal>",
 9483   sinflat := [ elt-fld^com, elt-fld^com ],
 9484   souflat := [ elt-fld^com ],
 9485   soghash := "0d772f",
 9486   sig4hash := "+(elt-fld^com,elt-fld^com)" ),
 9487 rec(
 9488   kind := "OPERATION",
 9489   sin := [ [ elt-fld^fin, "x" ], [ elt-fld^fin, "y" ] ],
 9490   sou := [ [ elt-fld^fin ] ],
 9491   name := "+",
 9492   short := "Sum of x and y.",
 9493   ex := [  ],
 9494   hash := "94dbb3",
 9495   sig := "<elt-fld^fin> x + <elt-fld^fin> y",
 9496   sog := " -> <elt-fld^fin>",
 9497   docsrc := "<internal>",
 9498   sinflat := [ elt-fld^fin, elt-fld^fin ],
 9499   souflat := [ elt-fld^fin ],
 9500   soghash := "97e752",
 9501   sig4hash := "+(elt-fld^fin,elt-fld^fin)" ),
 9502 rec(
 9503   kind := "OPERATION",
 9504   sin := [ [ elt-res^rat, "x" ], [ elt-res^rat, "y" ] ],
 9505   sou := [ [ elt-res^rat ] ],
 9506   name := "+",
 9507   short := "Sum of x and y.",
 9508   ex := [  ],
 9509   hash := "5f9aec",
 9510   sig := "<elt-res^rat> x + <elt-res^rat> y",
 9511   sog := " -> <elt-res^rat>",
 9512   docsrc := "<internal>",
 9513   sinflat := [ elt-res^rat, elt-res^rat ],
 9514   souflat := [ elt-res^rat ],
 9515   soghash := "7a2c2e",
 9516   sig4hash := "+(elt-res^rat,elt-res^rat)" ),
 9517 rec(
 9518   kind := "OPERATION",
 9519   sin := [ [ elt-res^pad, "x" ], [ elt-res^pad, "y" ] ],
 9520   sou := [ [ elt-res^pad ] ],
 9521   name := "+",
 9522   short := "Sum of x and y.",
 9523   ex := [  ],
 9524   hash := "f9e752",
 9525   sig := "<elt-res^pad> x + <elt-res^pad> y",
 9526   sog := " -> <elt-res^pad>",
 9527   docsrc := "<internal>",
 9528   sinflat := [ elt-res^pad, elt-res^pad ],
 9529   souflat := [ elt-res^pad ],
 9530   soghash := "0061b4",
 9531   sig4hash := "+(elt-res^pad,elt-res^pad)" ),
 9532 rec(
 9533   kind := "OPERATION",
 9534   sin := [ [ elt-ord^pad, "x" ], [ elt-ord^pad, "y" ] ],
 9535   sou := [ [ elt-ord^pad ] ],
 9536   name := "+",
 9537   short := "Sum of x and y.",
 9538   ex := [  ],
 9539   hash := "f63716",
 9540   sig := "<elt-ord^pad> x + <elt-ord^pad> y",
 9541   sog := " -> <elt-ord^pad>",
 9542   docsrc := "<internal>",
 9543   sinflat := [ elt-ord^pad, elt-ord^pad ],
 9544   souflat := [ elt-ord^pad ],
 9545   soghash := "9ee81d",
 9546   sig4hash := "+(elt-ord^pad,elt-ord^pad)" ),
 9547 rec(
 9548   kind := "OPERATION",
 9549   sin := [ [ elt-fld^pad, "x" ], [ elt-fld^pad, "y" ] ],
 9550   sou := [ [ elt-fld^pad ] ],
 9551   name := "+",
 9552   short := "Sum of x and y.",
 9553   ex := [  ],
 9554   hash := "bf9496",
 9555   sig := "<elt-fld^pad> x + <elt-fld^pad> y",
 9556   sog := " -> <elt-fld^pad>",
 9557   docsrc := "<internal>",
 9558   sinflat := [ elt-fld^pad, elt-fld^pad ],
 9559   souflat := [ elt-fld^pad ],
 9560   soghash := "8c3f71",
 9561   sig4hash := "+(elt-fld^pad,elt-fld^pad)" ),
 9562 rec(
 9563   kind := "OPERATION",
 9564   sin := [ [ elt-fld^fra, "x" ], [ elt-fld^fra, "y" ] ],
 9565   sou := [ [ elt-fld^fra ] ],
 9566   name := "+",
 9567   short := "Sum of x and y.",
 9568   ex := [  ],
 9569   hash := "69d342",
 9570   sig := "<elt-fld^fra> x + <elt-fld^fra> y",
 9571   sog := " -> <elt-fld^fra>",
 9572   docsrc := "<internal>",
 9573   sinflat := [ elt-fld^fra, elt-fld^fra ],
 9574   souflat := [ elt-fld^fra ],
 9575   soghash := "74ef48",
 9576   sig4hash := "+(elt-fld^fra,elt-fld^fra)" ),
 9577 rec(
 9578   kind := "OPERATION",
 9579   sin := [ [ elt-rng^ser, "x" ], [ elt-rng^ser, "y" ] ],
 9580   sou := [ [ elt-rng^ser ] ],
 9581   name := "+",
 9582   short := "Sum of x and y.",
 9583   ex := [  ],
 9584   hash := "bd9934",
 9585   sig := "<elt-rng^ser> x + <elt-rng^ser> y",
 9586   sog := " -> <elt-rng^ser>",
 9587   docsrc := "<internal>",
 9588   sinflat := [ elt-rng^ser, elt-rng^ser ],
 9589   souflat := [ elt-rng^ser ],
 9590   soghash := "28734d",
 9591   sig4hash := "+(elt-rng^ser,elt-rng^ser)" ),
 9592 rec(
 9593   kind := "OPERATION",
 9594   sin := [ [ elt-grp^abl, "x" ], [ elt-grp^abl, "y" ] ],
 9595   sou := [ [ elt-grp^abl ] ],
 9596   name := "+",
 9597   short := "Sum of x and y.",
 9598   ex := [  ],
 9599   hash := "430302",
 9600   sig := "<elt-grp^abl> x + <elt-grp^abl> y",
 9601   sog := " -> <elt-grp^abl>",
 9602   docsrc := "<internal>",
 9603   sinflat := [ elt-grp^abl, elt-grp^abl ],
 9604   souflat := [ elt-grp^abl ],
 9605   soghash := "b42d93",
 9606   sig4hash := "+(elt-grp^abl,elt-grp^abl)" ),
 9607 rec(
 9608   kind := "OPERATION",
 9609   sin := [ [ elt-ord^num, "x" ], [ elt-ord^num, "y" ] ],
 9610   sou := [ [ elt-ord^num ] ],
 9611   name := "+",
 9612   short := "Sum of x and y.",
 9613   ex := [  ],
 9614   hash := "fe5666",
 9615   sig := "<elt-ord^num> x + <elt-ord^num> y",
 9616   sog := " -> <elt-ord^num>",
 9617   docsrc := "<internal>",
 9618   sinflat := [ elt-ord^num, elt-ord^num ],
 9619   souflat := [ elt-ord^num ],
 9620   soghash := "6b03f8",
 9621   sig4hash := "+(elt-ord^num,elt-ord^num)" ),
 9622 rec(
 9623   kind := "OPERATION",
 9624   sin := [ [ ord^num, "x" ], [ ord^num, "y" ] ],
 9625   sou := [ [ ord^num ] ],
 9626   name := "+",
 9627   short := "Sum of x and y.",
 9628   ex := [  ],
 9629   hash := "b19e9b",
 9630   sig := "<ord^num> x + <ord^num> y",
 9631   sog := " -> <ord^num>",
 9632   docsrc := "<internal>",
 9633   sinflat := [ ord^num, ord^num ],
 9634   souflat := [ ord^num ],
 9635   soghash := "2920b8",
 9636   sig4hash := "+(ord^num,ord^num)" ),
 9637 rec(
 9638   kind := "OPERATION",
 9639   sin := [ [ ord^fun, "x" ], [ ord^fun, "y" ] ],
 9640   sou := [ [ ord^fun ] ],
 9641   name := "+",
 9642   short := "Sum of x and y.",
 9643   ex := [  ],
 9644   hash := "d27408",
 9645   sig := "<ord^fun> x + <ord^fun> y",
 9646   sog := " -> <ord^fun>",
 9647   docsrc := "<internal>",
 9648   sinflat := [ ord^fun, ord^fun ],
 9649   souflat := [ ord^fun ],
 9650   soghash := "ab041b",
 9651   sig4hash := "+(ord^fun,ord^fun)" ),
 9652 rec(
 9653   kind := "OPERATION",
 9654   sin := [ [ elt-res^num, "x" ], [ elt-res^num, "y" ] ],
 9655   sou := [ [ elt-res^num ] ],
 9656   name := "+",
 9657   short := "Sum of x and y.",
 9658   ex := [  ],
 9659   hash := "ff2f7d",
 9660   sig := "<elt-res^num> x + <elt-res^num> y",
 9661   sog := " -> <elt-res^num>",
 9662   docsrc := "<internal>",
 9663   sinflat := [ elt-res^num, elt-res^num ],
 9664   souflat := [ elt-res^num ],
 9665   soghash := "a87f47",
 9666   sig4hash := "+(elt-res^num,elt-res^num)" ),
 9667 rec(
 9668   kind := "OPERATION",
 9669   sin := [ [ elt-fld^fun, "x" ], [ elt-fld^fun, "y" ] ],
 9670   sou := [ [ elt-fld^fun ] ],
 9671   name := "+",
 9672   short := "Sum of x and y.",
 9673   ex := [  ],
 9674   hash := "99b3fa",
 9675   sig := "<elt-fld^fun> x + <elt-fld^fun> y",
 9676   sog := " -> <elt-fld^fun>",
 9677   docsrc := "<internal>",
 9678   sinflat := [ elt-fld^fun, elt-fld^fun ],
 9679   souflat := [ elt-fld^fun ],
 9680   soghash := "23d8b4",
 9681   sig4hash := "+(elt-fld^fun,elt-fld^fun)" ),
 9682 rec(
 9683   kind := "OPERATION",
 9684   sin := [ [ elt-ord^fun, "x" ], [ elt-ord^fun, "y" ] ],
 9685   sou := [ [ elt-ord^fun ] ],
 9686   name := "+",
 9687   short := "Sum of x and y.",
 9688   ex := [  ],
 9689   hash := "b9a29c",
 9690   sig := "<elt-ord^fun> x + <elt-ord^fun> y",
 9691   sog := " -> <elt-ord^fun>",
 9692   docsrc := "<internal>",
 9693   sinflat := [ elt-ord^fun, elt-ord^fun ],
 9694   souflat := [ elt-ord^fun ],
 9695   soghash := "0fe368",
 9696   sig4hash := "+(elt-ord^fun,elt-ord^fun)" ),
 9697 rec(
 9698   kind := "OPERATION",
 9699   sin := [ [ elt-dvs/fld^fun, "x" ], [ elt-dvs/fld^fun, "y" ] ],
 9700   sou := [ [ elt-dvs/fld^fun ] ],
 9701   name := "+",
 9702   short := "Sum of x and y.",
 9703   ex := [  ],
 9704   hash := "116c84",
 9705   sig := "<elt-dvs/fld^fun> x + <elt-dvs/fld^fun> y",
 9706   sog := " -> <elt-dvs/fld^fun>",
 9707   docsrc := "<internal>",
 9708   sinflat := [ elt-dvs/fld^fun, elt-dvs/fld^fun ],
 9709   souflat := [ elt-dvs/fld^fun ],
 9710   soghash := "34cafb",
 9711   sig4hash := "+(elt-dvs/fld^fun,elt-dvs/fld^fun)" ),
 9712 rec(
 9713   kind := "OPERATION",
 9714   sin := [ [ elt-pls/fld^fun, "x" ], [ elt-dvs/fld^fun, "y" ] ],
 9715   sou := [ [ elt-dvs/fld^fun ] ],
 9716   name := "+",
 9717   short := "Sum of x and y.",
 9718   ex := [  ],
 9719   hash := "9a6451",
 9720   sig := "<elt-pls/fld^fun> x + <elt-dvs/fld^fun> y",
 9721   sog := " -> <elt-dvs/fld^fun>",
 9722   docsrc := "<internal>",
 9723   sinflat := [ elt-pls/fld^fun, elt-dvs/fld^fun ],
 9724   souflat := [ elt-dvs/fld^fun ],
 9725   soghash := "34cafb",
 9726   sig4hash := "+(elt-pls/fld^fun,elt-dvs/fld^fun)" ),
 9727 rec(
 9728   kind := "OPERATION",
 9729   sin := [ [ elt-dvs/fld^fun, "x" ], [ elt-pls/fld^fun, "y" ] ],
 9730   sou := [ [ elt-dvs/fld^fun ] ],
 9731   name := "+",
 9732   short := "Sum of x and y.",
 9733   ex := [  ],
 9734   hash := "6c8bc0",
 9735   sig := "<elt-dvs/fld^fun> x + <elt-pls/fld^fun> y",
 9736   sog := " -> <elt-dvs/fld^fun>",
 9737   docsrc := "<internal>",
 9738   sinflat := [ elt-dvs/fld^fun, elt-pls/fld^fun ],
 9739   souflat := [ elt-dvs/fld^fun ],
 9740   soghash := "34cafb",
 9741   sig4hash := "+(elt-dvs/fld^fun,elt-pls/fld^fun)" ),
 9742 rec(
 9743   kind := "OPERATION",
 9744   sin := [ [ elt-pls/fld^fun, "x" ], [ elt-pls/fld^fun, "y" ] ],
 9745   sou := [ [ elt-dvs/fld^fun ] ],
 9746   name := "+",
 9747   short := "Sum of x and y.",
 9748   ex := [  ],
 9749   hash := "a848e9",
 9750   sig := "<elt-pls/fld^fun> x + <elt-pls/fld^fun> y",
 9751   sog := " -> <elt-dvs/fld^fun>",
 9752   docsrc := "<internal>",
 9753   sinflat := [ elt-pls/fld^fun, elt-pls/fld^fun ],
 9754   souflat := [ elt-dvs/fld^fun ],
 9755   soghash := "34cafb",
 9756   sig4hash := "+(elt-pls/fld^fun,elt-pls/fld^fun)" ),
 9757 rec(
 9758   kind := "OPERATION",
 9759   sin := [ [ elt-dif/fld^fun, "x" ], [ elt-dif/fld^fun, "y" ] ],
 9760   sou := [ [ elt-dif/fld^fun ] ],
 9761   name := "+",
 9762   short := "Sum of x and y.",
 9763   ex := [  ],
 9764   hash := "1f37ab",
 9765   sig := "<elt-dif/fld^fun> x + <elt-dif/fld^fun> y",
 9766   sog := " -> <elt-dif/fld^fun>",
 9767   docsrc := "<internal>",
 9768   sinflat := [ elt-dif/fld^fun, elt-dif/fld^fun ],
 9769   souflat := [ elt-dif/fld^fun ],
 9770   soghash := "fb8974",
 9771   sig4hash := "+(elt-dif/fld^fun,elt-dif/fld^fun)" ),
 9772 rec(
 9773   kind := "OPERATION",
 9774   sin := [ [ elt-ord^inf, "x" ], [ any, "y" ] ],
 9775   sou := [ [ elt-ord^inf ] ],
 9776   name := "+",
 9777   short := "Sum of x and y.",
 9778   ex := [  ],
 9779   hash := "1361ce",
 9780   sig := "<elt-ord^inf> x + <any> y",
 9781   sog := " -> <elt-ord^inf>",
 9782   docsrc := "<internal>",
 9783   sinflat := [ elt-ord^inf, any ],
 9784   souflat := [ elt-ord^inf ],
 9785   soghash := "08787a",
 9786   sig4hash := "+(elt-ord^inf,any)" ),
 9787 rec(
 9788   kind := "OPERATION",
 9789   sin := [ [ any, "x" ], [ elt-ord^inf, "y" ] ],
 9790   sou := [ [ elt-ord^inf ] ],
 9791   name := "+",
 9792   short := "Sum of x and y.",
 9793   ex := [  ],
 9794   hash := "28c8d2",
 9795   sig := "<any> x + <elt-ord^inf> y",
 9796   sog := " -> <elt-ord^inf>",
 9797   docsrc := "<internal>",
 9798   sinflat := [ any, elt-ord^inf ],
 9799   souflat := [ elt-ord^inf ],
 9800   soghash := "08787a",
 9801   sig4hash := "+(any,elt-ord^inf)" ),
 9802 rec(
 9803   kind := "OPERATION",
 9804   sin := [ [ elt-ord^inf, "x" ], [ elt-ord^inf, "y" ] ],
 9805   sou := [ [ elt-ord^inf ] ],
 9806   name := "+",
 9807   short := "Sum of x and y.",
 9808   ex := [  ],
 9809   hash := "ba191d",
 9810   sig := "<elt-ord^inf> x + <elt-ord^inf> y",
 9811   sog := " -> <elt-ord^inf>",
 9812   docsrc := "<internal>",
 9813   sinflat := [ elt-ord^inf, elt-ord^inf ],
 9814   souflat := [ elt-ord^inf ],
 9815   soghash := "08787a",
 9816   sig4hash := "+(elt-ord^inf,elt-ord^inf)" ),
 9817 rec(
 9818   kind := "OPERATION",
 9819   sin := [ [ elt-mdl^ded, "x" ], [ elt-mdl^ded, "y" ] ],
 9820   sou := [ [ elt-mdl^ded ] ],
 9821   name := "+",
 9822   short := "Sum of x and y.",
 9823   ex := [  ],
 9824   hash := "1f84f1",
 9825   sig := "<elt-mdl^ded> x + <elt-mdl^ded> y",
 9826   sog := " -> <elt-mdl^ded>",
 9827   docsrc := "<internal>",
 9828   sinflat := [ elt-mdl^ded, elt-mdl^ded ],
 9829   souflat := [ elt-mdl^ded ],
 9830   soghash := "2fccf1",
 9831   sig4hash := "+(elt-mdl^ded,elt-mdl^ded)" ),
 9832 rec(
 9833   kind := "OPERATION",
 9834   sin := [ [ elt-ids^fra/ord^num, "I" ], [ elt-ids^fra/ord^num, "J" ] ],
 9835   sou := [ [ elt-ids^fra/ord^num ] ],
 9836   name := "+",
 9837   short := "Sum of ideals I and J; I and J must be defined over the same order.",
 9838   ex := [  ],
 9839   hash := "e139be",
 9840   sig := "<elt-ids^fra/ord^num> I + <elt-ids^fra/ord^num> J",
 9841   sog := " -> <elt-ids^fra/ord^num>",
 9842   docsrc := "<internal>",
 9843   sinflat := [ elt-ids^fra/ord^num, elt-ids^fra/ord^num ],
 9844   souflat := [ elt-ids^fra/ord^num ],
 9845   soghash := "ca011c",
 9846   sig4hash := "+(elt-ids^fra/ord^num,elt-ids^fra/ord^num)" ),
 9847 rec(
 9848   kind := "OPERATION",
 9849   sin := [ [ elt-ids^int/ord^fun, "I" ], [ elt-ids^int/ord^fun, "J" ] ],
 9850   sou := [ [ elt-ids^int/ord^fun ] ],
 9851   name := "+",
 9852   short := "Sum of ideals I and J; I and J must be defined over the same order.",
 9853   ex := [  ],
 9854   hash := "da2302",
 9855   sig := "<elt-ids^int/ord^fun> I + <elt-ids^int/ord^fun> J",
 9856   sog := " -> <elt-ids^int/ord^fun>",
 9857   docsrc := "<internal>",
 9858   sinflat := [ elt-ids^int/ord^fun, elt-ids^int/ord^fun ],
 9859   souflat := [ elt-ids^int/ord^fun ],
 9860   soghash := "918914",
 9861   sig4hash := "+(elt-ids^int/ord^fun,elt-ids^int/ord^fun)" ),
 9862 rec(
 9863   kind := "OPERATION",
 9864   sin := [ [ seq(), "A" ], [ seq(), "B" ] ],
 9865   sou := [ [ seq() ] ],
 9866   name := "+",
 9867   short := "The sum of the integers whose factorization tuples are A and B, represented as a factorization tuple.",
 9868   ex := [  ],
 9869   hash := "2184f2",
 9870   sig := "<seq()> A + <seq()> B",
 9871   sog := " -> <seq()>",
 9872   docsrc := "<internal>",
 9873   sinflat := [ seq(), seq() ],
 9874   souflat := [ seq() ],
 9875   soghash := "4bf3a0",
 9876   sig4hash := "+(seq(),seq())" ),
 9877 rec(
 9878   kind := "OPERATION",
 9879   sin := [ [ mdl^vec, "M" ], [ mdl^vec, "N" ] ],
 9880   sou := [ [ mdl^vec ] ],
 9881   name := "+",
 9882   short := "The sum of ideals I and J.",
 9883   ex := [  ],
 9884   hash := "057455",
 9885   sig := "<mdl^vec> M + <mdl^vec> N",
 9886   sog := " -> <mdl^vec>",
 9887   docsrc := "<internal>",
 9888   sinflat := [ mdl^vec, mdl^vec ],
 9889   souflat := [ mdl^vec ],
 9890   soghash := "886ffa",
 9891   sig4hash := "+(mdl^vec,mdl^vec)" ),
 9892 rec(
 9893   kind := "OPERATION",
 9894   sin := [ [ mdl^mat, "M" ], [ mdl^mat, "N" ] ],
 9895   sou := [ [ mdl^mat ] ],
 9896   name := "+",
 9897   short := "The sum of ideals I and J.",
 9898   ex := [  ],
 9899   hash := "889a24",
 9900   sig := "<mdl^mat> M + <mdl^mat> N",
 9901   sog := " -> <mdl^mat>",
 9902   docsrc := "<internal>",
 9903   sinflat := [ mdl^mat, mdl^mat ],
 9904   souflat := [ mdl^mat ],
 9905   soghash := "5c8c42",
 9906   sig4hash := "+(mdl^mat,mdl^mat)" ),
 9907 rec(
 9908   kind := "OPERATION",
 9909   sin := [ [ mdl, "M" ], [ mdl, "N" ] ],
 9910   sou := [ [ mdl ] ],
 9911   name := "+",
 9912   short := "The sum of ideals I and J.",
 9913   ex := [  ],
 9914   hash := "a58e00",
 9915   sig := "<mdl> M + <mdl> N",
 9916   sog := " -> <mdl>",
 9917   docsrc := "<internal>",
 9918   sinflat := [ mdl, mdl ],
 9919   souflat := [ mdl ],
 9920   soghash := "acbc30",
 9921   sig4hash := "+(mdl,mdl)" ),
 9922 rec(
 9923   kind := "OPERATION",
 9924   sin := [ [ alg^pol, "I" ], [ alg^pol, "J" ] ],
 9925   sou := [ [ alg^pol ] ],
 9926   name := "+",
 9927   short := "The sum of ideals I and J.",
 9928   ex := [  ],
 9929   hash := "fed97c",
 9930   sig := "<alg^pol> I + <alg^pol> J",
 9931   sog := " -> <alg^pol>",
 9932   docsrc := "<internal>",
 9933   sinflat := [ alg^pol, alg^pol ],
 9934   souflat := [ alg^pol ],
 9935   soghash := "75868e",
 9936   sig4hash := "+(alg^pol,alg^pol)" ),
 9937 rec(
 9938   kind := "OPERATION",
 9939   sin := [ [ mdl^ded, "M1" ], [ mdl^ded, "M2" ] ],
 9940   sou := [ [ mdl^ded ] ],
 9941   name := "+",
 9942   short := "The sum of modules M and N.",
 9943   ex := [  ],
 9944   hash := "b209ca",
 9945   sig := "<mdl^ded> M1 + <mdl^ded> M2",
 9946   sog := " -> <mdl^ded>",
 9947   docsrc := "<internal>",
 9948   sinflat := [ mdl^ded, mdl^ded ],
 9949   souflat := [ mdl^ded ],
 9950   soghash := "5ba52c",
 9951   sig4hash := "+(mdl^ded,mdl^ded)" ),
 9952 rec(
 9953   kind := "OPERATION",
 9954   sin := [ [ res^rat, "R" ], [ res^rat, "S" ] ],
 9955   sou := [ [ res^rat ] ],
 9956   name := "+",
 9957   short := "Sum of rings R and S.",
 9958   ex := [  ],
 9959   hash := "130ccf",
 9960   sig := "<res^rat> R + <res^rat> S",
 9961   sog := " -> <res^rat>",
 9962   docsrc := "<internal>",
 9963   sinflat := [ res^rat, res^rat ],
 9964   souflat := [ res^rat ],
 9965   soghash := "a3bb08",
 9966   sig4hash := "+(res^rat,res^rat)" ),
 9967 rec(
 9968   kind := "OPERATION",
 9969   sin := [ [ ord^rat, "R" ], [ ord^rat, "S" ] ],
 9970   sou := [ [ ord^rat ] ],
 9971   name := "+",
 9972   short := "Sum of rings R and S.",
 9973   ex := [  ],
 9974   hash := "564416",
 9975   sig := "<ord^rat> R + <ord^rat> S",
 9976   sog := " -> <ord^rat>",
 9977   docsrc := "<internal>",
 9978   sinflat := [ ord^rat, ord^rat ],
 9979   souflat := [ ord^rat ],
 9980   soghash := "ef1cfa",
 9981   sig4hash := "+(ord^rat,ord^rat)" ),
 9982 rec(
 9983   kind := "OPERATION",
 9984   sin := [ [ fld^fin, "F" ], [ fld^fin, "E" ] ],
 9985   sou := [ [ fld^fin ] ],
 9986   name := "+",
 9987   short := "Sum of finite fields F and E.",
 9988   ex := [  ],
 9989   hash := "883c6f",
 9990   sig := "<fld^fin> F + <fld^fin> E",
 9991   sog := " -> <fld^fin>",
 9992   docsrc := "<internal>",
 9993   sinflat := [ fld^fin, fld^fin ],
 9994   souflat := [ fld^fin ],
 9995   soghash := "267be8",
 9996   sig4hash := "+(fld^fin,fld^fin)" ),
 9997 rec(
 9998   kind := "OPERATION",
 9999   sin := [ [ elt-rng, "x" ] ],
10000   sou := [ [ elt-rng ] ],
10001   name := "+",
10002   short := "Return +x (i.e. x).",
10003   ex := [  ],
10004   hash := "c11247",
10005   sig := " + <elt-rng> x",
10006   sog := " -> <elt-rng>",
10007   docsrc := "<internal>",
10008   sinflat := [ elt-rng ],
10009   souflat := [ elt-rng ],
10010   soghash := "7ef0ef",
10011   sig4hash := "+(elt-rng)" ),
10012 rec(
10013   kind := "OPERATION",
10014   sin := [ [ elt-dvs/fld^num, "d1" ], [ elt-dvs/fld^num, "d2" ] ],
10015   sou := [ [ elt-dvs/fld^num ] ],
10016   name := "+",
10017   short := "The sum of the divisors (and places) of a number field.",
10018   ex := [  ],
10019   hash := "dc0712",
10020   sig := "<elt-dvs/fld^num> d1 + <elt-dvs/fld^num> d2",
10021   sog := " -> <elt-dvs/fld^num>",
10022   docsrc := "<internal>",
10023   sinflat := [ elt-dvs/fld^num, elt-dvs/fld^num ],
10024   souflat := [ elt-dvs/fld^num ],
10025   soghash := "87f535",
10026   sig4hash := "+(elt-dvs/fld^num,elt-dvs/fld^num)" ),
10027 rec(
10028   kind := "OPERATION",
10029   sin := [ [ elt-dvs/fld^num, "d" ], [ elt-pls/fld^num, "p" ] ],
10030   sou := [ [ elt-dvs/fld^num ] ],
10031   name := "+",
10032   short := "The sum of the divisors (and places) of a number field.",
10033   ex := [  ],
10034   hash := "f3a0cf",
10035   sig := "<elt-dvs/fld^num> d + <elt-pls/fld^num> p",
10036   sog := " -> <elt-dvs/fld^num>",
10037   docsrc := "<internal>",
10038   sinflat := [ elt-dvs/fld^num, elt-pls/fld^num ],
10039   souflat := [ elt-dvs/fld^num ],
10040   soghash := "87f535",
10041   sig4hash := "+(elt-dvs/fld^num,elt-pls/fld^num)" ),
10042 rec(
10043   kind := "OPERATION",
10044   sin := [ [ elt-pls/fld^num, "p" ], [ elt-dvs/fld^num, "d" ] ],
10045   sou := [ [ elt-dvs/fld^num ] ],
10046   name := "+",
10047   short := "The sum of the divisors (and places) of a number field.",
10048   ex := [  ],
10049   hash := "38af93",
10050   sig := "<elt-pls/fld^num> p + <elt-dvs/fld^num> d",
10051   sog := " -> <elt-dvs/fld^num>",
10052   docsrc := "<internal>",
10053   sinflat := [ elt-pls/fld^num, elt-dvs/fld^num ],
10054   souflat := [ elt-dvs/fld^num ],
10055   soghash := "87f535",
10056   sig4hash := "+(elt-pls/fld^num,elt-dvs/fld^num)" ),
10057 rec(
10058   kind := "OPERATION",
10059   sin := [ [ elt-pls/fld^num, "p1" ], [ elt-pls/fld^num, "p2" ] ],
10060   sou := [ [ elt-dvs/fld^num ] ],
10061   name := "+",
10062   short := "The sum of the divisors (and places) of a number field.",
10063   ex := [  ],
10064   hash := "719540",
10065   sig := "<elt-pls/fld^num> p1 + <elt-pls/fld^num> p2",
10066   sog := " -> <elt-dvs/fld^num>",
10067   docsrc := "<internal>",
10068   sinflat := [ elt-pls/fld^num, elt-pls/fld^num ],
10069   souflat := [ elt-dvs/fld^num ],
10070   soghash := "87f535",
10071   sig4hash := "+(elt-pls/fld^num,elt-pls/fld^num)" ),
10072 rec(
10073   kind := "OPERATION",
10074   sin := [ [ elt-ord^rat, "x" ] ],
10075   sou := [ [ elt-ord^rat ] ],
10076   name := "-",
10077   short := "Negation of x.",
10078   ex := [  ],
10079   hash := "1eb812",
10080   sig := " - <elt-ord^rat> x",
10081   sog := " -> <elt-ord^rat>",
10082   docsrc := "<internal>",
10083   sinflat := [ elt-ord^rat ],
10084   souflat := [ elt-ord^rat ],
10085   soghash := "898213",
10086   sig4hash := "-(elt-ord^rat)" ),
10087 rec(
10088   kind := "OPERATION",
10089   sin := [ [ elt-fld^rat, "x" ] ],
10090   sou := [ [ elt-fld^rat ] ],
10091   name := "-",
10092   short := "Negation of x.",
10093   ex := [  ],
10094   hash := "d5bdc1",
10095   sig := " - <elt-fld^rat> x",
10096   sog := " -> <elt-fld^rat>",
10097   docsrc := "<internal>",
10098   sinflat := [ elt-fld^rat ],
10099   souflat := [ elt-fld^rat ],
10100   soghash := "89f5fc",
10101   sig4hash := "-(elt-fld^rat)" ),
10102 rec(
10103   kind := "OPERATION",
10104   sin := [ [ elt-fld^rea, "x" ] ],
10105   sou := [ [ elt-fld^rea ] ],
10106   name := "-",
10107   short := "Negation of x.",
10108   ex := [  ],
10109   hash := "64d3bf",
10110   sig := " - <elt-fld^rea> x",
10111   sog := " -> <elt-fld^rea>",
10112   docsrc := "<internal>",
10113   sinflat := [ elt-fld^rea ],
10114   souflat := [ elt-fld^rea ],
10115   soghash := "7f2490",
10116   sig4hash := "-(elt-fld^rea)" ),
10117 rec(
10118   kind := "OPERATION",
10119   sin := [ [ elt-fld^com, "x" ] ],
10120   sou := [ [ elt-fld^com ] ],
10121   name := "-",
10122   short := "Negation of x.",
10123   ex := [  ],
10124   hash := "6ed7ac",
10125   sig := " - <elt-fld^com> x",
10126   sog := " -> <elt-fld^com>",
10127   docsrc := "<internal>",
10128   sinflat := [ elt-fld^com ],
10129   souflat := [ elt-fld^com ],
10130   soghash := "0d772f",
10131   sig4hash := "-(elt-fld^com)" ),
10132 rec(
10133   kind := "OPERATION",
10134   sin := [ [ elt-fld^fin, "x" ] ],
10135   sou := [ [ elt-fld^fin ] ],
10136   name := "-",
10137   short := "Negation of x.",
10138   ex := [  ],
10139   hash := "9bd2a8",
10140   sig := " - <elt-fld^fin> x",
10141   sog := " -> <elt-fld^fin>",
10142   docsrc := "<internal>",
10143   sinflat := [ elt-fld^fin ],
10144   souflat := [ elt-fld^fin ],
10145   soghash := "97e752",
10146   sig4hash := "-(elt-fld^fin)" ),
10147 rec(
10148   kind := "OPERATION",
10149   sin := [ [ elt-alg^pol, "x" ] ],
10150   sou := [ [ elt-alg^pol ] ],
10151   name := "-",
10152   short := "Negation of x.",
10153   ex := [  ],
10154   hash := "b2084c",
10155   sig := " - <elt-alg^pol> x",
10156   sog := " -> <elt-alg^pol>",
10157   docsrc := "<internal>",
10158   sinflat := [ elt-alg^pol ],
10159   souflat := [ elt-alg^pol ],
10160   soghash := "ba7338",
10161   sig4hash := "-(elt-alg^pol)" ),
10162 rec(
10163   kind := "OPERATION",
10164   sin := [ [ elt-fld^pol, "x" ] ],
10165   sou := [ [ elt-fld^pol ] ],
10166   name := "-",
10167   short := "Negation of x.",
10168   ex := [  ],
10169   hash := "3c64b7",
10170   sig := " - <elt-fld^pol> x",
10171   sog := " -> <elt-fld^pol>",
10172   docsrc := "<internal>",
10173   sinflat := [ elt-fld^pol ],
10174   souflat := [ elt-fld^pol ],
10175   soghash := "540d59",
10176   sig4hash := "-(elt-fld^pol)" ),
10177 rec(
10178   kind := "OPERATION",
10179   sin := [ [ elt-rng, "x" ] ],
10180   sou := [ [ elt-rng ] ],
10181   name := "-",
10182   short := "Negation of x.",
10183   ex := [  ],
10184   hash := "545d6d",
10185   sig := " - <elt-rng> x",
10186   sog := " -> <elt-rng>",
10187   docsrc := "<internal>",
10188   sinflat := [ elt-rng ],
10189   souflat := [ elt-rng ],
10190   soghash := "7ef0ef",
10191   sig4hash := "-(elt-rng)" ),
10192 rec(
10193   kind := "OPERATION",
10194   sin := [ [ elt-res^pol, "x" ] ],
10195   sou := [ [ elt-res^pol ] ],
10196   name := "-",
10197   short := "Negation of x.",
10198   ex := [  ],
10199   hash := "772456",
10200   sig := " - <elt-res^pol> x",
10201   sog := " -> <elt-res^pol>",
10202   docsrc := "<internal>",
10203   sinflat := [ elt-res^pol ],
10204   souflat := [ elt-res^pol ],
10205   soghash := "8ffe0c",
10206   sig4hash := "-(elt-res^pol)" ),
10207 rec(
10208   kind := "OPERATION",
10209   sin := [ [ elt-mdl^vec, "x" ] ],
10210   sou := [ [ elt-mdl^vec ] ],
10211   name := "-",
10212   short := "Negation of x.",
10213   ex := [  ],
10214   hash := "2371d9",
10215   sig := " - <elt-mdl^vec> x",
10216   sog := " -> <elt-mdl^vec>",
10217   docsrc := "<internal>",
10218   sinflat := [ elt-mdl^vec ],
10219   souflat := [ elt-mdl^vec ],
10220   soghash := "b46581",
10221   sig4hash := "-(elt-mdl^vec)" ),
10222 rec(
10223   kind := "OPERATION",
10224   sin := [ [ elt-mdl^mat, "x" ] ],
10225   sou := [ [ elt-mdl^mat ] ],
10226   name := "-",
10227   short := "Negation of x.",
10228   ex := [  ],
10229   hash := "dc0dae",
10230   sig := " - <elt-mdl^mat> x",
10231   sog := " -> <elt-mdl^mat>",
10232   docsrc := "<internal>",
10233   sinflat := [ elt-mdl^mat ],
10234   souflat := [ elt-mdl^mat ],
10235   soghash := "5284ac",
10236   sig4hash := "-(elt-mdl^mat)" ),
10237 rec(
10238   kind := "OPERATION",
10239   sin := [ [ elt-mdl, "x" ] ],
10240   sou := [ [ elt-mdl ] ],
10241   name := "-",
10242   short := "Negation of x.",
10243   ex := [  ],
10244   hash := "d7d7b2",
10245   sig := " - <elt-mdl> x",
10246   sog := " -> <elt-mdl>",
10247   docsrc := "<internal>",
10248   sinflat := [ elt-mdl ],
10249   souflat := [ elt-mdl ],
10250   soghash := "97b5cd",
10251   sig4hash := "-(elt-mdl)" ),
10252 rec(
10253   kind := "OPERATION",
10254   sin := [ [ elt-res^rat, "x" ] ],
10255   sou := [ [ elt-res^rat ] ],
10256   name := "-",
10257   short := "Negation of x.",
10258   ex := [  ],
10259   hash := "2bbd7f",
10260   sig := " - <elt-res^rat> x",
10261   sog := " -> <elt-res^rat>",
10262   docsrc := "<internal>",
10263   sinflat := [ elt-res^rat ],
10264   souflat := [ elt-res^rat ],
10265   soghash := "7a2c2e",
10266   sig4hash := "-(elt-res^rat)" ),
10267 rec(
10268   kind := "OPERATION",
10269   sin := [ [ elt-res^pad, "x" ] ],
10270   sou := [ [ elt-res^pad ] ],
10271   name := "-",
10272   short := "Negation of x.",
10273   ex := [  ],
10274   hash := "40738e",
10275   sig := " - <elt-res^pad> x",
10276   sog := " -> <elt-res^pad>",
10277   docsrc := "<internal>",
10278   sinflat := [ elt-res^pad ],
10279   souflat := [ elt-res^pad ],
10280   soghash := "0061b4",
10281   sig4hash := "-(elt-res^pad)" ),
10282 rec(
10283   kind := "OPERATION",
10284   sin := [ [ elt-ord^pad, "x" ] ],
10285   sou := [ [ elt-ord^pad ] ],
10286   name := "-",
10287   short := "Negation of x.",
10288   ex := [  ],
10289   hash := "67ab80",
10290   sig := " - <elt-ord^pad> x",
10291   sog := " -> <elt-ord^pad>",
10292   docsrc := "<internal>",
10293   sinflat := [ elt-ord^pad ],
10294   souflat := [ elt-ord^pad ],
10295   soghash := "9ee81d",
10296   sig4hash := "-(elt-ord^pad)" ),
10297 rec(
10298   kind := "OPERATION",
10299   sin := [ [ elt-fld^pad, "x" ] ],
10300   sou := [ [ elt-fld^pad ] ],
10301   name := "-",
10302   short := "Negation of x.",
10303   ex := [  ],
10304   hash := "e6e4de",
10305   sig := " - <elt-fld^pad> x",
10306   sog := " -> <elt-fld^pad>",
10307   docsrc := "<internal>",
10308   sinflat := [ elt-fld^pad ],
10309   souflat := [ elt-fld^pad ],
10310   soghash := "8c3f71",
10311   sig4hash := "-(elt-fld^pad)" ),
10312 rec(
10313   kind := "OPERATION",
10314   sin := [ [ elt-fld^fra, "x" ] ],
10315   sou := [ [ elt-fld^fra ] ],
10316   name := "-",
10317   short := "Negation of x.",
10318   ex := [  ],
10319   hash := "b89a5e",
10320   sig := " - <elt-fld^fra> x",
10321   sog := " -> <elt-fld^fra>",
10322   docsrc := "<internal>",
10323   sinflat := [ elt-fld^fra ],
10324   souflat := [ elt-fld^fra ],
10325   soghash := "74ef48",
10326   sig4hash := "-(elt-fld^fra)" ),
10327 rec(
10328   kind := "OPERATION",
10329   sin := [ [ elt-rng^ser, "x" ] ],
10330   sou := [ [ elt-rng^ser ] ],
10331   name := "-",
10332   short := "Negation of x.",
10333   ex := [  ],
10334   hash := "5f9914",
10335   sig := " - <elt-rng^ser> x",
10336   sog := " -> <elt-rng^ser>",
10337   docsrc := "<internal>",
10338   sinflat := [ elt-rng^ser ],
10339   souflat := [ elt-rng^ser ],
10340   soghash := "28734d",
10341   sig4hash := "-(elt-rng^ser)" ),
10342 rec(
10343   kind := "OPERATION",
10344   sin := [ [ elt-grp^abl, "x" ] ],
10345   sou := [ [ elt-grp^abl ] ],
10346   name := "-",
10347   short := "Negation of x.",
10348   ex := [  ],
10349   hash := "191cfd",
10350   sig := " - <elt-grp^abl> x",
10351   sog := " -> <elt-grp^abl>",
10352   docsrc := "<internal>",
10353   sinflat := [ elt-grp^abl ],
10354   souflat := [ elt-grp^abl ],
10355   soghash := "b42d93",
10356   sig4hash := "-(elt-grp^abl)" ),
10357 rec(
10358   kind := "OPERATION",
10359   sin := [ [ elt-ord^num, "x" ] ],
10360   sou := [ [ elt-ord^num ] ],
10361   name := "-",
10362   short := "Negation of x.",
10363   ex := [  ],
10364   hash := "47a5d6",
10365   sig := " - <elt-ord^num> x",
10366   sog := " -> <elt-ord^num>",
10367   docsrc := "<internal>",
10368   sinflat := [ elt-ord^num ],
10369   souflat := [ elt-ord^num ],
10370   soghash := "6b03f8",
10371   sig4hash := "-(elt-ord^num)" ),
10372 rec(
10373   kind := "OPERATION",
10374   sin := [ [ elt-res^num, "x" ] ],
10375   sou := [ [ elt-res^num ] ],
10376   name := "-",
10377   short := "Negation of x.",
10378   ex := [  ],
10379   hash := "a53da3",
10380   sig := " - <elt-res^num> x",
10381   sog := " -> <elt-res^num>",
10382   docsrc := "<internal>",
10383   sinflat := [ elt-res^num ],
10384   souflat := [ elt-res^num ],
10385   soghash := "a87f47",
10386   sig4hash := "-(elt-res^num)" ),
10387 rec(
10388   kind := "OPERATION",
10389   sin := [ [ elt-fld^fun, "x" ] ],
10390   sou := [ [ elt-fld^fun ] ],
10391   name := "-",
10392   short := "Negation of x.",
10393   ex := [  ],
10394   hash := "d9093f",
10395   sig := " - <elt-fld^fun> x",
10396   sog := " -> <elt-fld^fun>",
10397   docsrc := "<internal>",
10398   sinflat := [ elt-fld^fun ],
10399   souflat := [ elt-fld^fun ],
10400   soghash := "23d8b4",
10401   sig4hash := "-(elt-fld^fun)" ),
10402 rec(
10403   kind := "OPERATION",
10404   sin := [ [ elt-ord^fun, "x" ] ],
10405   sou := [ [ elt-ord^fun ] ],
10406   name := "-",
10407   short := "Negation of x.",
10408   ex := [  ],
10409   hash := "a4c200",
10410   sig := " - <elt-ord^fun> x",
10411   sog := " -> <elt-ord^fun>",
10412   docsrc := "<internal>",
10413   sinflat := [ elt-ord^fun ],
10414   souflat := [ elt-ord^fun ],
10415   soghash := "0fe368",
10416   sig4hash := "-(elt-ord^fun)" ),
10417 rec(
10418   kind := "OPERATION",
10419   sin := [ [ elt-dvs/fld^fun, "x" ] ],
10420   sou := [ [ elt-dvs/fld^fun ] ],
10421   name := "-",
10422   short := "Negation of x.",
10423   ex := [  ],
10424   hash := "80ef57",
10425   sig := " - <elt-dvs/fld^fun> x",
10426   sog := " -> <elt-dvs/fld^fun>",
10427   docsrc := "<internal>",
10428   sinflat := [ elt-dvs/fld^fun ],
10429   souflat := [ elt-dvs/fld^fun ],
10430   soghash := "34cafb",
10431   sig4hash := "-(elt-dvs/fld^fun)" ),
10432 rec(
10433   kind := "OPERATION",
10434   sin := [ [ elt-pls/fld^fun, "x" ] ],
10435   sou := [ [ elt-dvs/fld^fun ] ],
10436   name := "-",
10437   short := "Negation of x.",
10438   ex := [  ],
10439   hash := "9da624",
10440   sig := " - <elt-pls/fld^fun> x",
10441   sog := " -> <elt-dvs/fld^fun>",
10442   docsrc := "<internal>",
10443   sinflat := [ elt-pls/fld^fun ],
10444   souflat := [ elt-dvs/fld^fun ],
10445   soghash := "34cafb",
10446   sig4hash := "-(elt-pls/fld^fun)" ),
10447 rec(
10448   kind := "OPERATION",
10449   sin := [ [ elt-dif/fld^fun, "x" ] ],
10450   sou := [ [ elt-dif/fld^fun ] ],
10451   name := "-",
10452   short := "Negation of x.",
10453   ex := [  ],
10454   hash := "890b10",
10455   sig := " - <elt-dif/fld^fun> x",
10456   sog := " -> <elt-dif/fld^fun>",
10457   docsrc := "<internal>",
10458   sinflat := [ elt-dif/fld^fun ],
10459   souflat := [ elt-dif/fld^fun ],
10460   soghash := "fb8974",
10461   sig4hash := "-(elt-dif/fld^fun)" ),
10462 rec(
10463   kind := "OPERATION",
10464   sin := [ [ elt-ord^inf, "x" ] ],
10465   sou := [ [ elt-ord^inf ] ],
10466   name := "-",
10467   short := "Negation of x.",
10468   ex := [  ],
10469   hash := "55a86d",
10470   sig := " - <elt-ord^inf> x",
10471   sog := " -> <elt-ord^inf>",
10472   docsrc := "<internal>",
10473   sinflat := [ elt-ord^inf ],
10474   souflat := [ elt-ord^inf ],
10475   soghash := "08787a",
10476   sig4hash := "-(elt-ord^inf)" ),
10477 rec(
10478   kind := "OPERATION",
10479   sin := [ [ elt-alg^mat, "x" ] ],
10480   sou := [ [ elt-alg^mat ] ],
10481   name := "-",
10482   short := "Negation of x.",
10483   ex := [  ],
10484   hash := "d311d7",
10485   sig := " - <elt-alg^mat> x",
10486   sog := " -> <elt-alg^mat>",
10487   docsrc := "<internal>",
10488   sinflat := [ elt-alg^mat ],
10489   souflat := [ elt-alg^mat ],
10490   soghash := "8dbb64",
10491   sig4hash := "-(elt-alg^mat)" ),
10492 rec(
10493   kind := "OPERATION",
10494   sin := [ [ elt-mdl^ded, "x" ] ],
10495   sou := [ [ elt-mdl^ded ] ],
10496   name := "-",
10497   short := "Negation of x.",
10498   ex := [  ],
10499   hash := "5f76dc",
10500   sig := " - <elt-mdl^ded> x",
10501   sog := " -> <elt-mdl^ded>",
10502   docsrc := "<internal>",
10503   sinflat := [ elt-mdl^ded ],
10504   souflat := [ elt-mdl^ded ],
10505   soghash := "2fccf1",
10506   sig4hash := "-(elt-mdl^ded)" ),
10507 rec(
10508   kind := "OPERATION",
10509   sin := [ [ elt-ord^rat, "x" ], [ elt-ord^rat, "y" ] ],
10510   sou := [ [ elt-ord^rat ] ],
10511   name := "-",
10512   short := "Difference of f and the scalar c.",
10513   ex := [  ],
10514   hash := "23ff06",
10515   sig := "<elt-ord^rat> x - <elt-ord^rat> y",
10516   sog := " -> <elt-ord^rat>",
10517   docsrc := "<internal>",
10518   sinflat := [ elt-ord^rat, elt-ord^rat ],
10519   souflat := [ elt-ord^rat ],
10520   soghash := "898213",
10521   sig4hash := "-(elt-ord^rat,elt-ord^rat)" ),
10522 rec(
10523   kind := "OPERATION",
10524   sin := [ [ elt-fld^rat, "x" ], [ elt-fld^rat, "y" ] ],
10525   sou := [ [ elt-fld^rat ] ],
10526   name := "-",
10527   short := "Difference of f and the scalar c.",
10528   ex := [  ],
10529   hash := "acacf0",
10530   sig := "<elt-fld^rat> x - <elt-fld^rat> y",
10531   sog := " -> <elt-fld^rat>",
10532   docsrc := "<internal>",
10533   sinflat := [ elt-fld^rat, elt-fld^rat ],
10534   souflat := [ elt-fld^rat ],
10535   soghash := "89f5fc",
10536   sig4hash := "-(elt-fld^rat,elt-fld^rat)" ),
10537 rec(
10538   kind := "OPERATION",
10539   sin := [ [ elt-fld^rea, "x" ], [ elt-fld^rea, "y" ] ],
10540   sou := [ [ elt-fld^rea ] ],
10541   name := "-",
10542   short := "Difference of f and the scalar c.",
10543   ex := [  ],
10544   hash := "cc9e0a",
10545   sig := "<elt-fld^rea> x - <elt-fld^rea> y",
10546   sog := " -> <elt-fld^rea>",
10547   docsrc := "<internal>",
10548   sinflat := [ elt-fld^rea, elt-fld^rea ],
10549   souflat := [ elt-fld^rea ],
10550   soghash := "7f2490",
10551   sig4hash := "-(elt-fld^rea,elt-fld^rea)" ),
10552 rec(
10553   kind := "OPERATION",
10554   sin := [ [ elt-fld^com, "x" ], [ elt-fld^com, "y" ] ],
10555   sou := [ [ elt-fld^com ] ],
10556   name := "-",
10557   short := "Difference of f and the scalar c.",
10558   ex := [  ],
10559   hash := "1c07a1",
10560   sig := "<elt-fld^com> x - <elt-fld^com> y",
10561   sog := " -> <elt-fld^com>",
10562   docsrc := "<internal>",
10563   sinflat := [ elt-fld^com, elt-fld^com ],
10564   souflat := [ elt-fld^com ],
10565   soghash := "0d772f",
10566   sig4hash := "-(elt-fld^com,elt-fld^com)" ),
10567 rec(
10568   kind := "OPERATION",
10569   sin := [ [ elt-alg^pol, "x" ], [ elt-alg^pol, "y" ] ],
10570   sou := [ [ elt-alg^pol ] ],
10571   name := "-",
10572   short := "Difference of f and the scalar c.",
10573   ex := [  ],
10574   hash := "c89f1d",
10575   sig := "<elt-alg^pol> x - <elt-alg^pol> y",
10576   sog := " -> <elt-alg^pol>",
10577   docsrc := "<internal>",
10578   sinflat := [ elt-alg^pol, elt-alg^pol ],
10579   souflat := [ elt-alg^pol ],
10580   soghash := "ba7338",
10581   sig4hash := "-(elt-alg^pol,elt-alg^pol)" ),
10582 rec(
10583   kind := "OPERATION",
10584   sin := [ [ elt-fld^pol, "x" ], [ elt-fld^pol, "y" ] ],
10585   sou := [ [ elt-fld^pol ] ],
10586   name := "-",
10587   short := "Difference of f and the scalar c.",
10588   ex := [  ],
10589   hash := "df84c5",
10590   sig := "<elt-fld^pol> x - <elt-fld^pol> y",
10591   sog := " -> <elt-fld^pol>",
10592   docsrc := "<internal>",
10593   sinflat := [ elt-fld^pol, elt-fld^pol ],
10594   souflat := [ elt-fld^pol ],
10595   soghash := "540d59",
10596   sig4hash := "-(elt-fld^pol,elt-fld^pol)" ),
10597 rec(
10598   kind := "OPERATION",
10599   sin := [ [ elt-rng, "x" ], [ elt-rng, "y" ] ],
10600   sou := [ [ elt-rng ] ],
10601   name := "-",
10602   short := "Difference of f and the scalar c.",
10603   ex := [  ],
10604   hash := "9efff3",
10605   sig := "<elt-rng> x - <elt-rng> y",
10606   sog := " -> <elt-rng>",
10607   docsrc := "<internal>",
10608   sinflat := [ elt-rng, elt-rng ],
10609   souflat := [ elt-rng ],
10610   soghash := "7ef0ef",
10611   sig4hash := "-(elt-rng,elt-rng)" ),
10612 rec(
10613   kind := "OPERATION",
10614   sin := [ [ elt-res^pol, "x" ], [ elt-res^pol, "y" ] ],
10615   sou := [ [ elt-res^pol ] ],
10616   name := "-",
10617   short := "Difference of f and the scalar c.",
10618   ex := [  ],
10619   hash := "6ce3e4",
10620   sig := "<elt-res^pol> x - <elt-res^pol> y",
10621   sog := " -> <elt-res^pol>",
10622   docsrc := "<internal>",
10623   sinflat := [ elt-res^pol, elt-res^pol ],
10624   souflat := [ elt-res^pol ],
10625   soghash := "8ffe0c",
10626   sig4hash := "-(elt-res^pol,elt-res^pol)" ),
10627 rec(
10628   kind := "OPERATION",
10629   sin := [ [ elt-fld^fin, "x" ], [ elt-fld^fin, "y" ] ],
10630   sou := [ [ elt-fld^fin ] ],
10631   name := "-",
10632   short := "Difference of f and the scalar c.",
10633   ex := [  ],
10634   hash := "5f50a9",
10635   sig := "<elt-fld^fin> x - <elt-fld^fin> y",
10636   sog := " -> <elt-fld^fin>",
10637   docsrc := "<internal>",
10638   sinflat := [ elt-fld^fin, elt-fld^fin ],
10639   souflat := [ elt-fld^fin ],
10640   soghash := "97e752",
10641   sig4hash := "-(elt-fld^fin,elt-fld^fin)" ),
10642 rec(
10643   kind := "OPERATION",
10644   sin := [ [ elt-alg^mat, "x" ], [ elt-alg^mat, "y" ] ],
10645   sou := [ [ elt-alg^mat ] ],
10646   name := "-",
10647   short := "Difference of f and the scalar c.",
10648   ex := [  ],
10649   hash := "fd316b",
10650   sig := "<elt-alg^mat> x - <elt-alg^mat> y",
10651   sog := " -> <elt-alg^mat>",
10652   docsrc := "<internal>",
10653   sinflat := [ elt-alg^mat, elt-alg^mat ],
10654   souflat := [ elt-alg^mat ],
10655   soghash := "8dbb64",
10656   sig4hash := "-(elt-alg^mat,elt-alg^mat)" ),
10657 rec(
10658   kind := "OPERATION",
10659   sin := [ [ elt-mdl^vec, "x" ], [ elt-mdl^vec, "y" ] ],
10660   sou := [ [ elt-mdl^vec ] ],
10661   name := "-",
10662   short := "Difference of f and the scalar c.",
10663   ex := [  ],
10664   hash := "c8309c",
10665   sig := "<elt-mdl^vec> x - <elt-mdl^vec> y",
10666   sog := " -> <elt-mdl^vec>",
10667   docsrc := "<internal>",
10668   sinflat := [ elt-mdl^vec, elt-mdl^vec ],
10669   souflat := [ elt-mdl^vec ],
10670   soghash := "b46581",
10671   sig4hash := "-(elt-mdl^vec,elt-mdl^vec)" ),
10672 rec(
10673   kind := "OPERATION",
10674   sin := [ [ elt-mdl^mat, "x" ], [ elt-mdl^mat, "y" ] ],
10675   sou := [ [ elt-mdl^mat ] ],
10676   name := "-",
10677   short := "Difference of f and the scalar c.",
10678   ex := [  ],
10679   hash := "87c7ba",
10680   sig := "<elt-mdl^mat> x - <elt-mdl^mat> y",
10681   sog := " -> <elt-mdl^mat>",
10682   docsrc := "<internal>",
10683   sinflat := [ elt-mdl^mat, elt-mdl^mat ],
10684   souflat := [ elt-mdl^mat ],
10685   soghash := "5284ac",
10686   sig4hash := "-(elt-mdl^mat,elt-mdl^mat)" ),
10687 rec(
10688   kind := "OPERATION",
10689   sin := [ [ elt-mdl, "x" ], [ elt-mdl, "y" ] ],
10690   sou := [ [ elt-mdl ] ],
10691   name := "-",
10692   short := "Difference of f and the scalar c.",
10693   ex := [  ],
10694   hash := "18316f",
10695   sig := "<elt-mdl> x - <elt-mdl> y",
10696   sog := " -> <elt-mdl>",
10697   docsrc := "<internal>",
10698   sinflat := [ elt-mdl, elt-mdl ],
10699   souflat := [ elt-mdl ],
10700   soghash := "97b5cd",
10701   sig4hash := "-(elt-mdl,elt-mdl)" ),
10702 rec(
10703   kind := "OPERATION",
10704   sin := [ [ elt-res^rat, "x" ], [ elt-res^rat, "y" ] ],
10705   sou := [ [ elt-res^rat ] ],
10706   name := "-",
10707   short := "Difference of f and the scalar c.",
10708   ex := [  ],
10709   hash := "72c468",
10710   sig := "<elt-res^rat> x - <elt-res^rat> y",
10711   sog := " -> <elt-res^rat>",
10712   docsrc := "<internal>",
10713   sinflat := [ elt-res^rat, elt-res^rat ],
10714   souflat := [ elt-res^rat ],
10715   soghash := "7a2c2e",
10716   sig4hash := "-(elt-res^rat,elt-res^rat)" ),
10717 rec(
10718   kind := "OPERATION",
10719   sin := [ [ elt-res^pad, "x" ], [ elt-res^pad, "y" ] ],
10720   sou := [ [ elt-res^pad ] ],
10721   name := "-",
10722   short := "Difference of f and the scalar c.",
10723   ex := [  ],
10724   hash := "c77aaf",
10725   sig := "<elt-res^pad> x - <elt-res^pad> y",
10726   sog := " -> <elt-res^pad>",
10727   docsrc := "<internal>",
10728   sinflat := [ elt-res^pad, elt-res^pad ],
10729   souflat := [ elt-res^pad ],
10730   soghash := "0061b4",
10731   sig4hash := "-(elt-res^pad,elt-res^pad)" ),
10732 rec(
10733   kind := "OPERATION",
10734   sin := [ [ elt-ord^pad, "x" ], [ elt-ord^pad, "y" ] ],
10735   sou := [ [ elt-ord^pad ] ],
10736   name := "-",
10737   short := "Difference of f and the scalar c.",
10738   ex := [  ],
10739   hash := "3eb458",
10740   sig := "<elt-ord^pad> x - <elt-ord^pad> y",
10741   sog := " -> <elt-ord^pad>",
10742   docsrc := "<internal>",
10743   sinflat := [ elt-ord^pad, elt-ord^pad ],
10744   souflat := [ elt-ord^pad ],
10745   soghash := "9ee81d",
10746   sig4hash := "-(elt-ord^pad,elt-ord^pad)" ),
10747 rec(
10748   kind := "OPERATION",
10749   sin := [ [ elt-fld^pad, "x" ], [ elt-fld^pad, "y" ] ],
10750   sou := [ [ elt-fld^pad ] ],
10751   name := "-",
10752   short := "Difference of f and the scalar c.",
10753   ex := [  ],
10754   hash := "b8e53c",
10755   sig := "<elt-fld^pad> x - <elt-fld^pad> y",
10756   sog := " -> <elt-fld^pad>",
10757   docsrc := "<internal>",
10758   sinflat := [ elt-fld^pad, elt-fld^pad ],
10759   souflat := [ elt-fld^pad ],
10760   soghash := "8c3f71",
10761   sig4hash := "-(elt-fld^pad,elt-fld^pad)" ),
10762 rec(
10763   kind := "OPERATION",
10764   sin := [ [ elt-fld^fra, "x" ], [ elt-fld^fra, "y" ] ],
10765   sou := [ [ elt-fld^fra ] ],
10766   name := "-",
10767   short := "Difference of f and the scalar c.",
10768   ex := [  ],
10769   hash := "d19437",
10770   sig := "<elt-fld^fra> x - <elt-fld^fra> y",
10771   sog := " -> <elt-fld^fra>",
10772   docsrc := "<internal>",
10773   sinflat := [ elt-fld^fra, elt-fld^fra ],
10774   souflat := [ elt-fld^fra ],
10775   soghash := "74ef48",
10776   sig4hash := "-(elt-fld^fra,elt-fld^fra)" ),
10777 rec(
10778   kind := "OPERATION",
10779   sin := [ [ elt-rng^ser, "x" ], [ elt-rng^ser, "y" ] ],
10780   sou := [ [ elt-rng^ser ] ],
10781   name := "-",
10782   short := "Difference of f and the scalar c.",
10783   ex := [  ],
10784   hash := "66baf1",
10785   sig := "<elt-rng^ser> x - <elt-rng^ser> y",
10786   sog := " -> <elt-rng^ser>",
10787   docsrc := "<internal>",
10788   sinflat := [ elt-rng^ser, elt-rng^ser ],
10789   souflat := [ elt-rng^ser ],
10790   soghash := "28734d",
10791   sig4hash := "-(elt-rng^ser,elt-rng^ser)" ),
10792 rec(
10793   kind := "OPERATION",
10794   sin := [ [ elt-grp^abl, "x" ], [ elt-grp^abl, "y" ] ],
10795   sou := [ [ elt-grp^abl ] ],
10796   name := "-",
10797   short := "Difference of f and the scalar c.",
10798   ex := [  ],
10799   hash := "f0ca70",
10800   sig := "<elt-grp^abl> x - <elt-grp^abl> y",
10801   sog := " -> <elt-grp^abl>",
10802   docsrc := "<internal>",
10803   sinflat := [ elt-grp^abl, elt-grp^abl ],
10804   souflat := [ elt-grp^abl ],
10805   soghash := "b42d93",
10806   sig4hash := "-(elt-grp^abl,elt-grp^abl)" ),
10807 rec(
10808   kind := "OPERATION",
10809   sin := [ [ elt-ord^num, "x" ], [ elt-ord^num, "y" ] ],
10810   sou := [ [ elt-ord^num ] ],
10811   name := "-",
10812   short := "Difference of f and the scalar c.",
10813   ex := [  ],
10814   hash := "20475b",
10815   sig := "<elt-ord^num> x - <elt-ord^num> y",
10816   sog := " -> <elt-ord^num>",
10817   docsrc := "<internal>",
10818   sinflat := [ elt-ord^num, elt-ord^num ],
10819   souflat := [ elt-ord^num ],
10820   soghash := "6b03f8",
10821   sig4hash := "-(elt-ord^num,elt-ord^num)" ),
10822 rec(
10823   kind := "OPERATION",
10824   sin := [ [ elt-res^num, "x" ], [ elt-res^num, "y" ] ],
10825   sou := [ [ elt-res^num ] ],
10826   name := "-",
10827   short := "Difference of f and the scalar c.",
10828   ex := [  ],
10829   hash := "f307dc",
10830   sig := "<elt-res^num> x - <elt-res^num> y",
10831   sog := " -> <elt-res^num>",
10832   docsrc := "<internal>",
10833   sinflat := [ elt-res^num, elt-res^num ],
10834   souflat := [ elt-res^num ],
10835   soghash := "a87f47",
10836   sig4hash := "-(elt-res^num,elt-res^num)" ),
10837 rec(
10838   kind := "OPERATION",
10839   sin := [ [ elt-fld^fun, "x" ], [ elt-fld^fun, "y" ] ],
10840   sou := [ [ elt-fld^fun ] ],
10841   name := "-",
10842   short := "Difference of f and the scalar c.",
10843   ex := [  ],
10844   hash := "584386",
10845   sig := "<elt-fld^fun> x - <elt-fld^fun> y",
10846   sog := " -> <elt-fld^fun>",
10847   docsrc := "<internal>",
10848   sinflat := [ elt-fld^fun, elt-fld^fun ],
10849   souflat := [ elt-fld^fun ],
10850   soghash := "23d8b4",
10851   sig4hash := "-(elt-fld^fun,elt-fld^fun)" ),
10852 rec(
10853   kind := "OPERATION",
10854   sin := [ [ elt-ord^fun, "x" ], [ elt-ord^fun, "y" ] ],
10855   sou := [ [ elt-ord^fun ] ],
10856   name := "-",
10857   short := "Difference of f and the scalar c.",
10858   ex := [  ],
10859   hash := "a41a54",
10860   sig := "<elt-ord^fun> x - <elt-ord^fun> y",
10861   sog := " -> <elt-ord^fun>",
10862   docsrc := "<internal>",
10863   sinflat := [ elt-ord^fun, elt-ord^fun ],
10864   souflat := [ elt-ord^fun ],
10865   soghash := "0fe368",
10866   sig4hash := "-(elt-ord^fun,elt-ord^fun)" ),
10867 rec(
10868   kind := "OPERATION",
10869   sin := [ [ elt-dvs/fld^fun, "x" ], [ elt-dvs/fld^fun, "y" ] ],
10870   sou := [ [ elt-dvs/fld^fun ] ],
10871   name := "-",
10872   short := "Difference of f and the scalar c.",
10873   ex := [  ],
10874   hash := "7cc02b",
10875   sig := "<elt-dvs/fld^fun> x - <elt-dvs/fld^fun> y",
10876   sog := " -> <elt-dvs/fld^fun>",
10877   docsrc := "<internal>",
10878   sinflat := [ elt-dvs/fld^fun, elt-dvs/fld^fun ],
10879   souflat := [ elt-dvs/fld^fun ],
10880   soghash := "34cafb",
10881   sig4hash := "-(elt-dvs/fld^fun,elt-dvs/fld^fun)" ),
10882 rec(
10883   kind := "OPERATION",
10884   sin := [ [ elt-pls/fld^fun, "x" ], [ elt-dvs/fld^fun, "y" ] ],
10885   sou := [ [ elt-dvs/fld^fun ] ],
10886   name := "-",
10887   short := "Difference of f and the scalar c.",
10888   ex := [  ],
10889   hash := "fb76d0",
10890   sig := "<elt-pls/fld^fun> x - <elt-dvs/fld^fun> y",
10891   sog := " -> <elt-dvs/fld^fun>",
10892   docsrc := "<internal>",
10893   sinflat := [ elt-pls/fld^fun, elt-dvs/fld^fun ],
10894   souflat := [ elt-dvs/fld^fun ],
10895   soghash := "34cafb",
10896   sig4hash := "-(elt-pls/fld^fun,elt-dvs/fld^fun)" ),
10897 rec(
10898   kind := "OPERATION",
10899   sin := [ [ elt-dvs/fld^fun, "x" ], [ elt-pls/fld^fun, "y" ] ],
10900   sou := [ [ elt-dvs/fld^fun ] ],
10901   name := "-",
10902   short := "Difference of f and the scalar c.",
10903   ex := [  ],
10904   hash := "c401e7",
10905   sig := "<elt-dvs/fld^fun> x - <elt-pls/fld^fun> y",
10906   sog := " -> <elt-dvs/fld^fun>",
10907   docsrc := "<internal>",
10908   sinflat := [ elt-dvs/fld^fun, elt-pls/fld^fun ],
10909   souflat := [ elt-dvs/fld^fun ],
10910   soghash := "34cafb",
10911   sig4hash := "-(elt-dvs/fld^fun,elt-pls/fld^fun)" ),
10912 rec(
10913   kind := "OPERATION",
10914   sin := [ [ elt-pls/fld^fun, "x" ], [ elt-pls/fld^fun, "y" ] ],
10915   sou := [ [ elt-dvs/fld^fun ] ],
10916   name := "-",
10917   short := "Difference of f and the scalar c.",
10918   ex := [  ],
10919   hash := "a2c7a5",
10920   sig := "<elt-pls/fld^fun> x - <elt-pls/fld^fun> y",
10921   sog := " -> <elt-dvs/fld^fun>",
10922   docsrc := "<internal>",
10923   sinflat := [ elt-pls/fld^fun, elt-pls/fld^fun ],
10924   souflat := [ elt-dvs/fld^fun ],
10925   soghash := "34cafb",
10926   sig4hash := "-(elt-pls/fld^fun,elt-pls/fld^fun)" ),
10927 rec(
10928   kind := "OPERATION",
10929   sin := [ [ elt-dif/fld^fun, "x" ], [ elt-dif/fld^fun, "y" ] ],
10930   sou := [ [ elt-dif/fld^fun ] ],
10931   name := "-",
10932   short := "Difference of f and the scalar c.",
10933   ex := [  ],
10934   hash := "4ce650",
10935   sig := "<elt-dif/fld^fun> x - <elt-dif/fld^fun> y",
10936   sog := " -> <elt-dif/fld^fun>",
10937   docsrc := "<internal>",
10938   sinflat := [ elt-dif/fld^fun, elt-dif/fld^fun ],
10939   souflat := [ elt-dif/fld^fun ],
10940   soghash := "fb8974",
10941   sig4hash := "-(elt-dif/fld^fun,elt-dif/fld^fun)" ),
10942 rec(
10943   kind := "OPERATION",
10944   sin := [ [ elt-ord^inf, "x" ], [ any, "y" ] ],
10945   sou := [ [ elt-ord^inf ] ],
10946   name := "-",
10947   short := "Difference of f and the scalar c.",
10948   ex := [  ],
10949   hash := "63b663",
10950   sig := "<elt-ord^inf> x - <any> y",
10951   sog := " -> <elt-ord^inf>",
10952   docsrc := "<internal>",
10953   sinflat := [ elt-ord^inf, any ],
10954   souflat := [ elt-ord^inf ],
10955   soghash := "08787a",
10956   sig4hash := "-(elt-ord^inf,any)" ),
10957 rec(
10958   kind := "OPERATION",
10959   sin := [ [ any, "x" ], [ elt-ord^inf, "y" ] ],
10960   sou := [ [ elt-ord^inf ] ],
10961   name := "-",
10962   short := "Difference of f and the scalar c.",
10963   ex := [  ],
10964   hash := "ff2ad4",
10965   sig := "<any> x - <elt-ord^inf> y",
10966   sog := " -> <elt-ord^inf>",
10967   docsrc := "<internal>",
10968   sinflat := [ any, elt-ord^inf ],
10969   souflat := [ elt-ord^inf ],
10970   soghash := "08787a",
10971   sig4hash := "-(any,elt-ord^inf)" ),
10972 rec(
10973   kind := "OPERATION",
10974   sin := [ [ elt-ord^inf, "x" ], [ elt-ord^inf, "y" ] ],
10975   sou := [ [ elt-ord^inf ] ],
10976   name := "-",
10977   short := "Difference of f and the scalar c.",
10978   ex := [  ],
10979   hash := "17cebe",
10980   sig := "<elt-ord^inf> x - <elt-ord^inf> y",
10981   sog := " -> <elt-ord^inf>",
10982   docsrc := "<internal>",
10983   sinflat := [ elt-ord^inf, elt-ord^inf ],
10984   souflat := [ elt-ord^inf ],
10985   soghash := "08787a",
10986   sig4hash := "-(elt-ord^inf,elt-ord^inf)" ),
10987 rec(
10988   kind := "OPERATION",
10989   sin := [ [ elt-mdl^ded, "x" ], [ elt-mdl^ded, "y" ] ],
10990   sou := [ [ elt-mdl^ded ] ],
10991   name := "-",
10992   short := "Difference of f and the scalar c.",
10993   ex := [  ],
10994   hash := "71a37f",
10995   sig := "<elt-mdl^ded> x - <elt-mdl^ded> y",
10996   sog := " -> <elt-mdl^ded>",
10997   docsrc := "<internal>",
10998   sinflat := [ elt-mdl^ded, elt-mdl^ded ],
10999   souflat := [ elt-mdl^ded ],
11000   soghash := "2fccf1",
11001   sig4hash := "-(elt-mdl^ded,elt-mdl^ded)" ),
11002 rec(
11003   kind := "OPERATION",
11004   sin := [ [ seq(), "A" ], [ seq(), "B" ] ],
11005   sou := [ [ seq() ] ],
11006   name := "-",
11007   short := "Difference of f and the scalar c.",
11008   ex := [  ],
11009   hash := "64a650",
11010   sig := "<seq()> A - <seq()> B",
11011   sog := " -> <seq()>",
11012   docsrc := "<internal>",
11013   sinflat := [ seq(), seq() ],
11014   souflat := [ seq() ],
11015   soghash := "4bf3a0",
11016   sig4hash := "-(seq(),seq())" ),
11017 rec(
11018   kind := "OPERATION",
11019   sin := [ [ elt-dvs/fld^num, "d" ] ],
11020   sou := [ [ elt-dvs/fld^num ] ],
11021   name := "-",
11022   short := "The negative of or difference between the number field divisors (and places).",
11023   ex := [  ],
11024   hash := "6ee450",
11025   sig := " - <elt-dvs/fld^num> d",
11026   sog := " -> <elt-dvs/fld^num>",
11027   docsrc := "<internal>",
11028   sinflat := [ elt-dvs/fld^num ],
11029   souflat := [ elt-dvs/fld^num ],
11030   soghash := "87f535",
11031   sig4hash := "-(elt-dvs/fld^num)" ),
11032 rec(
11033   kind := "OPERATION",
11034   sin := [ [ elt-pls/fld^num, "p" ] ],
11035   sou := [ [ elt-dvs/fld^num ] ],
11036   name := "-",
11037   short := "The negative of or difference between the number field divisors (and places).",
11038   ex := [  ],
11039   hash := "d78dd5",
11040   sig := " - <elt-pls/fld^num> p",
11041   sog := " -> <elt-dvs/fld^num>",
11042   docsrc := "<internal>",
11043   sinflat := [ elt-pls/fld^num ],
11044   souflat := [ elt-dvs/fld^num ],
11045   soghash := "87f535",
11046   sig4hash := "-(elt-pls/fld^num)" ),
11047 rec(
11048   kind := "OPERATION",
11049   sin := [ [ elt-dvs/fld^num, "d1" ], [ elt-dvs/fld^num, "d2" ] ],
11050   sou := [ [ elt-dvs/fld^num ] ],
11051   name := "-",
11052   short := "The negative of or difference between the number field divisors (and places).",
11053   ex := [  ],
11054   hash := "9a31fa",
11055   sig := "<elt-dvs/fld^num> d1 - <elt-dvs/fld^num> d2",
11056   sog := " -> <elt-dvs/fld^num>",
11057   docsrc := "<internal>",
11058   sinflat := [ elt-dvs/fld^num, elt-dvs/fld^num ],
11059   souflat := [ elt-dvs/fld^num ],
11060   soghash := "87f535",
11061   sig4hash := "-(elt-dvs/fld^num,elt-dvs/fld^num)" ),
11062 rec(
11063   kind := "OPERATION",
11064   sin := [ [ elt-dvs/fld^num, "d" ], [ elt-pls/fld^num, "p" ] ],
11065   sou := [ [ elt-dvs/fld^num ] ],
11066   name := "-",
11067   short := "The negative of or difference between the number field divisors (and places).",
11068   ex := [  ],
11069   hash := "1e319c",
11070   sig := "<elt-dvs/fld^num> d - <elt-pls/fld^num> p",
11071   sog := " -> <elt-dvs/fld^num>",
11072   docsrc := "<internal>",
11073   sinflat := [ elt-dvs/fld^num, elt-pls/fld^num ],
11074   souflat := [ elt-dvs/fld^num ],
11075   soghash := "87f535",
11076   sig4hash := "-(elt-dvs/fld^num,elt-pls/fld^num)" ),
11077 rec(
11078   kind := "OPERATION",
11079   sin := [ [ elt-pls/fld^num, "p" ], [ elt-dvs/fld^num, "d" ] ],
11080   sou := [ [ elt-dvs/fld^num ] ],
11081   name := "-",
11082   short := "The negative of or difference between the number field divisors (and places).",
11083   ex := [  ],
11084   hash := "bbb6f8",
11085   sig := "<elt-pls/fld^num> p - <elt-dvs/fld^num> d",
11086   sog := " -> <elt-dvs/fld^num>",
11087   docsrc := "<internal>",
11088   sinflat := [ elt-pls/fld^num, elt-dvs/fld^num ],
11089   souflat := [ elt-dvs/fld^num ],
11090   soghash := "87f535",
11091   sig4hash := "-(elt-pls/fld^num,elt-dvs/fld^num)" ),
11092 rec(
11093   kind := "OPERATION",
11094   sin := [ [ elt-pls/fld^num, "p1" ], [ elt-pls/fld^num, "p2" ] ],
11095   sou := [ [ elt-dvs/fld^num ] ],
11096   name := "-",
11097   short := "The negative of or difference between the number field divisors (and places).",
11098   ex := [  ],
11099   hash := "c757b8",
11100   sig := "<elt-pls/fld^num> p1 - <elt-pls/fld^num> p2",
11101   sog := " -> <elt-dvs/fld^num>",
11102   docsrc := "<internal>",
11103   sinflat := [ elt-pls/fld^num, elt-pls/fld^num ],
11104   souflat := [ elt-dvs/fld^num ],
11105   soghash := "87f535",
11106   sig4hash := "-(elt-pls/fld^num,elt-pls/fld^num)" ),
11107 rec(
11108   kind := "FUNCTION",
11109   sin := [ [ grp^abl, "G" ], [ elt-ord^rat, "i" ] ],
11110   sou := [ [ elt-grp^abl ] ],
11111   name := "Generator",
11112   short := "The i-th basis element.",
11113   ex := [ "x_G := AbelianGroup( [2,5] );\nGenerator(x_G, 1);\nGenerator(x_G, 2);\nNumberOfGenerators(x_G);" ],
11114   hash := "bef35b",
11115   sig := "Generator(<grp^abl> G, <elt-ord^rat> i)",
11116   sog := " -> <elt-grp^abl>",
11117   docsrc := "<internal>",
11118   sinflat := [ grp^abl, elt-ord^rat ],
11119   souflat := [ elt-grp^abl ],
11120   soghash := "da39a3",
11121   sig4hash := "Generator(grp^abl,elt-ord^rat)" ),
11122 rec(
11123   kind := "FUNCTION",
11124   sin := [ [ mdl^vec, "M" ], [ elt-ord^rat, "i" ] ],
11125   sou := [ [ elt-mdl^vec ] ],
11126   name := "Generator",
11127   short := "The i-th basis element.",
11128   ex := [ "x_V := VectorSpace( FiniteField( 5 ), 3);\nGenerator(x_V, 1);\nGenerator(x_V, 2);\nGenerator(x_V, 3);\nNumberOfGenerators(x_V);" ],
11129   hash := "228580",
11130   sig := "Generator(<mdl^vec> M, <elt-ord^rat> i)",
11131   sog := " -> <elt-mdl^vec>",
11132   docsrc := "<internal>",
11133   sinflat := [ mdl^vec, elt-ord^rat ],
11134   souflat := [ elt-mdl^vec ],
11135   soghash := "da39a3",
11136   sig4hash := "Generator(mdl^vec,elt-ord^rat)" ),
11137 rec(
11138   kind := "FUNCTION",
11139   sin := [ [ mdl^mat, "M" ], [ elt-ord^rat, "i" ] ],
11140   sou := [ [ elt-mdl^mat ] ],
11141   name := "Generator",
11142   short := "The i-th basis element.",
11143   ex := [ "x_M := RMatrixSpace( FiniteField( 5 ), 3, 3 );\nGenerator(x_M, 1);\nGenerator(x_M, 2);\nGenerator(x_M, 3);\nGenerator(x_M, 4);\nNumberOfGenerators(x_M);" ],
11144   hash := "20711c",
11145   sig := "Generator(<mdl^mat> M, <elt-ord^rat> i)",
11146   sog := " -> <elt-mdl^mat>",
11147   docsrc := "<internal>",
11148   sinflat := [ mdl^mat, elt-ord^rat ],
11149   souflat := [ elt-mdl^mat ],
11150   soghash := "da39a3",
11151   sig4hash := "Generator(mdl^mat,elt-ord^rat)" ),
11152 rec(
11153   kind := "FUNCTION",
11154   sin := [ [ mdl, "M" ], [ elt-ord^rat, "i" ] ],
11155   sou := [ [ elt-mdl ] ],
11156   name := "Generator",
11157   short := "The i-th basis element.",
11158   ex := [ "x_V := VectorSpace( FiniteField( 5 ), 3);\nGenerator(x_V, 1);\nGenerator(x_V, 2);\nGenerator(x_V, 3);\nNumberOfGenerators(x_V);" ],
11159   hash := "6ff760",
11160   sig := "Generator(<mdl> M, <elt-ord^rat> i)",
11161   sog := " -> <elt-mdl>",
11162   docsrc := "<internal>",
11163   sinflat := [ mdl, elt-ord^rat ],
11164   souflat := [ elt-mdl ],
11165   soghash := "da39a3",
11166   sig4hash := "Generator(mdl,elt-ord^rat)" ),
11167 rec(
11168   kind := "FUNCTION",
11169   sin := [ [ fld^fra, "F" ], [ elt-ord^rat, "i" ] ],
11170   sou := [ [ elt-fld^fra ] ],
11171   name := "Generator",
11172   short := "The i-th basis element.",
11173   ex := [  ],
11174   hash := "7421d8",
11175   sig := "Generator(<fld^fra> F, <elt-ord^rat> i)",
11176   sog := " -> <elt-fld^fra>",
11177   docsrc := "<internal>",
11178   sinflat := [ fld^fra, elt-ord^rat ],
11179   souflat := [ elt-fld^fra ],
11180   soghash := "74ef48",
11181   sig4hash := "Generator(fld^fra,elt-ord^rat)" ),
11182 rec(
11183   kind := "FUNCTION",
11184   sin := [ [ ord^num, "O" ], [ elt-ord^rat, "i" ] ],
11185   sou := [ [ elt-fld^fra ] ],
11186   name := "Generator",
11187   short := "The i-th basis element.",
11188   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_O := MaximalOrder( x_x^2 - 5 );\nGenerator(x_O, 1);\nGenerator(x_O, 2);\n" ],
11189   hash := "4b4b22",
11190   sig := "Generator(<ord^num> O, <elt-ord^rat> i)",
11191   sog := " -> <elt-fld^fra>",
11192   docsrc := "<internal>",
11193   sinflat := [ ord^num, elt-ord^rat ],
11194   souflat := [ elt-fld^fra ],
11195   soghash := "da39a3",
11196   sig4hash := "Generator(ord^num,elt-ord^rat)" ),
11197 rec(
11198   kind := "FUNCTION",
11199   sin := [ [ ord^fun, "O" ], [ elt-ord^rat, "i" ] ],
11200   sou := [ [ elt-fld^fra ] ],
11201   name := "Generator",
11202   short := "The i-th basis element.",
11203   ex := [  ],
11204   hash := "12da23",
11205   sig := "Generator(<ord^fun> O, <elt-ord^rat> i)",
11206   sog := " -> <elt-fld^fra>",
11207   docsrc := "<internal>",
11208   sinflat := [ ord^fun, elt-ord^rat ],
11209   souflat := [ elt-fld^fra ],
11210   soghash := "74ef48",
11211   sig4hash := "Generator(ord^fun,elt-ord^rat)" ),
11212 rec(
11213   kind := "FUNCTION",
11214   sin := [ [ fld^num, "K" ], [ elt-ord^rat, "i" ] ],
11215   sou := [ [ elt-fld^num ] ],
11216   name := "Generator",
11217   short := "A primitive element of K (i must be 1).",
11218   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_F := NumberField( x_x^2 - 5 );\nx_a := Generator(x_F, 1);\nx_a^2;\nParent(x_a);", "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_F := NumberField( [x_x^2 - 5, x_x^2 - 7 ] );\nx_a := Generator(x_F, 1);\nx_b := Generator(x_F, 2);\nx_a^2;\nx_b^2;\nParent(x_a);\nParent(x_b);" ],
11219   hash := "eae08f",
11220   sig := "Generator(<fld^num> K, <elt-ord^rat> i)",
11221   sog := " -> <elt-fld^num>",
11222   docsrc := "<internal>",
11223   sinflat := [ fld^num, elt-ord^rat ],
11224   souflat := [ elt-fld^num ],
11225   soghash := "da39a3",
11226   sig4hash := "Generator(fld^num,elt-ord^rat)" ),
11227 rec(
11228   kind := "FUNCTION",
11229   sin := [ [ fld^fun, "K" ], [ elt-ord^rat, "i" ] ],
11230   sou := [ [ elt-fld^fun ] ],
11231   name := "Generator",
11232   short := "A primitive element of K (i must be 1).",
11233   ex := [ "x_k := FiniteField(5);\nx_kx := PolynomialAlgebra(x_k);\nx_kxy := PolynomialAlgebra( x_kx );\nx_x := Generator(x_kx, 1);\nx_y := Generator(x_kxy, 1);\nx_F := FunctionField( x_y^2 - x_x^3 + 1 );\nx_a := Generator(x_F, 1);\nx_a^2;\nParent(x_a);", "x_k := FiniteField(5);\nx_kx := PolynomialAlgebra(x_k);\nx_kxy := PolynomialAlgebra( x_kx );\nx_x := Generator(x_kx, 1);\nx_y := Generator(x_kxy, 1);\nx_F := FunctionField( [x_y^2 - x_x - 1, x_y^2 - x_x - 2 ] );\nx_a := Generator(x_F, 1);\nx_b := Generator(x_F, 2);\nx_a^2;\nx_b^2;\nParent(x_a);\nParent(x_b);" ],
11234   hash := "d97a93",
11235   sig := "Generator(<fld^fun> K, <elt-ord^rat> i)",
11236   sog := " -> <elt-fld^fun>",
11237   docsrc := "<internal>",
11238   sinflat := [ fld^fun, elt-ord^rat ],
11239   souflat := [ elt-fld^fun ],
11240   soghash := "da39a3",
11241   sig4hash := "Generator(fld^fun,elt-ord^rat)" ),
11242 rec(
11243   kind := "FUNCTION",
11244   sin := [ [ fld^com, "K" ], [ elt-ord^rat, "i" ] ],
11245   sou := [ [ elt-fld^com ] ],
11246   name := "Generator",
11247   short := "A primitive element of K (i must be 1).",
11248   ex := [ "x_C := ComplexField(100);\nx_i := Generator(x_C, 1);\nx_i^2;" ],
11249   hash := "2c586c",
11250   sig := "Generator(<fld^com> K, <elt-ord^rat> i)",
11251   sog := " -> <elt-fld^com>",
11252   docsrc := "<internal>",
11253   sinflat := [ fld^com, elt-ord^rat ],
11254   souflat := [ elt-fld^com ],
11255   soghash := "da39a3",
11256   sig4hash := "Generator(fld^com,elt-ord^rat)" ),
11257 rec(
11258   kind := "FUNCTION",
11259   sin := [ [ fld^rat, "K" ], [ elt-ord^rat, "i" ] ],
11260   sou := [ [ elt-fld^rat ] ],
11261   name := "Generator",
11262   short := "A primitive element of K (i must be 1).",
11263   ex := [ "x_Q := RationalField();\nGenerator( x_Q, 1 );" ],
11264   hash := "75db40",
11265   sig := "Generator(<fld^rat> K, <elt-ord^rat> i)",
11266   sog := " -> <elt-fld^rat>",
11267   docsrc := "<internal>",
11268   sinflat := [ fld^rat, elt-ord^rat ],
11269   souflat := [ elt-fld^rat ],
11270   soghash := "da39a3",
11271   sig4hash := "Generator(fld^rat,elt-ord^rat)" ),
11272 rec(
11273   kind := "FUNCTION",
11274   sin := [ [ alg^pol, "A" ], [ elt-ord^rat, "i" ] ],
11275   sou := [ [ elt-alg^pol ] ],
11276   name := "Generator",
11277   short := "The uniformizing or inertial element of the local structure, depending on whether i is 1 or 2.",
11278   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nGenerator(x_R, 1);" ],
11279   hash := "416e8f",
11280   sig := "Generator(<alg^pol> A, <elt-ord^rat> i)",
11281   sog := " -> <elt-alg^pol>",
11282   docsrc := "<internal>",
11283   sinflat := [ alg^pol, elt-ord^rat ],
11284   souflat := [ elt-alg^pol ],
11285   soghash := "da39a3",
11286   sig4hash := "Generator(alg^pol,elt-ord^rat)" ),
11287 rec(
11288   kind := "FUNCTION",
11289   sin := [ [ res^pol, "A" ], [ elt-ord^rat, "i" ] ],
11290   sou := [ [ elt-res^pol ] ],
11291   name := "Generator",
11292   short := "The uniformizing or inertial element of the local structure, depending on whether i is 1 or 2.",
11293   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_Q := Quotient(x_R, x_x^2 + 1 );\nx_a := Generator(x_Q, 1);\nx_a^2;" ],
11294   hash := "50625c",
11295   sig := "Generator(<res^pol> A, <elt-ord^rat> i)",
11296   sog := " -> <elt-res^pol>",
11297   docsrc := "<internal>",
11298   sinflat := [ res^pol, elt-ord^rat ],
11299   souflat := [ elt-res^pol ],
11300   soghash := "da39a3",
11301   sig4hash := "Generator(res^pol,elt-ord^rat)" ),
11302 rec(
11303   kind := "FUNCTION",
11304   sin := [ [ res^pad, "R" ], [ elt-ord^rat, "i" ] ],
11305   sou := [ [ elt-res^pad ] ],
11306   name := "Generator",
11307   short := "The primitive element of R.",
11308   ex := [ "x_z5 := pAdicRing(5,30);\nx_r5 := Quotient(x_z5, 5^10);\nGenerator(x_r5, 1);" ],
11309   hash := "56efc7",
11310   sig := "Generator(<res^pad> R, <elt-ord^rat> i)",
11311   sog := " -> <elt-res^pad>",
11312   docsrc := "<internal>",
11313   sinflat := [ res^pad, elt-ord^rat ],
11314   souflat := [ elt-res^pad ],
11315   soghash := "da39a3",
11316   sig4hash := "Generator(res^pad,elt-ord^rat)" ),
11317 rec(
11318   kind := "FUNCTION",
11319   sin := [ [ ord^pad, "R" ], [ elt-ord^rat, "i" ] ],
11320   sou := [ [ elt-ord^pad ] ],
11321   name := "Generator",
11322   short := "The primitive element of R.",
11323   ex := [ "x_z5 := pAdicRing(5,30);\nGenerator(x_z5,1);" ],
11324   hash := "d717ba",
11325   sig := "Generator(<ord^pad> R, <elt-ord^rat> i)",
11326   sog := " -> <elt-ord^pad>",
11327   docsrc := "<internal>",
11328   sinflat := [ ord^pad, elt-ord^rat ],
11329   souflat := [ elt-ord^pad ],
11330   soghash := "da39a3",
11331   sig4hash := "Generator(ord^pad,elt-ord^rat)" ),
11332 rec(
11333   kind := "FUNCTION",
11334   sin := [ [ fld^pad, "R" ], [ elt-ord^rat, "i" ] ],
11335   sou := [ [ elt-fld^pad ] ],
11336   name := "Generator",
11337   short := "The primitive element of R.",
11338   ex := [ "x_q5 := pAdicField(5,30);\nGenerator(x_q5,1);" ],
11339   hash := "af0655",
11340   sig := "Generator(<fld^pad> R, <elt-ord^rat> i)",
11341   sog := " -> <elt-fld^pad>",
11342   docsrc := "<internal>",
11343   sinflat := [ fld^pad, elt-ord^rat ],
11344   souflat := [ elt-fld^pad ],
11345   soghash := "da39a3",
11346   sig4hash := "Generator(fld^pad,elt-ord^rat)" ),
11347 rec(
11348   kind := "FUNCTION",
11349   sin := [ [ fld^fin, "R" ], [ elt-ord^rat, "i" ] ],
11350   sou := [ [ elt-fld^fin ] ],
11351   name := "Generator",
11352   short := "The ith vector generating M as an element of the vector space over the field.",
11353   ex := [ "x_F := FiniteField(125);\nGenerator(x_F, 1);" ],
11354   hash := "b4dc97",
11355   sig := "Generator(<fld^fin> R, <elt-ord^rat> i)",
11356   sog := " -> <elt-fld^fin>",
11357   docsrc := "<internal>",
11358   sinflat := [ fld^fin, elt-ord^rat ],
11359   souflat := [ elt-fld^fin ],
11360   soghash := "da39a3",
11361   sig4hash := "Generator(fld^fin,elt-ord^rat)" ),
11362 rec(
11363   kind := "FUNCTION",
11364   sin := [ [ rng^ser, "R" ], [ elt-ord^rat, "i" ] ],
11365   sou := [ [ elt-rng^ser ] ],
11366   name := "Generator",
11367   short := "The ith vector generating M as an element of the vector space over the field.",
11368   ex := [ "x_R := PowerSeriesRing( FiniteField( 5 ) );\nGenerator(x_R, 1);" ],
11369   hash := "bfcc9d",
11370   sig := "Generator(<rng^ser> R, <elt-ord^rat> i)",
11371   sog := " -> <elt-rng^ser>",
11372   docsrc := "<internal>",
11373   sinflat := [ rng^ser, elt-ord^rat ],
11374   souflat := [ elt-rng^ser ],
11375   soghash := "da39a3",
11376   sig4hash := "Generator(rng^ser,elt-ord^rat)" ),
11377 rec(
11378   kind := "FUNCTION",
11379   sin := [ [ rng, "R" ], [ elt-ord^rat, "i" ] ],
11380   sou := [ [ elt-rng ] ],
11381   name := "Generator",
11382   short := "The ith vector generating M as an element of the vector space over the field.",
11383   ex := [  ],
11384   hash := "676767",
11385   sig := "Generator(<rng> R, <elt-ord^rat> i)",
11386   sog := " -> <elt-rng>",
11387   docsrc := "<internal>",
11388   sinflat := [ rng, elt-ord^rat ],
11389   souflat := [ elt-rng ],
11390   soghash := "7ef0ef",
11391   sig4hash := "Generator(rng,elt-ord^rat)" ),
11392 rec(
11393   kind := "FUNCTION",
11394   sin := [ [ mdl^ded, "M" ], [ elt-ord^rat, "i" ] ],
11395   sou := [ [ elt-mdl^vec ] ],
11396   name := "Generator",
11397   short := "The ith vector generating M as an element of the vector space over the field.",
11398   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_O := MaximalOrder(x_x^2 - 18);\nx_a := Element(x_O, [0,1]);\nx_Ox := PolynomialAlgebra( x_O );\nx_x := Generator(x_Ox, 1);\nx_OO := MaximalOrder( x_x^3 - 27*x_a );\nx_I := Factorization( 3*x_OO )[1][1];\nx_M := Module(x_I);\nxL := List( [1..3], i->Generator(x_M, i) );" ],
11399   hash := "4c2cbf",
11400   sig := "Generator(<mdl^ded> M, <elt-ord^rat> i)",
11401   sog := " -> <elt-mdl^vec>",
11402   docsrc := "<internal>",
11403   sinflat := [ mdl^ded, elt-ord^rat ],
11404   souflat := [ elt-mdl^vec ],
11405   soghash := "da39a3",
11406   sig4hash := "Generator(mdl^ded,elt-ord^rat)" ),
11407 rec(
11408   kind := "OPERATION",
11409   sin := [ [ grp^abl, "G" ], [ elt-ord^rat, "i" ] ],
11410   sou := [ [ elt-grp^abl ] ],
11411   name := ".",
11412   short := "The i-th basis element.",
11413   ex := [  ],
11414   hash := "c61e27",
11415   sig := "<grp^abl> G . <elt-ord^rat> i",
11416   sog := " -> <elt-grp^abl>",
11417   docsrc := "<internal>",
11418   sinflat := [ grp^abl, elt-ord^rat ],
11419   souflat := [ elt-grp^abl ],
11420   soghash := "b42d93",
11421   sig4hash := ".(grp^abl,elt-ord^rat)" ),
11422 rec(
11423   kind := "OPERATION",
11424   sin := [ [ mdl^vec, "M" ], [ elt-ord^rat, "i" ] ],
11425   sou := [ [ elt-mdl^vec ] ],
11426   name := ".",
11427   short := "The i-th basis element.",
11428   ex := [  ],
11429   hash := "ff057b",
11430   sig := "<mdl^vec> M . <elt-ord^rat> i",
11431   sog := " -> <elt-mdl^vec>",
11432   docsrc := "<internal>",
11433   sinflat := [ mdl^vec, elt-ord^rat ],
11434   souflat := [ elt-mdl^vec ],
11435   soghash := "b46581",
11436   sig4hash := ".(mdl^vec,elt-ord^rat)" ),
11437 rec(
11438   kind := "OPERATION",
11439   sin := [ [ mdl^mat, "M" ], [ elt-ord^rat, "i" ] ],
11440   sou := [ [ elt-mdl^mat ] ],
11441   name := ".",
11442   short := "The i-th basis element.",
11443   ex := [  ],
11444   hash := "737a5c",
11445   sig := "<mdl^mat> M . <elt-ord^rat> i",
11446   sog := " -> <elt-mdl^mat>",
11447   docsrc := "<internal>",
11448   sinflat := [ mdl^mat, elt-ord^rat ],
11449   souflat := [ elt-mdl^mat ],
11450   soghash := "5284ac",
11451   sig4hash := ".(mdl^mat,elt-ord^rat)" ),
11452 rec(
11453   kind := "OPERATION",
11454   sin := [ [ mdl, "M" ], [ elt-ord^rat, "i" ] ],
11455   sou := [ [ elt-mdl ] ],
11456   name := ".",
11457   short := "The i-th basis element.",
11458   ex := [  ],
11459   hash := "3d04c7",
11460   sig := "<mdl> M . <elt-ord^rat> i",
11461   sog := " -> <elt-mdl>",
11462   docsrc := "<internal>",
11463   sinflat := [ mdl, elt-ord^rat ],
11464   souflat := [ elt-mdl ],
11465   soghash := "97b5cd",
11466   sig4hash := ".(mdl,elt-ord^rat)" ),
11467 rec(
11468   kind := "OPERATION",
11469   sin := [ [ fld^fra, "F" ], [ elt-ord^rat, "i" ] ],
11470   sou := [ [ elt-fld^fra ] ],
11471   name := ".",
11472   short := "The i-th basis element.",
11473   ex := [  ],
11474   hash := "0c7daf",
11475   sig := "<fld^fra> F . <elt-ord^rat> i",
11476   sog := " -> <elt-fld^fra>",
11477   docsrc := "<internal>",
11478   sinflat := [ fld^fra, elt-ord^rat ],
11479   souflat := [ elt-fld^fra ],
11480   soghash := "74ef48",
11481   sig4hash := ".(fld^fra,elt-ord^rat)" ),
11482 rec(
11483   kind := "OPERATION",
11484   sin := [ [ ord^num, "O" ], [ elt-ord^rat, "i" ] ],
11485   sou := [ [ elt-fld^fra ] ],
11486   name := ".",
11487   short := "The i-th basis element.",
11488   ex := [  ],
11489   hash := "f2726a",
11490   sig := "<ord^num> O . <elt-ord^rat> i",
11491   sog := " -> <elt-fld^fra>",
11492   docsrc := "<internal>",
11493   sinflat := [ ord^num, elt-ord^rat ],
11494   souflat := [ elt-fld^fra ],
11495   soghash := "74ef48",
11496   sig4hash := ".(ord^num,elt-ord^rat)" ),
11497 rec(
11498   kind := "OPERATION",
11499   sin := [ [ ord^fun, "O" ], [ elt-ord^rat, "i" ] ],
11500   sou := [ [ elt-fld^fra ] ],
11501   name := ".",
11502   short := "The i-th basis element.",
11503   ex := [  ],
11504   hash := "f77154",
11505   sig := "<ord^fun> O . <elt-ord^rat> i",
11506   sog := " -> <elt-fld^fra>",
11507   docsrc := "<internal>",
11508   sinflat := [ ord^fun, elt-ord^rat ],
11509   souflat := [ elt-fld^fra ],
11510   soghash := "74ef48",
11511   sig4hash := ".(ord^fun,elt-ord^rat)" ),
11512 rec(
11513   kind := "OPERATION",
11514   sin := [ [ fld^num, "K" ], [ elt-ord^rat, "i" ] ],
11515   sou := [ [ elt-fld^num ] ],
11516   name := ".",
11517   short := "A primitive element of K (i must be 1).",
11518   ex := [  ],
11519   hash := "c2bf1d",
11520   sig := "<fld^num> K . <elt-ord^rat> i",
11521   sog := " -> <elt-fld^num>",
11522   docsrc := "<internal>",
11523   sinflat := [ fld^num, elt-ord^rat ],
11524   souflat := [ elt-fld^num ],
11525   soghash := "7a0611",
11526   sig4hash := ".(fld^num,elt-ord^rat)" ),
11527 rec(
11528   kind := "OPERATION",
11529   sin := [ [ fld^fun, "K" ], [ elt-ord^rat, "i" ] ],
11530   sou := [ [ elt-fld^fun ] ],
11531   name := ".",
11532   short := "A primitive element of K (i must be 1).",
11533   ex := [  ],
11534   hash := "9ce6f1",
11535   sig := "<fld^fun> K . <elt-ord^rat> i",
11536   sog := " -> <elt-fld^fun>",
11537   docsrc := "<internal>",
11538   sinflat := [ fld^fun, elt-ord^rat ],
11539   souflat := [ elt-fld^fun ],
11540   soghash := "23d8b4",
11541   sig4hash := ".(fld^fun,elt-ord^rat)" ),
11542 rec(
11543   kind := "OPERATION",
11544   sin := [ [ fld^com, "K" ], [ elt-ord^rat, "i" ] ],
11545   sou := [ [ elt-fld^com ] ],
11546   name := ".",
11547   short := "A primitive element of K (i must be 1).",
11548   ex := [  ],
11549   hash := "48446e",
11550   sig := "<fld^com> K . <elt-ord^rat> i",
11551   sog := " -> <elt-fld^com>",
11552   docsrc := "<internal>",
11553   sinflat := [ fld^com, elt-ord^rat ],
11554   souflat := [ elt-fld^com ],
11555   soghash := "0d772f",
11556   sig4hash := ".(fld^com,elt-ord^rat)" ),
11557 rec(
11558   kind := "OPERATION",
11559   sin := [ [ fld^rat, "K" ], [ elt-ord^rat, "i" ] ],
11560   sou := [ [ elt-fld^rat ] ],
11561   name := ".",
11562   short := "A primitive element of K (i must be 1).",
11563   ex := [  ],
11564   hash := "ddfe0a",
11565   sig := "<fld^rat> K . <elt-ord^rat> i",
11566   sog := " -> <elt-fld^rat>",
11567   docsrc := "<internal>",
11568   sinflat := [ fld^rat, elt-ord^rat ],
11569   souflat := [ elt-fld^rat ],
11570   soghash := "89f5fc",
11571   sig4hash := ".(fld^rat,elt-ord^rat)" ),
11572 rec(
11573   kind := "OPERATION",
11574   sin := [ [ alg^pol, "A" ], [ elt-ord^rat, "i" ] ],
11575   sou := [ [ elt-alg^pol ] ],
11576   name := ".",
11577   short := "The uniformizing or inertial element of the local structure, depending on whether i is 1 or 2.",
11578   ex := [  ],
11579   hash := "6e0860",
11580   sig := "<alg^pol> A . <elt-ord^rat> i",
11581   sog := " -> <elt-alg^pol>",
11582   docsrc := "<internal>",
11583   sinflat := [ alg^pol, elt-ord^rat ],
11584   souflat := [ elt-alg^pol ],
11585   soghash := "ba7338",
11586   sig4hash := ".(alg^pol,elt-ord^rat)" ),
11587 rec(
11588   kind := "OPERATION",
11589   sin := [ [ res^pol, "A" ], [ elt-ord^rat, "i" ] ],
11590   sou := [ [ elt-res^pol ] ],
11591   name := ".",
11592   short := "The uniformizing or inertial element of the local structure, depending on whether i is 1 or 2.",
11593   ex := [  ],
11594   hash := "cdd7b9",
11595   sig := "<res^pol> A . <elt-ord^rat> i",
11596   sog := " -> <elt-res^pol>",
11597   docsrc := "<internal>",
11598   sinflat := [ res^pol, elt-ord^rat ],
11599   souflat := [ elt-res^pol ],
11600   soghash := "8ffe0c",
11601   sig4hash := ".(res^pol,elt-ord^rat)" ),
11602 rec(
11603   kind := "OPERATION",
11604   sin := [ [ res^pad, "R" ], [ elt-ord^rat, "i" ] ],
11605   sou := [ [ elt-res^pad ] ],
11606   name := ".",
11607   short := "The primitive element of R.",
11608   ex := [  ],
11609   hash := "b132f6",
11610   sig := "<res^pad> R . <elt-ord^rat> i",
11611   sog := " -> <elt-res^pad>",
11612   docsrc := "<internal>",
11613   sinflat := [ res^pad, elt-ord^rat ],
11614   souflat := [ elt-res^pad ],
11615   soghash := "0061b4",
11616   sig4hash := ".(res^pad,elt-ord^rat)" ),
11617 rec(
11618   kind := "OPERATION",
11619   sin := [ [ ord^pad, "R" ], [ elt-ord^rat, "i" ] ],
11620   sou := [ [ elt-ord^pad ] ],
11621   name := ".",
11622   short := "The primitive element of R.",
11623   ex := [  ],
11624   hash := "54aba9",
11625   sig := "<ord^pad> R . <elt-ord^rat> i",
11626   sog := " -> <elt-ord^pad>",
11627   docsrc := "<internal>",
11628   sinflat := [ ord^pad, elt-ord^rat ],
11629   souflat := [ elt-ord^pad ],
11630   soghash := "9ee81d",
11631   sig4hash := ".(ord^pad,elt-ord^rat)" ),
11632 rec(
11633   kind := "OPERATION",
11634   sin := [ [ fld^pad, "R" ], [ elt-ord^rat, "i" ] ],
11635   sou := [ [ elt-fld^pad ] ],
11636   name := ".",
11637   short := "The primitive element of R.",
11638   ex := [  ],
11639   hash := "c647c8",
11640   sig := "<fld^pad> R . <elt-ord^rat> i",
11641   sog := " -> <elt-fld^pad>",
11642   docsrc := "<internal>",
11643   sinflat := [ fld^pad, elt-ord^rat ],
11644   souflat := [ elt-fld^pad ],
11645   soghash := "8c3f71",
11646   sig4hash := ".(fld^pad,elt-ord^rat)" ),
11647 rec(
11648   kind := "OPERATION",
11649   sin := [ [ fld^fin, "R" ], [ elt-ord^rat, "i" ] ],
11650   sou := [ [ elt-fld^fin ] ],
11651   name := ".",
11652   short := "The ith vector generating M as an element of the vector space over the field.",
11653   ex := [  ],
11654   hash := "58e6f5",
11655   sig := "<fld^fin> R . <elt-ord^rat> i",
11656   sog := " -> <elt-fld^fin>",
11657   docsrc := "<internal>",
11658   sinflat := [ fld^fin, elt-ord^rat ],
11659   souflat := [ elt-fld^fin ],
11660   soghash := "97e752",
11661   sig4hash := ".(fld^fin,elt-ord^rat)" ),
11662 rec(
11663   kind := "OPERATION",
11664   sin := [ [ rng^ser, "R" ], [ elt-ord^rat, "i" ] ],
11665   sou := [ [ elt-rng^ser ] ],
11666   name := ".",
11667   short := "The ith vector generating M as an element of the vector space over the field.",
11668   ex := [  ],
11669   hash := "dfffc7",
11670   sig := "<rng^ser> R . <elt-ord^rat> i",
11671   sog := " -> <elt-rng^ser>",
11672   docsrc := "<internal>",
11673   sinflat := [ rng^ser, elt-ord^rat ],
11674   souflat := [ elt-rng^ser ],
11675   soghash := "28734d",
11676   sig4hash := ".(rng^ser,elt-ord^rat)" ),
11677 rec(
11678   kind := "OPERATION",
11679   sin := [ [ rng, "R" ], [ elt-ord^rat, "i" ] ],
11680   sou := [ [ elt-rng ] ],
11681   name := ".",
11682   short := "The ith vector generating M as an element of the vector space over the field.",
11683   ex := [  ],
11684   hash := "1ca758",
11685   sig := "<rng> R . <elt-ord^rat> i",
11686   sog := " -> <elt-rng>",
11687   docsrc := "<internal>",
11688   sinflat := [ rng, elt-ord^rat ],
11689   souflat := [ elt-rng ],
11690   soghash := "7ef0ef",
11691   sig4hash := ".(rng,elt-ord^rat)" ),
11692 rec(
11693   kind := "OPERATION",
11694   sin := [ [ mdl^ded, "M" ], [ elt-ord^rat, "i" ] ],
11695   sou := [ [ elt-mdl^vec ] ],
11696   name := ".",
11697   short := "The ith vector generating M as an element of the vector space over the field.",
11698   ex := [  ],
11699   hash := "5104be",
11700   sig := "<mdl^ded> M . <elt-ord^rat> i",
11701   sog := " -> <elt-mdl^vec>",
11702   docsrc := "<internal>",
11703   sinflat := [ mdl^ded, elt-ord^rat ],
11704   souflat := [ elt-mdl^vec ],
11705   soghash := "b46581",
11706   sig4hash := ".(mdl^ded,elt-ord^rat)" ),
11707 rec(
11708   kind := "OPERATION",
11709   sin := [ [ elt-ord^rat, "x" ], [ elt-ord^rat, "y" ] ],
11710   sou := [ [ elt-fld^rat ] ],
11711   name := "/",
11712   short := "Quotient of x by y.",
11713   ex := [  ],
11714   hash := "77833f",
11715   sig := "<elt-ord^rat> x / <elt-ord^rat> y",
11716   sog := " -> <elt-fld^rat>",
11717   docsrc := "<internal>",
11718   sinflat := [ elt-ord^rat, elt-ord^rat ],
11719   souflat := [ elt-fld^rat ],
11720   soghash := "89f5fc",
11721   sig4hash := "/(elt-ord^rat,elt-ord^rat)" ),
11722 rec(
11723   kind := "OPERATION",
11724   sin := [ [ elt-fld^rat, "x" ], [ elt-fld^rat, "y" ] ],
11725   sou := [ [ elt-fld^rat ] ],
11726   name := "/",
11727   short := "Quotient of x by y.",
11728   ex := [  ],
11729   hash := "78c4e6",
11730   sig := "<elt-fld^rat> x / <elt-fld^rat> y",
11731   sog := " -> <elt-fld^rat>",
11732   docsrc := "<internal>",
11733   sinflat := [ elt-fld^rat, elt-fld^rat ],
11734   souflat := [ elt-fld^rat ],
11735   soghash := "89f5fc",
11736   sig4hash := "/(elt-fld^rat,elt-fld^rat)" ),
11737 rec(
11738   kind := "OPERATION",
11739   sin := [ [ elt-fld^rea, "x" ], [ elt-fld^rea, "y" ] ],
11740   sou := [ [ elt-fld^rea ] ],
11741   name := "/",
11742   short := "Quotient of x by y.",
11743   ex := [  ],
11744   hash := "ba88f2",
11745   sig := "<elt-fld^rea> x / <elt-fld^rea> y",
11746   sog := " -> <elt-fld^rea>",
11747   docsrc := "<internal>",
11748   sinflat := [ elt-fld^rea, elt-fld^rea ],
11749   souflat := [ elt-fld^rea ],
11750   soghash := "7f2490",
11751   sig4hash := "/(elt-fld^rea,elt-fld^rea)" ),
11752 rec(
11753   kind := "OPERATION",
11754   sin := [ [ elt-fld^com, "x" ], [ elt-fld^com, "y" ] ],
11755   sou := [ [ elt-fld^com ] ],
11756   name := "/",
11757   short := "Quotient of x by y.",
11758   ex := [  ],
11759   hash := "5412b3",
11760   sig := "<elt-fld^com> x / <elt-fld^com> y",
11761   sog := " -> <elt-fld^com>",
11762   docsrc := "<internal>",
11763   sinflat := [ elt-fld^com, elt-fld^com ],
11764   souflat := [ elt-fld^com ],
11765   soghash := "0d772f",
11766   sig4hash := "/(elt-fld^com,elt-fld^com)" ),
11767 rec(
11768   kind := "OPERATION",
11769   sin := [ [ elt-fld^fin, "x" ], [ elt-fld^fin, "y" ] ],
11770   sou := [ [ elt-fld^fin ] ],
11771   name := "/",
11772   short := "Quotient of x by y.",
11773   ex := [  ],
11774   hash := "829cf9",
11775   sig := "<elt-fld^fin> x / <elt-fld^fin> y",
11776   sog := " -> <elt-fld^fin>",
11777   docsrc := "<internal>",
11778   sinflat := [ elt-fld^fin, elt-fld^fin ],
11779   souflat := [ elt-fld^fin ],
11780   soghash := "97e752",
11781   sig4hash := "/(elt-fld^fin,elt-fld^fin)" ),
11782 rec(
11783   kind := "OPERATION",
11784   sin := [ [ elt-alg^pol, "x" ], [ elt-alg^pol, "y" ] ],
11785   sou := [ [ elt-fld^pol ] ],
11786   name := "/",
11787   short := "Quotient of x by y.",
11788   ex := [  ],
11789   hash := "fb7bf1",
11790   sig := "<elt-alg^pol> x / <elt-alg^pol> y",
11791   sog := " -> <elt-fld^pol>",
11792   docsrc := "<internal>",
11793   sinflat := [ elt-alg^pol, elt-alg^pol ],
11794   souflat := [ elt-fld^pol ],
11795   soghash := "540d59",
11796   sig4hash := "/(elt-alg^pol,elt-alg^pol)" ),
11797 rec(
11798   kind := "OPERATION",
11799   sin := [ [ elt-rng, "x" ], [ elt-rng, "y" ] ],
11800   sou := [ [ elt-rng ] ],
11801   name := "/",
11802   short := "Quotient of x by y.",
11803   ex := [  ],
11804   hash := "0cce58",
11805   sig := "<elt-rng> x / <elt-rng> y",
11806   sog := " -> <elt-rng>",
11807   docsrc := "<internal>",
11808   sinflat := [ elt-rng, elt-rng ],
11809   souflat := [ elt-rng ],
11810   soghash := "7ef0ef",
11811   sig4hash := "/(elt-rng,elt-rng)" ),
11812 rec(
11813   kind := "OPERATION",
11814   sin := [ [ elt-res^rat, "x" ], [ elt-res^rat, "y" ] ],
11815   sou := [ [ elt-res^rat ] ],
11816   name := "/",
11817   short := "Quotient of x by y.",
11818   ex := [  ],
11819   hash := "22ce53",
11820   sig := "<elt-res^rat> x / <elt-res^rat> y",
11821   sog := " -> <elt-res^rat>",
11822   docsrc := "<internal>",
11823   sinflat := [ elt-res^rat, elt-res^rat ],
11824   souflat := [ elt-res^rat ],
11825   soghash := "7a2c2e",
11826   sig4hash := "/(elt-res^rat,elt-res^rat)" ),
11827 rec(
11828   kind := "OPERATION",
11829   sin := [ [ elt-ord^pad, "x" ], [ elt-ord^pad, "y" ] ],
11830   sou := [ [ elt-ord^pad ] ],
11831   name := "/",
11832   short := "Quotient of x by y.",
11833   ex := [  ],
11834   hash := "109b0a",
11835   sig := "<elt-ord^pad> x / <elt-ord^pad> y",
11836   sog := " -> <elt-ord^pad>",
11837   docsrc := "<internal>",
11838   sinflat := [ elt-ord^pad, elt-ord^pad ],
11839   souflat := [ elt-ord^pad ],
11840   soghash := "9ee81d",
11841   sig4hash := "/(elt-ord^pad,elt-ord^pad)" ),
11842 rec(
11843   kind := "OPERATION",
11844   sin := [ [ elt-fld^pad, "x" ], [ elt-fld^pad, "y" ] ],
11845   sou := [ [ elt-fld^pad ] ],
11846   name := "/",
11847   short := "Quotient of x by y.",
11848   ex := [  ],
11849   hash := "5d0a7e",
11850   sig := "<elt-fld^pad> x / <elt-fld^pad> y",
11851   sog := " -> <elt-fld^pad>",
11852   docsrc := "<internal>",
11853   sinflat := [ elt-fld^pad, elt-fld^pad ],
11854   souflat := [ elt-fld^pad ],
11855   soghash := "8c3f71",
11856   sig4hash := "/(elt-fld^pad,elt-fld^pad)" ),
11857 rec(
11858   kind := "OPERATION",
11859   sin := [ [ elt-res^pol, "x" ], [ elt-res^pol, "y" ] ],
11860   sou := [ [ elt-res^pol ] ],
11861   name := "/",
11862   short := "Quotient of x by y.",
11863   ex := [  ],
11864   hash := "49bff8",
11865   sig := "<elt-res^pol> x / <elt-res^pol> y",
11866   sog := " -> <elt-res^pol>",
11867   docsrc := "<internal>",
11868   sinflat := [ elt-res^pol, elt-res^pol ],
11869   souflat := [ elt-res^pol ],
11870   soghash := "8ffe0c",
11871   sig4hash := "/(elt-res^pol,elt-res^pol)" ),
11872 rec(
11873   kind := "OPERATION",
11874   sin := [ [ elt-fld^fra, "x" ], [ elt-fld^fra, "y" ] ],
11875   sou := [ [ elt-fld^fra ] ],
11876   name := "/",
11877   short := "Quotient of x by y.",
11878   ex := [  ],
11879   hash := "1e1fcb",
11880   sig := "<elt-fld^fra> x / <elt-fld^fra> y",
11881   sog := " -> <elt-fld^fra>",
11882   docsrc := "<internal>",
11883   sinflat := [ elt-fld^fra, elt-fld^fra ],
11884   souflat := [ elt-fld^fra ],
11885   soghash := "74ef48",
11886   sig4hash := "/(elt-fld^fra,elt-fld^fra)" ),
11887 rec(
11888   kind := "OPERATION",
11889   sin := [ [ elt-fld^fra, "x" ], [ elt-ord^rat, "y" ] ],
11890   sou := [ [ elt-fld^fra ] ],
11891   name := "/",
11892   short := "Quotient of x by y.",
11893   ex := [  ],
11894   hash := "781c13",
11895   sig := "<elt-fld^fra> x / <elt-ord^rat> y",
11896   sog := " -> <elt-fld^fra>",
11897   docsrc := "<internal>",
11898   sinflat := [ elt-fld^fra, elt-ord^rat ],
11899   souflat := [ elt-fld^fra ],
11900   soghash := "74ef48",
11901   sig4hash := "/(elt-fld^fra,elt-ord^rat)" ),
11902 rec(
11903   kind := "OPERATION",
11904   sin := [ [ elt-ord^num, "x" ], [ elt-ord^num, "y" ] ],
11905   sou := [ [ elt-fld^fra ] ],
11906   name := "/",
11907   short := "Quotient of x by y.",
11908   ex := [  ],
11909   hash := "238a94",
11910   sig := "<elt-ord^num> x / <elt-ord^num> y",
11911   sog := " -> <elt-fld^fra>",
11912   docsrc := "<internal>",
11913   sinflat := [ elt-ord^num, elt-ord^num ],
11914   souflat := [ elt-fld^fra ],
11915   soghash := "74ef48",
11916   sig4hash := "/(elt-ord^num,elt-ord^num)" ),
11917 rec(
11918   kind := "OPERATION",
11919   sin := [ [ elt-ord^num, "x" ], [ elt-ord^rat, "y" ] ],
11920   sou := [ [ elt-fld^fra ] ],
11921   name := "/",
11922   short := "Quotient of x by y.",
11923   ex := [  ],
11924   hash := "ca36a7",
11925   sig := "<elt-ord^num> x / <elt-ord^rat> y",
11926   sog := " -> <elt-fld^fra>",
11927   docsrc := "<internal>",
11928   sinflat := [ elt-ord^num, elt-ord^rat ],
11929   souflat := [ elt-fld^fra ],
11930   soghash := "74ef48",
11931   sig4hash := "/(elt-ord^num,elt-ord^rat)" ),
11932 rec(
11933   kind := "OPERATION",
11934   sin := [ [ elt-ids^fra/ord^num, "x" ], [ elt-ids^fra/ord^num, "y" ] ],
11935   sou := [ [ elt-ids^fra/ord^num ] ],
11936   name := "/",
11937   short := "Quotient of x by y.",
11938   ex := [  ],
11939   hash := "e51526",
11940   sig := "<elt-ids^fra/ord^num> x / <elt-ids^fra/ord^num> y",
11941   sog := " -> <elt-ids^fra/ord^num>",
11942   docsrc := "<internal>",
11943   sinflat := [ elt-ids^fra/ord^num, elt-ids^fra/ord^num ],
11944   souflat := [ elt-ids^fra/ord^num ],
11945   soghash := "ca011c",
11946   sig4hash := "/(elt-ids^fra/ord^num,elt-ids^fra/ord^num)" ),
11947 rec(
11948   kind := "OPERATION",
11949   sin := [ [ elt-fld^fun, "x" ], [ elt-fld^fun, "y" ] ],
11950   sou := [ [ elt-fld^fun ] ],
11951   name := "/",
11952   short := "Quotient of x by y.",
11953   ex := [  ],
11954   hash := "553b27",
11955   sig := "<elt-fld^fun> x / <elt-fld^fun> y",
11956   sog := " -> <elt-fld^fun>",
11957   docsrc := "<internal>",
11958   sinflat := [ elt-fld^fun, elt-fld^fun ],
11959   souflat := [ elt-fld^fun ],
11960   soghash := "23d8b4",
11961   sig4hash := "/(elt-fld^fun,elt-fld^fun)" ),
11962 rec(
11963   kind := "OPERATION",
11964   sin := [ [ elt-ord^fun, "x" ], [ elt-ord^fun, "y" ] ],
11965   sou := [ [ elt-fld^fun ] ],
11966   name := "/",
11967   short := "Quotient of x by y.",
11968   ex := [  ],
11969   hash := "e6b0c9",
11970   sig := "<elt-ord^fun> x / <elt-ord^fun> y",
11971   sog := " -> <elt-fld^fun>",
11972   docsrc := "<internal>",
11973   sinflat := [ elt-ord^fun, elt-ord^fun ],
11974   souflat := [ elt-fld^fun ],
11975   soghash := "23d8b4",
11976   sig4hash := "/(elt-ord^fun,elt-ord^fun)" ),
11977 rec(
11978   kind := "OPERATION",
11979   sin := [ [ elt-ord^fun, "x" ], [ elt-rng, "y" ] ],
11980   sou := [ [ elt-fld^fun ] ],
11981   name := "/",
11982   short := "Quotient of x by y.",
11983   ex := [  ],
11984   hash := "3d7eec",
11985   sig := "<elt-ord^fun> x / <elt-rng> y",
11986   sog := " -> <elt-fld^fun>",
11987   docsrc := "<internal>",
11988   sinflat := [ elt-ord^fun, elt-rng ],
11989   souflat := [ elt-fld^fun ],
11990   soghash := "23d8b4",
11991   sig4hash := "/(elt-ord^fun,elt-rng)" ),
11992 rec(
11993   kind := "OPERATION",
11994   sin := [ [ elt-fld^fun, "x" ], [ elt-rng, "y" ] ],
11995   sou := [ [ elt-fld^fun ] ],
11996   name := "/",
11997   short := "Quotient of x by y.",
11998   ex := [  ],
11999   hash := "e9735a",
12000   sig := "<elt-fld^fun> x / <elt-rng> y",
12001   sog := " -> <elt-fld^fun>",
12002   docsrc := "<internal>",
12003   sinflat := [ elt-fld^fun, elt-rng ],
12004   souflat := [ elt-fld^fun ],
12005   soghash := "23d8b4",
12006   sig4hash := "/(elt-fld^fun,elt-rng)" ),
12007 rec(
12008   kind := "OPERATION",
12009   sin := [ [ elt-dif/fld^fun, "x" ], [ elt-dif/fld^fun, "y" ] ],
12010   sou := [ [ elt-fld^fun ] ],
12011   name := "/",
12012   short := "Quotient of x by y.",
12013   ex := [  ],
12014   hash := "08af13",
12015   sig := "<elt-dif/fld^fun> x / <elt-dif/fld^fun> y",
12016   sog := " -> <elt-fld^fun>",
12017   docsrc := "<internal>",
12018   sinflat := [ elt-dif/fld^fun, elt-dif/fld^fun ],
12019   souflat := [ elt-fld^fun ],
12020   soghash := "23d8b4",
12021   sig4hash := "/(elt-dif/fld^fun,elt-dif/fld^fun)" ),
12022 rec(
12023   kind := "OPERATION",
12024   sin := [ [ elt-dif/fld^fun, "x" ], [ elt-rng, "y" ] ],
12025   sou := [ [ elt-dif/fld^fun ] ],
12026   name := "/",
12027   short := "Quotient of x by y.",
12028   ex := [  ],
12029   hash := "8e0999",
12030   sig := "<elt-dif/fld^fun> x / <elt-rng> y",
12031   sog := " -> <elt-dif/fld^fun>",
12032   docsrc := "<internal>",
12033   sinflat := [ elt-dif/fld^fun, elt-rng ],
12034   souflat := [ elt-dif/fld^fun ],
12035   soghash := "fb8974",
12036   sig4hash := "/(elt-dif/fld^fun,elt-rng)" ),
12037 rec(
12038   kind := "OPERATION",
12039   sin := [ [ elt-ids^int/ord^fun, "x" ], [ elt-ids^int/ord^fun, "y" ] ],
12040   sou := [ [ elt-ids^int/ord^fun ] ],
12041   name := "/",
12042   short := "Quotient of x by y.",
12043   ex := [  ],
12044   hash := "cb6ee8",
12045   sig := "<elt-ids^int/ord^fun> x / <elt-ids^int/ord^fun> y",
12046   sog := " -> <elt-ids^int/ord^fun>",
12047   docsrc := "<internal>",
12048   sinflat := [ elt-ids^int/ord^fun, elt-ids^int/ord^fun ],
12049   souflat := [ elt-ids^int/ord^fun ],
12050   soghash := "918914",
12051   sig4hash := "/(elt-ids^int/ord^fun,elt-ids^int/ord^fun)" ),
12052 rec(
12053   kind := "OPERATION",
12054   sin := [ [ elt-rng, "x" ], [ elt-ids^int/ord^fun, "y" ] ],
12055   sou := [ [ elt-ids^int/ord^fun ] ],
12056   name := "/",
12057   short := "Quotient of x by y.",
12058   ex := [  ],
12059   hash := "e5f5c1",
12060   sig := "<elt-rng> x / <elt-ids^int/ord^fun> y",
12061   sog := " -> <elt-ids^int/ord^fun>",
12062   docsrc := "<internal>",
12063   sinflat := [ elt-rng, elt-ids^int/ord^fun ],
12064   souflat := [ elt-ids^int/ord^fun ],
12065   soghash := "918914",
12066   sig4hash := "/(elt-rng,elt-ids^int/ord^fun)" ),
12067 rec(
12068   kind := "OPERATION",
12069   sin := [ [ elt-ord^inf, "x" ], [ any, "y" ] ],
12070   sou := [ [ elt-ord^inf ] ],
12071   name := "/",
12072   short := "Quotient of x by y.",
12073   ex := [  ],
12074   hash := "44a57f",
12075   sig := "<elt-ord^inf> x / <any> y",
12076   sog := " -> <elt-ord^inf>",
12077   docsrc := "<internal>",
12078   sinflat := [ elt-ord^inf, any ],
12079   souflat := [ elt-ord^inf ],
12080   soghash := "08787a",
12081   sig4hash := "/(elt-ord^inf,any)" ),
12082 rec(
12083   kind := "OPERATION",
12084   sin := [ [ any, "x" ], [ elt-ord^inf, "y" ] ],
12085   sou := [ [ any ] ],
12086   name := "/",
12087   short := "Quotient of x by y.",
12088   ex := [  ],
12089   hash := "065a64",
12090   sig := "<any> x / <elt-ord^inf> y",
12091   sog := " -> <any>",
12092   docsrc := "<internal>",
12093   sinflat := [ any, elt-ord^inf ],
12094   souflat := [ any ],
12095   soghash := "c5fe02",
12096   sig4hash := "/(any,elt-ord^inf)" ),
12097 rec(
12098   kind := "OPERATION",
12099   sin := [ [ elt-ord^inf, "x" ], [ elt-ord^inf, "y" ] ],
12100   sou := [ [ elt-ord^inf ] ],
12101   name := "/",
12102   short := "Quotient of x by y.",
12103   ex := [  ],
12104   hash := "ca50f2",
12105   sig := "<elt-ord^inf> x / <elt-ord^inf> y",
12106   sog := " -> <elt-ord^inf>",
12107   docsrc := "<internal>",
12108   sinflat := [ elt-ord^inf, elt-ord^inf ],
12109   souflat := [ elt-ord^inf ],
12110   soghash := "08787a",
12111   sig4hash := "/(elt-ord^inf,elt-ord^inf)" ),
12112 rec(
12113   kind := "OPERATION",
12114   sin := [ [ elt-res^num, "x" ], [ elt-res^num, "y" ] ],
12115   sou := [ [ elt-res^num ] ],
12116   name := "/",
12117   short := "Quotient of x by y.",
12118   ex := [  ],
12119   hash := "7ccbe9",
12120   sig := "<elt-res^num> x / <elt-res^num> y",
12121   sog := " -> <elt-res^num>",
12122   docsrc := "<internal>",
12123   sinflat := [ elt-res^num, elt-res^num ],
12124   souflat := [ elt-res^num ],
12125   soghash := "a87f47",
12126   sig4hash := "/(elt-res^num,elt-res^num)" ),
12127 rec(
12128   kind := "OPERATION",
12129   sin := [ [ seq(), "A" ], [ seq(), "B" ] ],
12130   sou := [ [ seq() ] ],
12131   name := "/",
12132   short := "The quotient of the integers whose factorization tuples are A and B, represented as a factorization tuple (the division must be exact).",
12133   ex := [  ],
12134   hash := "63f63f",
12135   sig := "<seq()> A / <seq()> B",
12136   sog := " -> <seq()>",
12137   docsrc := "<internal>",
12138   sinflat := [ seq(), seq() ],
12139   souflat := [ seq() ],
12140   soghash := "4bf3a0",
12141   sig4hash := "/(seq(),seq())" ),
12142 rec(
12143   kind := "OPERATION",
12144   sin := [ [ elt-alg^pol, "f" ], [ elt-rng, "c" ] ],
12145   sou := [ [ elt-alg^pol ] ],
12146   name := "/",
12147   short := "Product of X and the scalar (1 / c).",
12148   ex := [  ],
12149   hash := "e1edd4",
12150   sig := "<elt-alg^pol> f / <elt-rng> c",
12151   sog := " -> <elt-alg^pol>",
12152   docsrc := "<internal>",
12153   sinflat := [ elt-alg^pol, elt-rng ],
12154   souflat := [ elt-alg^pol ],
12155   soghash := "ba7338",
12156   sig4hash := "/(elt-alg^pol,elt-rng)" ),
12157 rec(
12158   kind := "OPERATION",
12159   sin := [ [ elt-mdl^mat, "X" ], [ elt-rng, "c" ] ],
12160   sou := [ [ elt-mdl^mat ] ],
12161   name := "/",
12162   short := "Product of X and the scalar (1 / c).",
12163   ex := [  ],
12164   hash := "71a89b",
12165   sig := "<elt-mdl^mat> X / <elt-rng> c",
12166   sog := " -> <elt-mdl^mat>",
12167   docsrc := "<internal>",
12168   sinflat := [ elt-mdl^mat, elt-rng ],
12169   souflat := [ elt-mdl^mat ],
12170   soghash := "5284ac",
12171   sig4hash := "/(elt-mdl^mat,elt-rng)" ),
12172 rec(
12173   kind := "OPERATION",
12174   sin := [ [ elt-mdl^vec, "u" ], [ elt-rng, "c" ] ],
12175   sou := [ [ elt-mdl^vec ] ],
12176   name := "/",
12177   short := "Product of u and the scalar (1 / c).",
12178   ex := [  ],
12179   hash := "47d84d",
12180   sig := "<elt-mdl^vec> u / <elt-rng> c",
12181   sog := " -> <elt-mdl^vec>",
12182   docsrc := "<internal>",
12183   sinflat := [ elt-mdl^vec, elt-rng ],
12184   souflat := [ elt-mdl^vec ],
12185   soghash := "b46581",
12186   sig4hash := "/(elt-mdl^vec,elt-rng)" ),
12187 rec(
12188   kind := "OPERATION",
12189   sin := [ [ elt-mdl, "u" ], [ elt-rng, "c" ] ],
12190   sou := [ [ elt-mdl ] ],
12191   name := "/",
12192   short := "Product of u and the scalar (1 / c).",
12193   ex := [  ],
12194   hash := "c6023b",
12195   sig := "<elt-mdl> u / <elt-rng> c",
12196   sog := " -> <elt-mdl>",
12197   docsrc := "<internal>",
12198   sinflat := [ elt-mdl, elt-rng ],
12199   souflat := [ elt-mdl ],
12200   soghash := "97b5cd",
12201   sig4hash := "/(elt-mdl,elt-rng)" ),
12202 rec(
12203   kind := "OPERATION",
12204   sin := [ [ elt-mdl^ded, "u" ], [ elt-rng, "c" ] ],
12205   sou := [ [ elt-mdl^ded ] ],
12206   name := "/",
12207   short := "Product of u and the scalar (1 / c).",
12208   ex := [  ],
12209   hash := "3d613e",
12210   sig := "<elt-mdl^ded> u / <elt-rng> c",
12211   sog := " -> <elt-mdl^ded>",
12212   docsrc := "<internal>",
12213   sinflat := [ elt-mdl^ded, elt-rng ],
12214   souflat := [ elt-mdl^ded ],
12215   soghash := "2fccf1",
12216   sig4hash := "/(elt-mdl^ded,elt-rng)" ),
12217 rec(
12218   kind := "OPERATION",
12219   sin := [ [ grp^abl, "G" ], [ grp^abl, "N" ] ],
12220   sou := [ [ grp^abl ] ],
12221   name := "/",
12222   short := "Construct the quotient of the group G by the normal subgroup N.",
12223   ex := [  ],
12224   hash := "44eb5e",
12225   sig := "<grp^abl> G / <grp^abl> N",
12226   sog := " -> <grp^abl>",
12227   docsrc := "<internal>",
12228   sinflat := [ grp^abl, grp^abl ],
12229   souflat := [ grp^abl ],
12230   soghash := "cde424",
12231   sig4hash := "/(grp^abl,grp^abl)" ),
12232 rec(
12233   kind := "OPERATION",
12234   sin := [ [ mdl^vec, "M" ], [ mdl^vec, "N" ] ],
12235   sou := [ [ mdl^vec ], [ map() ] ],
12236   opt := [ [ elt-ord^rat, "Results", "1 <= Results <= 2" ] ],
12237   name := "/",
12238   short := " The quotient of x by y.",
12239   ex := [  ],
12240   hash := "0a5141",
12241   sig := "<mdl^vec> M / <mdl^vec> N",
12242   sog := " -> <mdl^vec>, <map()>",
12243   docsrc := "<internal>",
12244   sinflat := [ mdl^vec, mdl^vec ],
12245   souflat := [ mdl^vec, map() ],
12246   soghash := "09f404",
12247   sig4hash := "/(mdl^vec,mdl^vec)" ),
12248 rec(
12249   kind := "OPERATION",
12250   sin := [ [ mdl^mat, "M" ], [ mdl^mat, "N" ] ],
12251   sou := [ [ mdl^mat ] ],
12252   name := "/",
12253   short := " The quotient of x by y.",
12254   ex := [  ],
12255   hash := "857ad1",
12256   sig := "<mdl^mat> M / <mdl^mat> N",
12257   sog := " -> <mdl^mat>",
12258   docsrc := "<internal>",
12259   sinflat := [ mdl^mat, mdl^mat ],
12260   souflat := [ mdl^mat ],
12261   soghash := "5c8c42",
12262   sig4hash := "/(mdl^mat,mdl^mat)" ),
12263 rec(
12264   kind := "OPERATION",
12265   sin := [ [ mdl, "M" ], [ mdl, "N" ] ],
12266   sou := [ [ mdl ] ],
12267   name := "/",
12268   short := " The quotient of x by y.",
12269   ex := [  ],
12270   hash := "8c651b",
12271   sig := "<mdl> M / <mdl> N",
12272   sog := " -> <mdl>",
12273   docsrc := "<internal>",
12274   sinflat := [ mdl, mdl ],
12275   souflat := [ mdl ],
12276   soghash := "acbc30",
12277   sig4hash := "/(mdl,mdl)" ),
12278 rec(
12279   kind := "OPERATION",
12280   sin := [ [ elt-rng^ser, "x" ], [ elt-rng^ser, "y" ] ],
12281   sou := [ [ elt-rng^ser ] ],
12282   name := "/",
12283   short := " The quotient of x by y.",
12284   ex := [  ],
12285   hash := "3105af",
12286   sig := "<elt-rng^ser> x / <elt-rng^ser> y",
12287   sog := " -> <elt-rng^ser>",
12288   docsrc := "<internal>",
12289   sinflat := [ elt-rng^ser, elt-rng^ser ],
12290   souflat := [ elt-rng^ser ],
12291   soghash := "28734d",
12292   sig4hash := "/(elt-rng^ser,elt-rng^ser)" ),
12293 rec(
12294   kind := "OPERATION",
12295   sin := [ [ elt-ids^fra/ord^num, "I" ], [ elt-rng, "x" ] ],
12296   sou := [ [ elt-ids^fra/ord^num ] ],
12297   name := "/",
12298   short := "The (possibly fractional) ideal I/x.",
12299   ex := [  ],
12300   hash := "5a626d",
12301   sig := "<elt-ids^fra/ord^num> I / <elt-rng> x",
12302   sog := " -> <elt-ids^fra/ord^num>",
12303   docsrc := "<internal>",
12304   sinflat := [ elt-ids^fra/ord^num, elt-rng ],
12305   souflat := [ elt-ids^fra/ord^num ],
12306   soghash := "ca011c",
12307   sig4hash := "/(elt-ids^fra/ord^num,elt-rng)" ),
12308 rec(
12309   kind := "OPERATION",
12310   sin := [ [ elt-ids^int/ord^fun, "I" ], [ elt-rng, "x" ] ],
12311   sou := [ [ elt-ids^int/ord^fun ] ],
12312   name := "/",
12313   short := "The (possibly fractional) ideal I/x.",
12314   ex := [  ],
12315   hash := "c6a6b4",
12316   sig := "<elt-ids^int/ord^fun> I / <elt-rng> x",
12317   sog := " -> <elt-ids^int/ord^fun>",
12318   docsrc := "<internal>",
12319   sinflat := [ elt-ids^int/ord^fun, elt-rng ],
12320   souflat := [ elt-ids^int/ord^fun ],
12321   soghash := "918914",
12322   sig4hash := "/(elt-ids^int/ord^fun,elt-rng)" ),
12323 rec(
12324   kind := "FUNCTION",
12325   sin := [ [ any, "x" ], [ map(), "f" ] ],
12326   sou := [ [ any ] ],
12327   name := "Preimage",
12328   short := "The preimage of x under f.",
12329   ex := [ "x_R := PolynomialAlgebra( IntegerRing() );\nx_x := Generator(x_R, 1);\nx_O := MaximalOrder( x_x^5-5*x_x^3+7*x_x^2-15*x_x+16 );\nx_G := ClassGroup(x_O);\nx_f := x_G.ext1;\nx_I := Factorization( 7*x_O )[1][1];\nx_g := Preimage(x_I, x_f);\nx_J := x_f(x_g);\nIsPrincipal(x_I / x_J);" ],
12330   hash := "90f13e",
12331   sig := "Preimage(<any> x, <map()> f)",
12332   sog := " -> <any>",
12333   docsrc := "<internal>",
12334   sinflat := [ any, map() ],
12335   souflat := [ any ],
12336   soghash := "da39a3",
12337   sig4hash := "Preimage(any,map())" ),
12338 rec(
12339   kind := "FUNCTION",
12340   sin := [ [ grp^abl, "G" ] ],
12341   sou := [ [ seq() ], [ seq() ] ],
12342   opt := [ [ elt-ord^rat, "Results", "1 <= Results <= 2" ] ],
12343   name := "AbelianBasis",
12344   ex := [ "x_G := AbelianGroup([2, 5, 5]);\nAbelianBasis(x_G);" ],
12345   hash := "7fa635",
12346   sig := "AbelianBasis(<grp^abl> G [, optargs])",
12347   sog := " -> <seq()>, <seq()>",
12348   docsrc := "<internal>",
12349   sinflat := [ grp^abl ],
12350   souflat := [ seq(), seq() ],
12351   soghash := "da39a3",
12352   sig4hash := "AbelianBasis(grp^abl)",
12353   short := "An abelian basis and the abelian invariants for the abelian group G." ),
12354 rec(