"Fossies" - the Fresh Open Source Software Archive

Member "pari-2.13.1/src/test/32/compat" (26 Oct 2020, 163681 Bytes) of package /linux/misc/pari-2.13.1.tar.gz:


As a special service "Fossies" has tried to format the requested text file into HTML format (style: standard) with prefixed line numbers. Alternatively you can here view or download the uninterpreted source code file. See also the latest Fossies "Diffs" side-by-side code changes report for "compat": 2.13.0_vs_2.13.1.

    1   ***   too few arguments: abs()
    2   ***                          ^-
    3   ***   at top-level: addell()
    4   ***                 ^--------
    5   ***   not a function in function call
    6 A function with that name existed in GP-1.39.15. Please update your script.
    7 
    8 New syntax: addell(e,z1,z2) ===> elladd(e,z1,z2)
    9 
   10 elladd(E,z1,z2): sum of the points z1 and z2 on elliptic curve E.
   11 
   12 
   13 []
   14   ***   at top-level: adj()
   15   ***                 ^-----
   16   ***   not a function in function call
   17 A function with that name existed in GP-1.39.15. Please update your script.
   18 
   19 New syntax: adj(x) ===> matadjoint(x)
   20 
   21 matadjoint(M,{flag=0}): adjoint matrix of M using Leverrier-Faddeev's 
   22 algorithm. If flag is 1, compute the characteristic polynomial independently 
   23 first.
   24 
   25 
   26   ***   at top-level: akell()
   27   ***                 ^-------
   28   ***   not a function in function call
   29 A function with that name existed in GP-1.39.15. Please update your script.
   30 
   31 New syntax: akell(e,n) ===> ellak(e,n)
   32 
   33 ellak(E,n): computes the n-th Fourier coefficient of the L-function of the 
   34 elliptic curve E (assumes E is an integral model).
   35 
   36 
   37   ***   at top-level: algdep2()
   38   ***                 ^---------
   39   ***   not a function in function call
   40 A function with that name existed in GP-1.39.15. Please update your script.
   41 
   42 New syntax: algdep2(x,n,dec) ===> algdep(x,n,dec)
   43 
   44 algdep(z,k,{flag=0}): algebraic relations up to degree n of z, using 
   45 lindep([1,z,...,z^(k-1)], flag).
   46 
   47 
   48   ***   at top-level: algtobasis()
   49   ***                 ^------------
   50   ***   not a function in function call
   51 A function with that name existed in GP-1.39.15. Please update your script.
   52 
   53 New syntax: algtobasis(nf,x) ===> nfalgtobasis(nf,x)
   54 
   55 nfalgtobasis(nf,x): transforms the algebraic number x into a column vector on 
   56 the integral basis nf.zk.
   57 
   58 
   59   ***   at top-level: anell()
   60   ***                 ^-------
   61   ***   not a function in function call
   62 A function with that name existed in GP-1.39.15. Please update your script.
   63 
   64 New syntax: anell(e,n) ===> ellan(e,n)
   65 
   66 ellan(E,n): computes the first n Fourier coefficients of the L-function of the 
   67 elliptic curve E defined over a number field (n<2^24 on a 32-bit machine).
   68 
   69 
   70   ***   at top-level: apell()
   71   ***                 ^-------
   72   ***   not a function in function call
   73 A function with that name existed in GP-1.39.15. Please update your script.
   74 
   75 New syntax: apell(e,n) ===> ellap(e,n)
   76 
   77 ellap(E,{p}): given an elliptic curve E defined over a finite field Fq, return 
   78 the trace of Frobenius a_p = q+1-#E(Fq); for other fields of definition K, p 
   79 must define a finite residue field, (p prime for K = Qp or Q; p a maximal ideal 
   80 for K a number field), return the order of the (nonsingular) reduction of E.
   81 
   82 
   83   ***   at top-level: apell2()
   84   ***                 ^--------
   85   ***   not a function in function call
   86 A function with that name existed in GP-1.39.15. Please update your script.
   87 
   88 New syntax: apell2(e,n) ===> ellap(e,n)
   89 
   90 ellap(E,{p}): given an elliptic curve E defined over a finite field Fq, return 
   91 the trace of Frobenius a_p = q+1-#E(Fq); for other fields of definition K, p 
   92 must define a finite residue field, (p prime for K = Qp or Q; p a maximal ideal 
   93 for K a number field), return the order of the (nonsingular) reduction of E.
   94 
   95 
   96   ***   at top-level: apprpadic()
   97   ***                 ^-----------
   98   ***   not a function in function call
   99 A function with that name existed in GP-1.39.15. Please update your script.
  100 
  101 New syntax: apprpadic(x,a) ===> padicappr(x,a)
  102 
  103 padicappr(pol,a): p-adic roots of the polynomial pol congruent to a mod p.
  104 
  105 
  106   ***   at top-level: assmat()
  107   ***                 ^--------
  108   ***   not a function in function call
  109 A function with that name existed in GP-1.39.15. Please update your script.
  110 
  111 New syntax: assmat(x) ===> matcompanion(x)
  112 
  113 matcompanion(x): companion matrix to polynomial x.
  114 
  115 
  116   ***   at top-level: basis()
  117   ***                 ^-------
  118   ***   not a function in function call
  119 A function with that name existed in GP-1.39.15. Please update your script.
  120 
  121 New syntax: basis(x) ===> nfbasis(x)
  122 
  123 nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the 
  124 polynomial T, using the round 4 algorithm. An argument [T,listP] is possible, 
  125 where listP is a list of primes or a prime bound, to get an order which is 
  126 maximal at certain primes only. If present, dK is set to the discriminant of 
  127 the returned order.
  128 
  129 
  130   ***   at top-level: basis2()
  131   ***                 ^--------
  132   ***   not a function in function call
  133 A function with that name existed in GP-1.39.15. Please update your script.
  134 
  135 New syntax: basis2(x) ===> nfbasis(x,2)
  136 
  137 nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the 
  138 polynomial T, using the round 4 algorithm. An argument [T,listP] is possible, 
  139 where listP is a list of primes or a prime bound, to get an order which is 
  140 maximal at certain primes only. If present, dK is set to the discriminant of 
  141 the returned order.
  142 
  143 
  144   ***   at top-level: basistoalg()
  145   ***                 ^------------
  146   ***   not a function in function call
  147 A function with that name existed in GP-1.39.15. Please update your script.
  148 
  149 New syntax: basistoalg(nf,x) ===> nfbasistoalg(nf,x)
  150 
  151 nfbasistoalg(nf,x): transforms the column vector x on the integral basis into 
  152 an algebraic number.
  153 
  154 
  155   ***   at top-level: bilhell()
  156   ***                 ^---------
  157   ***   not a function in function call
  158 A function with that name existed in GP-1.39.15. Please update your script.
  159 
  160 New syntax: bilhell(e,z1,z2) ===> ellbil(e,z1,z2)
  161 
  162 ellbil(E,z1,z2): deprecated alias for ellheight(E,P,Q).
  163 
  164 
  165   ***   at top-level: bin()
  166   ***                 ^-----
  167   ***   not a function in function call
  168 A function with that name existed in GP-1.39.15. Please update your script.
  169 
  170 New syntax: bin(x,y) ===> binomial(x,y)
  171 
  172 binomial(x,{k}): binomial coefficient x*(x-1)...*(x-k+1)/k! defined for k in Z 
  173 and any x. If k is omitted and x an integer, return the vector 
  174 [binomial(x,0),...,binomial(x,x)].
  175 
  176 
  177   ***   at top-level: boundcf()
  178   ***                 ^---------
  179   ***   not a function in function call
  180 A function with that name existed in GP-1.39.15. Please update your script.
  181 
  182 New syntax: boundcf(x,lmax) ===> contfrac(x,,lmax)
  183 
  184 contfrac(x,{b},{nmax}): continued fraction expansion of x (x rational,real or 
  185 rational function). b and nmax are both optional, where b is the vector of 
  186 numerators of the continued fraction, and nmax is a bound for the number of 
  187 terms in the continued fraction expansion.
  188 
  189 
  190   ***   at top-level: boundfact()
  191   ***                 ^-----------
  192   ***   not a function in function call
  193 A function with that name existed in GP-1.39.15. Please update your script.
  194 
  195 New syntax: boundfact(x,lim) ===> factor(x,lim)
  196 
  197 factor(x,{D}): factorization of x over domain D. If x and D are both integers, 
  198 return partial factorization, using primes < D.
  199 
  200 
  201   ***   at top-level: buchcertify()
  202   ***                 ^-------------
  203   ***   not a function in function call
  204 A function with that name existed in GP-1.39.15. Please update your script.
  205 
  206 New syntax: buchcertify(bnf) ===> bnfcertify(bnf)
  207 
  208 bnfcertify(bnf,{flag = 0}): certify the correctness (i.e. remove the GRH) of 
  209 the bnf data output by bnfinit. If flag is present, only certify that the class 
  210 group is a quotient of the one computed in bnf (much simpler in general).
  211 
  212 
  213   ***   at top-level: buchfu()
  214   ***                 ^--------
  215   ***   not a function in function call
  216 A function with that name existed in GP-1.39.15. Please update your script.
  217 
  218 This function no longer exists
  219 
  220 
  221   ***   at top-level: buchgen()
  222   ***                 ^---------
  223   ***   not a function in function call
  224 A function with that name existed in GP-1.39.15. Please update your script.
  225 
  226 This function no longer exists
  227 
  228 
  229   ***   at top-level: buchgenforcefu()
  230   ***                 ^----------------
  231   ***   not a function in function call
  232 A function with that name existed in GP-1.39.15. Please update your script.
  233 
  234 This function no longer exists
  235 
  236 
  237   ***   at top-level: buchgenfu()
  238   ***                 ^-----------
  239   ***   not a function in function call
  240 A function with that name existed in GP-1.39.15. Please update your script.
  241 
  242 This function no longer exists
  243 
  244 
  245   ***   at top-level: buchimag()
  246   ***                 ^----------
  247   ***   not a function in function call
  248 A function with that name existed in GP-1.39.15. Please update your script.
  249 
  250 New syntax: buchimag(D,c1,c2,g) ===> quadclassunit(D,,[c1,c2,g])
  251 
  252 quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group 
  253 and the regulator of the quadratic field of discriminant D. See manual for the 
  254 optional technical parameters.
  255 
  256 
  257   ***   at top-level: buchinit()
  258   ***                 ^----------
  259   ***   not a function in function call
  260 A function with that name existed in GP-1.39.15. Please update your script.
  261 
  262 New syntax: buchinit(P) ===> bnfinit(P,2)
  263 
  264 bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in 
  265 ideal and unit group computations, including fundamental units if they are not 
  266 too large. flag and tech are both optional. flag can be any of 0: default, 1: 
  267 include all data in algebraic form (compact units). See manual for details 
  268 about tech.
  269 
  270 
  271   ***   at top-level: buchinitforcefu()
  272   ***                 ^-----------------
  273   ***   not a function in function call
  274 A function with that name existed in GP-1.39.15. Please update your script.
  275 
  276 New syntax: buchinitforcefu(P) ===> bnfinit(P,1)
  277 
  278 bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in 
  279 ideal and unit group computations, including fundamental units if they are not 
  280 too large. flag and tech are both optional. flag can be any of 0: default, 1: 
  281 include all data in algebraic form (compact units). See manual for details 
  282 about tech.
  283 
  284 
  285   ***   at top-level: buchinitfu()
  286   ***                 ^------------
  287   ***   not a function in function call
  288 A function with that name existed in GP-1.39.15. Please update your script.
  289 
  290 New syntax: buchinitfu(P) ===> bnfinit(P)
  291 
  292 bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in 
  293 ideal and unit group computations, including fundamental units if they are not 
  294 too large. flag and tech are both optional. flag can be any of 0: default, 1: 
  295 include all data in algebraic form (compact units). See manual for details 
  296 about tech.
  297 
  298 
  299   ***   at top-level: buchnarrow()
  300   ***                 ^------------
  301   ***   not a function in function call
  302 A function with that name existed in GP-1.39.15. Please update your script.
  303 
  304 New syntax: buchnarrow(bnf) ===> bnfnarrow(bnf)
  305 
  306 bnfnarrow(bnf): given a big number field as output by bnfinit, gives as a 
  307 3-component vector the structure of the narrow class group.
  308 
  309 
  310   ***   at top-level: buchray()
  311   ***                 ^---------
  312   ***   not a function in function call
  313 A function with that name existed in GP-1.39.15. Please update your script.
  314 
  315 New syntax: buchray(bnf,ideal) ===> bnrinit(bnf,ideal)
  316 
  317 bnrinit(bnf,f,{flag=0},{cycmod}): given a bnf as output by bnfinit and a 
  318 modulus f, initializes data linked to the ray class group structure 
  319 corresponding to this module. flag is optional, and can be 0: default, 1: 
  320 compute also the generators. If the positive integer cycmod is present, only 
  321 compute the ray class group modulo cycmod-th powers.
  322 
  323 
  324   ***   at top-level: buchrayinit()
  325   ***                 ^-------------
  326   ***   not a function in function call
  327 A function with that name existed in GP-1.39.15. Please update your script.
  328 
  329 New syntax: buchrayinit(bnf,ideal) ===> bnrinit(bnf,ideal)
  330 
  331 bnrinit(bnf,f,{flag=0},{cycmod}): given a bnf as output by bnfinit and a 
  332 modulus f, initializes data linked to the ray class group structure 
  333 corresponding to this module. flag is optional, and can be 0: default, 1: 
  334 compute also the generators. If the positive integer cycmod is present, only 
  335 compute the ray class group modulo cycmod-th powers.
  336 
  337 
  338   ***   at top-level: buchrayinitgen()
  339   ***                 ^----------------
  340   ***   not a function in function call
  341 A function with that name existed in GP-1.39.15. Please update your script.
  342 
  343 New syntax: buchrayinitgen(bnf,ideal) ===> bnrinit(bnf,ideal,1)
  344 
  345 bnrinit(bnf,f,{flag=0},{cycmod}): given a bnf as output by bnfinit and a 
  346 modulus f, initializes data linked to the ray class group structure 
  347 corresponding to this module. flag is optional, and can be 0: default, 1: 
  348 compute also the generators. If the positive integer cycmod is present, only 
  349 compute the ray class group modulo cycmod-th powers.
  350 
  351 
  352   ***   at top-level: buchreal()
  353   ***                 ^----------
  354   ***   not a function in function call
  355 A function with that name existed in GP-1.39.15. Please update your script.
  356 
  357 New syntax: buchreal(D) ===> quadclassunit(D)
  358 
  359 quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group 
  360 and the regulator of the quadratic field of discriminant D. See manual for the 
  361 optional technical parameters.
  362 
  363 
  364   ***   at top-level: bytesize()
  365   ***                 ^----------
  366   ***   not a function in function call
  367 A function with that name existed in GP-1.39.15. Please update your script.
  368 
  369 New syntax: bytesize(x) ===> sizebyte(x)
  370 
  371 sizebyte(x): number of bytes occupied by the complete tree of the object x.
  372 
  373 
  374   ***   at top-level: cf()
  375   ***                 ^----
  376   ***   not a function in function call
  377 A function with that name existed in GP-1.39.15. Please update your script.
  378 
  379 New syntax: cf(x) ===> contfrac(x)
  380 
  381 contfrac(x,{b},{nmax}): continued fraction expansion of x (x rational,real or 
  382 rational function). b and nmax are both optional, where b is the vector of 
  383 numerators of the continued fraction, and nmax is a bound for the number of 
  384 terms in the continued fraction expansion.
  385 
  386 
  387   ***   at top-level: cf2()
  388   ***                 ^-----
  389   ***   not a function in function call
  390 A function with that name existed in GP-1.39.15. Please update your script.
  391 
  392 New syntax: cf2(b,x) ===> contfrac(x,b)
  393 
  394 contfrac(x,{b},{nmax}): continued fraction expansion of x (x rational,real or 
  395 rational function). b and nmax are both optional, where b is the vector of 
  396 numerators of the continued fraction, and nmax is a bound for the number of 
  397 terms in the continued fraction expansion.
  398 
  399 
  400   ***   at top-level: changevar()
  401   ***                 ^-----------
  402   ***   not a function in function call
  403 A function with that name existed in GP-1.39.15. Please update your script.
  404 
  405 This function no longer exists
  406 
  407 
  408   ***   at top-level: char()
  409   ***                 ^------
  410   ***   not a function in function call
  411 A function with that name existed in GP-1.39.15. Please update your script.
  412 
  413 New syntax: char(x,y) ===> charpoly(x,y)
  414 
  415 charpoly(A,{v='x},{flag=5}): det(v*Id-A)=characteristic polynomial of the 
  416 matrix or polmod A. flag is optional and ignored unless A is a matrix; it may 
  417 be set to 0 (Le Verrier), 1 (Lagrange interpolation), 2 (Hessenberg form), 3 
  418 (Berkowitz), 4 (modular) if A is integral, or 5 (default, choose best method). 
  419 Algorithms 0 (Le Verrier) and 1 (Lagrange) assume that n! is invertible, where 
  420 n is the dimension of the matrix.
  421 
  422 
  423   ***   at top-level: char1()
  424   ***                 ^-------
  425   ***   not a function in function call
  426 A function with that name existed in GP-1.39.15. Please update your script.
  427 
  428 New syntax: char1(x,y) ===> charpoly(x,y,1)
  429 
  430 charpoly(A,{v='x},{flag=5}): det(v*Id-A)=characteristic polynomial of the 
  431 matrix or polmod A. flag is optional and ignored unless A is a matrix; it may 
  432 be set to 0 (Le Verrier), 1 (Lagrange interpolation), 2 (Hessenberg form), 3 
  433 (Berkowitz), 4 (modular) if A is integral, or 5 (default, choose best method). 
  434 Algorithms 0 (Le Verrier) and 1 (Lagrange) assume that n! is invertible, where 
  435 n is the dimension of the matrix.
  436 
  437 
  438   ***   at top-level: char2()
  439   ***                 ^-------
  440   ***   not a function in function call
  441 A function with that name existed in GP-1.39.15. Please update your script.
  442 
  443 New syntax: char2(x,y) ===> charpoly(x,y,2)
  444 
  445 charpoly(A,{v='x},{flag=5}): det(v*Id-A)=characteristic polynomial of the 
  446 matrix or polmod A. flag is optional and ignored unless A is a matrix; it may 
  447 be set to 0 (Le Verrier), 1 (Lagrange interpolation), 2 (Hessenberg form), 3 
  448 (Berkowitz), 4 (modular) if A is integral, or 5 (default, choose best method). 
  449 Algorithms 0 (Le Verrier) and 1 (Lagrange) assume that n! is invertible, where 
  450 n is the dimension of the matrix.
  451 
  452 
  453   ***   at top-level: chell()
  454   ***                 ^-------
  455   ***   not a function in function call
  456 A function with that name existed in GP-1.39.15. Please update your script.
  457 
  458 New syntax: chell(x,y) ===> ellchangecurve(x,y)
  459 
  460 ellchangecurve(E,v): change data on elliptic curve according to v=[u,r,s,t].
  461 
  462 
  463   ***   at top-level: chptell()
  464   ***                 ^---------
  465   ***   not a function in function call
  466 A function with that name existed in GP-1.39.15. Please update your script.
  467 
  468 New syntax: chptell(x,y) ===> ellchangepoint(x,y)
  469 
  470 ellchangepoint(x,v): change data on point or vector of points x on an elliptic 
  471 curve according to v=[u,r,s,t].
  472 
  473 
  474   ***   at top-level: classno()
  475   ***                 ^---------
  476   ***   not a function in function call
  477 A function with that name existed in GP-1.39.15. Please update your script.
  478 
  479 New syntax: classno(x) ===> qfbclassno(x)
  480 
  481 qfbclassno(D,{flag=0}): class number of discriminant D using Shanks's method by 
  482 default. If (optional) flag is set to 1, use Euler products.
  483 
  484 
  485   ***   at top-level: classno2()
  486   ***                 ^----------
  487   ***   not a function in function call
  488 A function with that name existed in GP-1.39.15. Please update your script.
  489 
  490 New syntax: classno2(x) ===> qfbclassno(x,1)
  491 
  492 qfbclassno(D,{flag=0}): class number of discriminant D using Shanks's method by 
  493 default. If (optional) flag is set to 1, use Euler products.
  494 
  495 
  496   ***   at top-level: coeff()
  497   ***                 ^-------
  498   ***   not a function in function call
  499 A function with that name existed in GP-1.39.15. Please update your script.
  500 
  501 New syntax: coeff(x,s) ===> polcoeff(x,s)
  502 
  503 polcoeff(x,n,{v}): deprecated alias for polcoef.
  504 
  505 
  506   ***   at top-level: compimag()
  507   ***                 ^----------
  508   ***   not a function in function call
  509 A function with that name existed in GP-1.39.15. Please update your script.
  510 
  511 New syntax: compimag(x,y) ===> x*y
  512 
  513 x*y: product of x and y.
  514 
  515 
  516   ***   at top-level: compo()
  517   ***                 ^-------
  518   ***   not a function in function call
  519 A function with that name existed in GP-1.39.15. Please update your script.
  520 
  521 New syntax: compo(x,s) ===> component(x,s)
  522 
  523 component(x,n): the n'th component of the internal representation of x. For 
  524 vectors or matrices, it is simpler to use x[]. For list objects such as nf, 
  525 bnf, bnr or ell, it is much easier to use member functions starting with ".".
  526 
  527 
  528   ***   at top-level: compositum()
  529   ***                 ^------------
  530   ***   not a function in function call
  531 A function with that name existed in GP-1.39.15. Please update your script.
  532 
  533 New syntax: compositum(pol1,pol2) ===> polcompositum(pol1,pol2)
  534 
  535 polcompositum(P,Q,{flag=0}): vector of all possible compositums of the number 
  536 fields defined by the polynomials P and Q; flag is optional, whose binary 
  537 digits mean 1: output for each compositum, not only the compositum polynomial 
  538 pol, but a vector [R,a,b,k] where a (resp. b) is a root of P (resp. Q) 
  539 expressed as a polynomial modulo R, and a small integer k such that al2+k*al1 
  540 is the chosen root of R; 2: assume that the number fields defined by P and Q 
  541 are linearly disjoint.
  542 
  543 
  544   ***   at top-level: compositum2()
  545   ***                 ^-------------
  546   ***   not a function in function call
  547 A function with that name existed in GP-1.39.15. Please update your script.
  548 
  549 New syntax: compositum2(pol1,pol2) ===> polcompositum(pol1,pol2,1)
  550 
  551 polcompositum(P,Q,{flag=0}): vector of all possible compositums of the number 
  552 fields defined by the polynomials P and Q; flag is optional, whose binary 
  553 digits mean 1: output for each compositum, not only the compositum polynomial 
  554 pol, but a vector [R,a,b,k] where a (resp. b) is a root of P (resp. Q) 
  555 expressed as a polynomial modulo R, and a small integer k such that al2+k*al1 
  556 is the chosen root of R; 2: assume that the number fields defined by P and Q 
  557 are linearly disjoint.
  558 
  559 
  560   ***   at top-level: comprealraw()
  561   ***                 ^-------------
  562   ***   not a function in function call
  563 A function with that name existed in GP-1.39.15. Please update your script.
  564 
  565 New syntax: comprealraw(x,y) ===> qfbcompraw(x,y)
  566 
  567 qfbcompraw(x,y): Gaussian composition without reduction of the binary quadratic 
  568 forms x and y.
  569 
  570 
  571   ***   at top-level: conductor()
  572   ***                 ^-----------
  573   ***   not a function in function call
  574 A function with that name existed in GP-1.39.15. Please update your script.
  575 
  576 New syntax: conductor(a1) ===> bnrconductor(a1)
  577 
  578 bnrconductor(A,{B},{C},{flag=0}): conductor f of the subfield of the ray class 
  579 field given by A,B,C. flag is optional and can be 0: default, 1: returns [f, 
  580 Cl_f, H], H subgroup of the ray class group modulo f defining the extension, 2: 
  581 returns [f, bnr(f), H].
  582 
  583 
  584   ***   at top-level: conductorofchar()
  585   ***                 ^-----------------
  586   ***   not a function in function call
  587 A function with that name existed in GP-1.39.15. Please update your script.
  588 
  589 New syntax: conductorofchar(bnr,chi) ===> bnrconductorofchar(bnr,chi)
  590 
  591 bnrconductorofchar(bnr,chi): this function is obsolete, use bnrconductor.
  592 
  593 
  594   ***   at top-level: convol()
  595   ***                 ^--------
  596   ***   not a function in function call
  597 A function with that name existed in GP-1.39.15. Please update your script.
  598 
  599 New syntax: convol(x,y) ===> serconvol(x,y)
  600 
  601 serconvol(x,y): convolution (or Hadamard product) of two power series.
  602 
  603 
  604   ***   at top-level: core2()
  605   ***                 ^-------
  606   ***   not a function in function call
  607 A function with that name existed in GP-1.39.15. Please update your script.
  608 
  609 New syntax: core2(x) ===> core(x,1)
  610 
  611 core(n,{flag=0}): unique squarefree integer d dividing n such that n/d is a 
  612 square. If (optional) flag is nonzero, output the two-component row vector 
  613 [d,f], where d is the unique squarefree integer dividing n such that n/d=f^2 is 
  614 a square.
  615 
  616 
  617   ***   at top-level: coredisc2()
  618   ***                 ^-----------
  619   ***   not a function in function call
  620 A function with that name existed in GP-1.39.15. Please update your script.
  621 
  622 New syntax: coredisc2(x) ===> coredisc(x,1)
  623 
  624 coredisc(n,{flag=0}): discriminant of the quadratic field Q(sqrt(n)). If 
  625 (optional) flag is nonzero, output a two-component row vector [d,f], where d is 
  626 the discriminant of the quadratic field Q(sqrt(n)) and n=df^2. f may be a half 
  627 integer.
  628 
  629 
  630   ***   at top-level: cvtoi()
  631   ***                 ^-------
  632   ***   not a function in function call
  633 A function with that name existed in GP-1.39.15. Please update your script.
  634 
  635 New syntax: cvtoi(x) ===> truncate(x,&e)
  636 
  637 truncate(x,{&e}): truncation of x; when x is a power series,take away the 
  638 O(X^). If e is present, do not take into account loss of integer part 
  639 precision, and set e = error estimate in bits.
  640 
  641 
  642   ***   at top-level: cyclo()
  643   ***                 ^-------
  644   ***   not a function in function call
  645 A function with that name existed in GP-1.39.15. Please update your script.
  646 
  647 New syntax: cyclo(n) ===> polcyclo(n)
  648 
  649 polcyclo(n,{a = 'x}): n-th cyclotomic polynomial evaluated at a.
  650 
  651 
  652   ***   at top-level: decodefactor()
  653   ***                 ^--------------
  654   ***   not a function in function call
  655 A function with that name existed in GP-1.39.15. Please update your script.
  656 
  657 New syntax: decodefactor(fa) ===> factorback(fa)
  658 
  659 factorback(f,{e}): given a factorization f, gives the factored object back. If 
  660 e is present, f has to be a vector of the same length, and we return the 
  661 product of the f[i]^e[i].
  662 
  663 
  664   ***   at top-level: decodemodule()
  665   ***                 ^--------------
  666   ***   not a function in function call
  667 A function with that name existed in GP-1.39.15. Please update your script.
  668 
  669 New syntax: decodemodule(nf,fa) ===> bnfdecodemodule(nf,fa)
  670 
  671 bnfdecodemodule(nf,m): given a coded module m as in bnrdisclist, gives the true 
  672 module.
  673 
  674 
  675   ***   at top-level: degree()
  676   ***                 ^--------
  677   ***   not a function in function call
  678 A function with that name existed in GP-1.39.15. Please update your script.
  679 
  680 New syntax: degree(x) ===> poldegree(x)
  681 
  682 poldegree(x,{v}): degree of the polynomial or rational function x with respect 
  683 to main variable if v is omitted, with respect to v otherwise. For scalar x, 
  684 return 0 if x is nonzero and -oo otherwise.
  685 
  686 
  687   ***   at top-level: denom()
  688   ***                 ^-------
  689   ***   not a function in function call
  690 A function with that name existed in GP-1.39.15. Please update your script.
  691 
  692 New syntax: denom(x) ===> denominator(x)
  693 
  694 denominator(f,{D}): denominator of f.
  695 
  696 
  697   ***   at top-level: deplin()
  698   ***                 ^--------
  699   ***   not a function in function call
  700 A function with that name existed in GP-1.39.15. Please update your script.
  701 
  702 New syntax: deplin(x) ===> lindep(x,-1)
  703 
  704 lindep(v,{flag=0}): integral linear dependencies between components of v. flag 
  705 is optional, and can be 0: default, guess a suitable accuracy, or positive: 
  706 accuracy to use for the computation, in decimal digits.
  707 
  708 
  709   ***   at top-level: det()
  710   ***                 ^-----
  711   ***   not a function in function call
  712 A function with that name existed in GP-1.39.15. Please update your script.
  713 
  714 New syntax: det(x) ===> matdet(x)
  715 
  716 matdet(x,{flag=0}): determinant of the matrix x using an appropriate algorithm 
  717 depending on the coefficients. If (optional) flag is set to 1, use classical 
  718 Gaussian elimination (usually worse than the default).
  719 
  720 
  721   ***   at top-level: det2()
  722   ***                 ^------
  723   ***   not a function in function call
  724 A function with that name existed in GP-1.39.15. Please update your script.
  725 
  726 New syntax: det2(x) ===> matdet(x,1)
  727 
  728 matdet(x,{flag=0}): determinant of the matrix x using an appropriate algorithm 
  729 depending on the coefficients. If (optional) flag is set to 1, use classical 
  730 Gaussian elimination (usually worse than the default).
  731 
  732 
  733   ***   at top-level: detint()
  734   ***                 ^--------
  735   ***   not a function in function call
  736 A function with that name existed in GP-1.39.15. Please update your script.
  737 
  738 New syntax: detint(x) ===> matdetint(x)
  739 
  740 matdetint(B): some multiple of the determinant of the lattice generated by the 
  741 columns of B (0 if not of maximal rank). Useful with mathnfmod.
  742 
  743 
  744   ***   at top-level: diagonal()
  745   ***                 ^----------
  746   ***   not a function in function call
  747 A function with that name existed in GP-1.39.15. Please update your script.
  748 
  749 New syntax: diagonal(x) ===> matdiagonal(x)
  750 
  751 matdiagonal(x): creates the diagonal matrix whose diagonal entries are the 
  752 entries of the vector x.
  753 
  754 
  755   ***   at top-level: disc()
  756   ***                 ^------
  757   ***   not a function in function call
  758 A function with that name existed in GP-1.39.15. Please update your script.
  759 
  760 New syntax: disc(x) ===> poldisc(x)
  761 
  762 poldisc(pol,{v}): discriminant of the polynomial pol, with respect to main 
  763 variable if v is omitted, with respect to v otherwise.
  764 
  765 
  766   ***   at top-level: discf()
  767   ***                 ^-------
  768   ***   not a function in function call
  769 A function with that name existed in GP-1.39.15. Please update your script.
  770 
  771 New syntax: discf(x) ===> nfdisc(x)
  772 
  773 nfdisc(T): discriminant of the number field defined by the polynomial T. An 
  774 argument [T,listP] is possible, where listP is a list of primes or a prime 
  775 bound.
  776 
  777 
  778   ***   at top-level: discf2()
  779   ***                 ^--------
  780   ***   not a function in function call
  781 A function with that name existed in GP-1.39.15. Please update your script.
  782 
  783 New syntax: discf2(x) ===> nfdisc(x,2)
  784 
  785 nfdisc(T): discriminant of the number field defined by the polynomial T. An 
  786 argument [T,listP] is possible, where listP is a list of primes or a prime 
  787 bound.
  788 
  789 
  790   ***   at top-level: discrayabs()
  791   ***                 ^------------
  792   ***   not a function in function call
  793 A function with that name existed in GP-1.39.15. Please update your script.
  794 
  795 New syntax: discrayabs(bnr,subgroup) ===> bnrdisc(bnr,subgroup)
  796 
  797 bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field 
  798 defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus] 
  799 or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit, 
  800 and subgroup is the HNF matrix of a subgroup of the corresponding ray class 
  801 group (if omitted, the trivial subgroup). flag is optional whose binary digits 
  802 mean 1: give relative data; 2: return 0 if modulus is not the conductor.
  803 
  804 
  805   ***   at top-level: discrayabscond()
  806   ***                 ^----------------
  807   ***   not a function in function call
  808 A function with that name existed in GP-1.39.15. Please update your script.
  809 
  810 New syntax: discrayabscond(bnr) ===> bnrdisc(bnr,,,2)
  811 
  812 bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field 
  813 defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus] 
  814 or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit, 
  815 and subgroup is the HNF matrix of a subgroup of the corresponding ray class 
  816 group (if omitted, the trivial subgroup). flag is optional whose binary digits 
  817 mean 1: give relative data; 2: return 0 if modulus is not the conductor.
  818 
  819 
  820   ***   at top-level: discrayabslist()
  821   ***                 ^----------------
  822   ***   not a function in function call
  823 A function with that name existed in GP-1.39.15. Please update your script.
  824 
  825 New syntax: discrayabslist(bnf,list) ===> bnrdisclist(bnf,list)
  826 
  827 bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all 
  828 conductors up to norm bound. The ramified Archimedean places are given by arch; 
  829 all possible values are taken if arch is omitted. Supports the alternative 
  830 syntax bnrdisclist(bnf,list), where list is as output by ideallist or 
  831 ideallistarch (with units).
  832 
  833 
  834   ***   at top-level: discrayabslistarch()
  835   ***                 ^--------------------
  836   ***   not a function in function call
  837 A function with that name existed in GP-1.39.15. Please update your script.
  838 
  839 New syntax: discrayabslistarch(bnf,arch,bound) ===> bnrdisclist(bnf,bound,arch)
  840 
  841 bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all 
  842 conductors up to norm bound. The ramified Archimedean places are given by arch; 
  843 all possible values are taken if arch is omitted. Supports the alternative 
  844 syntax bnrdisclist(bnf,list), where list is as output by ideallist or 
  845 ideallistarch (with units).
  846 
  847 
  848   ***   at top-level: discrayabslistarchall()
  849   ***                 ^-----------------------
  850   ***   not a function in function call
  851 A function with that name existed in GP-1.39.15. Please update your script.
  852 
  853 New syntax: discrayabslistarchall(bnf,bound) ===> bnrdisclist(bnf,bound,,1)
  854 
  855 bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all 
  856 conductors up to norm bound. The ramified Archimedean places are given by arch; 
  857 all possible values are taken if arch is omitted. Supports the alternative 
  858 syntax bnrdisclist(bnf,list), where list is as output by ideallist or 
  859 ideallistarch (with units).
  860 
  861 
  862   ***   at top-level: discrayabslistlong()
  863   ***                 ^--------------------
  864   ***   not a function in function call
  865 A function with that name existed in GP-1.39.15. Please update your script.
  866 
  867 New syntax: discrayabslistlong(bnf,bound) ===> bnrdisclist(bnf,bound)
  868 
  869 bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all 
  870 conductors up to norm bound. The ramified Archimedean places are given by arch; 
  871 all possible values are taken if arch is omitted. Supports the alternative 
  872 syntax bnrdisclist(bnf,list), where list is as output by ideallist or 
  873 ideallistarch (with units).
  874 
  875 
  876   ***   at top-level: discrayrel()
  877   ***                 ^------------
  878   ***   not a function in function call
  879 A function with that name existed in GP-1.39.15. Please update your script.
  880 
  881 New syntax: discrayrel(bnr,subgroup) ===> bnrdisc(bnr,subgroup,,1)
  882 
  883 bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field 
  884 defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus] 
  885 or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit, 
  886 and subgroup is the HNF matrix of a subgroup of the corresponding ray class 
  887 group (if omitted, the trivial subgroup). flag is optional whose binary digits 
  888 mean 1: give relative data; 2: return 0 if modulus is not the conductor.
  889 
  890 
  891   ***   at top-level: discrayrelcond()
  892   ***                 ^----------------
  893   ***   not a function in function call
  894 A function with that name existed in GP-1.39.15. Please update your script.
  895 
  896 New syntax: discrayrelcond(bnr,subgroup) ===> bnrdisc(bnr,subgroup,,3)
  897 
  898 bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field 
  899 defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus] 
  900 or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit, 
  901 and subgroup is the HNF matrix of a subgroup of the corresponding ray class 
  902 group (if omitted, the trivial subgroup). flag is optional whose binary digits 
  903 mean 1: give relative data; 2: return 0 if modulus is not the conductor.
  904 
  905 
  906   ***   at top-level: divres()
  907   ***                 ^--------
  908   ***   not a function in function call
  909 A function with that name existed in GP-1.39.15. Please update your script.
  910 
  911 New syntax: divres(x,y) ===> divrem(x,y)
  912 
  913 divrem(x,y,{v}): euclidean division of x by y giving as a 2-dimensional column 
  914 vector the quotient and the remainder, with respect to v (to main variable if v 
  915 is omitted).
  916 
  917 
  918   ***   at top-level: divsum()
  919   ***                 ^--------
  920   ***   not a function in function call
  921 A function with that name existed in GP-1.39.15. Please update your script.
  922 
  923 New syntax: divsum(n,X,expr) ===> sumdiv(n,X,expr)
  924 
  925 sumdiv(n,X,expr): sum of expression expr, X running over the divisors of n.
  926 
  927 
  928   ***   at top-level: eigen()
  929   ***                 ^-------
  930   ***   not a function in function call
  931 A function with that name existed in GP-1.39.15. Please update your script.
  932 
  933 New syntax: eigen(x) ===> mateigen(x)
  934 
  935 mateigen(x,{flag=0}): complex eigenvectors of the matrix x given as columns of 
  936 a matrix H. If flag=1, return [L,H], where L contains the eigenvalues and H the 
  937 corresponding eigenvectors.
  938 
  939 
  940   ***   at top-level: euler()
  941   ***                 ^-------
  942   ***   not a function in function call
  943 A function with that name existed in GP-1.39.15. Please update your script.
  944 
  945 New syntax: euler ===> Euler
  946 
  947 Euler=Euler(): Euler's constant with current precision.
  948 
  949 
  950   ***   at top-level: extract()
  951   ***                 ^---------
  952   ***   not a function in function call
  953 A function with that name existed in GP-1.39.15. Please update your script.
  954 
  955 New syntax: extract(x,y) ===> vecextract(x,y)
  956 
  957 vecextract(x,y,{z}): extraction of the components of the matrix or vector x 
  958 according to y and z. If z is omitted, y represents columns, otherwise y 
  959 corresponds to rows and z to columns. y and z can be vectors (of indices), 
  960 strings (indicating ranges as in "1..10") or masks (integers whose binary 
  961 representation indicates the indices to extract, from left to right 1, 2, 4, 8, 
  962 etc.).
  963 
  964 
  965   ***   at top-level: fact()
  966   ***                 ^------
  967   ***   not a function in function call
  968 A function with that name existed in GP-1.39.15. Please update your script.
  969 
  970 New syntax: fact(x) ===> factorial(x)
  971 
  972 factorial(x): factorial of x, the result being given as a real number.
  973 
  974 
  975   ***   at top-level: factcantor()
  976   ***                 ^------------
  977   ***   not a function in function call
  978 A function with that name existed in GP-1.39.15. Please update your script.
  979 
  980 New syntax: factcantor(x,p) ===> factorcantor(x,p)
  981 
  982 factorcantor(x,p): this function is obsolete, use factormod.
  983 
  984 
  985   ***   at top-level: factfq()
  986   ***                 ^--------
  987   ***   not a function in function call
  988 A function with that name existed in GP-1.39.15. Please update your script.
  989 
  990 New syntax: factfq(x,p,a) ===> factorff(x,p,a)
  991 
  992 factorff(x,{p},{a}): obsolete, use factormod.
  993 
  994 
  995   ***   at top-level: factmod()
  996   ***                 ^---------
  997   ***   not a function in function call
  998 A function with that name existed in GP-1.39.15. Please update your script.
  999 
 1000 New syntax: factmod(x,p) ===> factormod(x,p)
 1001 
 1002 factormod(f,{D},{flag=0}): factors the polynomial f over the finite field 
 1003 defined by the domain D; flag is optional, and can be 0: default or 1: only the 
 1004 degrees of the irreducible factors are given.
 1005 
 1006 
 1007   ***   at top-level: factoredbasis()
 1008   ***                 ^---------------
 1009   ***   not a function in function call
 1010 A function with that name existed in GP-1.39.15. Please update your script.
 1011 
 1012 New syntax: factoredbasis(x,p) ===> nfbasis(x,,p)
 1013 
 1014 nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the 
 1015 polynomial T, using the round 4 algorithm. An argument [T,listP] is possible, 
 1016 where listP is a list of primes or a prime bound, to get an order which is 
 1017 maximal at certain primes only. If present, dK is set to the discriminant of 
 1018 the returned order.
 1019 
 1020 
 1021   ***   at top-level: factoreddiscf()
 1022   ***                 ^---------------
 1023   ***   not a function in function call
 1024 A function with that name existed in GP-1.39.15. Please update your script.
 1025 
 1026 New syntax: factoreddiscf(x,p) ===> nfdisc(x,,p)
 1027 
 1028 nfdisc(T): discriminant of the number field defined by the polynomial T. An 
 1029 argument [T,listP] is possible, where listP is a list of primes or a prime 
 1030 bound.
 1031 
 1032 
 1033   ***   at top-level: factoredpolred()
 1034   ***                 ^----------------
 1035   ***   not a function in function call
 1036 A function with that name existed in GP-1.39.15. Please update your script.
 1037 
 1038 New syntax: factoredpolred(x,p) ===> polred(x,,p)
 1039 
 1040 polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T 
 1041 (gives minimal polynomials only). The following binary digits of (optional) 
 1042 flag are significant 1: partial reduction, 2: gives also elements.
 1043 
 1044 
 1045   ***   at top-level: factoredpolred2()
 1046   ***                 ^-----------------
 1047   ***   not a function in function call
 1048 A function with that name existed in GP-1.39.15. Please update your script.
 1049 
 1050 New syntax: factoredpolred2(x,p) ===> polred(x,2,p)
 1051 
 1052 polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T 
 1053 (gives minimal polynomials only). The following binary digits of (optional) 
 1054 flag are significant 1: partial reduction, 2: gives also elements.
 1055 
 1056 
 1057   ***   at top-level: factorpadic2()
 1058   ***                 ^--------------
 1059   ***   not a function in function call
 1060 A function with that name existed in GP-1.39.15. Please update your script.
 1061 
 1062 New syntax: factorpadic2(x,p,r) ===> factorpadic(x,p,r,1)
 1063 
 1064 factorpadic(pol,p,r): p-adic factorization of the polynomial pol to precision 
 1065 r.
 1066 
 1067 
 1068   ***   at top-level: factpol()
 1069   ***                 ^---------
 1070   ***   not a function in function call
 1071 A function with that name existed in GP-1.39.15. Please update your script.
 1072 
 1073 New syntax: factpol(x,l,hint) ===> factor(x)
 1074 
 1075 factor(x,{D}): factorization of x over domain D. If x and D are both integers, 
 1076 return partial factorization, using primes < D.
 1077 
 1078 
 1079   ***   at top-level: factpol2()
 1080   ***                 ^----------
 1081   ***   not a function in function call
 1082 A function with that name existed in GP-1.39.15. Please update your script.
 1083 
 1084 New syntax: factpol2(x,l,hint) ===> factor(x)
 1085 
 1086 factor(x,{D}): factorization of x over domain D. If x and D are both integers, 
 1087 return partial factorization, using primes < D.
 1088 
 1089 
 1090   ***   at top-level: fibo()
 1091   ***                 ^------
 1092   ***   not a function in function call
 1093 A function with that name existed in GP-1.39.15. Please update your script.
 1094 
 1095 New syntax: fibo(x) ===> fibonacci(x)
 1096 
 1097 fibonacci(x): fibonacci number of index x (x C-integer).
 1098 
 1099 
 1100   ***   at top-level: fpn()
 1101   ***                 ^-----
 1102   ***   not a function in function call
 1103 A function with that name existed in GP-1.39.15. Please update your script.
 1104 
 1105 New syntax: fpn(p,n) ===> ffinit(p,n)
 1106 
 1107 ffinit(p,n,{v='x}): monic irreducible polynomial of degree n over F_p[v].
 1108 
 1109 
 1110   ***   at top-level: galois()
 1111   ***                 ^--------
 1112   ***   not a function in function call
 1113 A function with that name existed in GP-1.39.15. Please update your script.
 1114 
 1115 New syntax: galois(x) ===> polgalois(x)
 1116 
 1117 polgalois(T): Galois group of the polynomial T (see manual for group coding). 
 1118 Return [n, s, k, name] where n is the group order, s the signature, k the index 
 1119 and name is the GAP4 name of the transitive group.
 1120 
 1121 
 1122   ***   at top-level: galoisapply()
 1123   ***                 ^-------------
 1124   ***   not a function in function call
 1125 A function with that name existed in GP-1.39.15. Please update your script.
 1126 
 1127 New syntax: galoisapply(nf,aut,x) ===> nfgaloisapply(nf,aut,x)
 1128 
 1129 nfgaloisapply(nf,aut,x): apply the Galois automorphism aut to the object x 
 1130 (element or ideal) in the number field nf.
 1131 
 1132 
 1133   ***   at top-level: galoisconj()
 1134   ***                 ^------------
 1135   ***   not a function in function call
 1136 A function with that name existed in GP-1.39.15. Please update your script.
 1137 
 1138 New syntax: galoisconj(nf) ===> nfgaloisconj(nf)
 1139 
 1140 nfgaloisconj(nf,{flag=0},{d}): list of conjugates of a root of the polynomial 
 1141 x=nf.pol in the same number field. flag is optional (set to 0 by default), 
 1142 meaning 0: use combination of flag 4 and 1, always complete; 1: use nfroots; 4: 
 1143 use Allombert's algorithm, complete if the field is Galois of degree <= 35 (see 
 1144 manual for details). nf can be simply a polynomial.
 1145 
 1146 
 1147   ***   at top-level: galoisconj1()
 1148   ***                 ^-------------
 1149   ***   not a function in function call
 1150 A function with that name existed in GP-1.39.15. Please update your script.
 1151 
 1152 New syntax: galoisconj1(nf) ===> nfgaloisconj(nf,2)
 1153 
 1154 nfgaloisconj(nf,{flag=0},{d}): list of conjugates of a root of the polynomial 
 1155 x=nf.pol in the same number field. flag is optional (set to 0 by default), 
 1156 meaning 0: use combination of flag 4 and 1, always complete; 1: use nfroots; 4: 
 1157 use Allombert's algorithm, complete if the field is Galois of degree <= 35 (see 
 1158 manual for details). nf can be simply a polynomial.
 1159 
 1160 
 1161   ***   at top-level: galoisconjforce()
 1162   ***                 ^-----------------
 1163   ***   not a function in function call
 1164 A function with that name existed in GP-1.39.15. Please update your script.
 1165 
 1166 New syntax: galoisconjforce ===> nfgaloisconj(nf,1)
 1167 
 1168 nfgaloisconj(nf,{flag=0},{d}): list of conjugates of a root of the polynomial 
 1169 x=nf.pol in the same number field. flag is optional (set to 0 by default), 
 1170 meaning 0: use combination of flag 4 and 1, always complete; 1: use nfroots; 4: 
 1171 use Allombert's algorithm, complete if the field is Galois of degree <= 35 (see 
 1172 manual for details). nf can be simply a polynomial.
 1173 
 1174 
 1175   ***   at top-level: gamh()
 1176   ***                 ^------
 1177   ***   not a function in function call
 1178 A function with that name existed in GP-1.39.15. Please update your script.
 1179 
 1180 New syntax: gamh(x) ===> gammah(x)
 1181 
 1182 gammah(x): gamma of x+1/2 (x integer).
 1183 
 1184 
 1185   ***   at top-level: gauss()
 1186   ***                 ^-------
 1187   ***   not a function in function call
 1188 A function with that name existed in GP-1.39.15. Please update your script.
 1189 
 1190 New syntax: gauss(a,b) ===> matsolve(a,b)
 1191 
 1192 matsolve(M,B): solution of MX=B (M matrix, B column vector or matrix).
 1193 
 1194 
 1195   ***   at top-level: gaussmodulo()
 1196   ***                 ^-------------
 1197   ***   not a function in function call
 1198 A function with that name existed in GP-1.39.15. Please update your script.
 1199 
 1200 New syntax: gaussmodulo(M,D,Y) ===> matsolvemod(M,D,Y)
 1201 
 1202 matsolvemod(M,D,B,{flag=0}): one solution of system of congruences MX=B mod D 
 1203 (M matrix, B and D column vectors). If (optional) flag is nonzero return all 
 1204 solutions.
 1205 
 1206 
 1207   ***   at top-level: gaussmodulo2()
 1208   ***                 ^--------------
 1209   ***   not a function in function call
 1210 A function with that name existed in GP-1.39.15. Please update your script.
 1211 
 1212 New syntax: gaussmodulo2(M,D,Y) ===> matsolvemod(M,D,Y,1)
 1213 
 1214 matsolvemod(M,D,B,{flag=0}): one solution of system of congruences MX=B mod D 
 1215 (M matrix, B and D column vectors). If (optional) flag is nonzero return all 
 1216 solutions.
 1217 
 1218 
 1219   ***   at top-level: globalred()
 1220   ***                 ^-----------
 1221   ***   not a function in function call
 1222 A function with that name existed in GP-1.39.15. Please update your script.
 1223 
 1224 New syntax: globalred(x,y) ===> ellglobalred(x,y)
 1225 
 1226 ellglobalred(E): E being an elliptic curve over a number field, returns [N, v, 
 1227 c, faN, L], where N is the conductor of E, c is the product of the local 
 1228 Tamagawa numbers c_p, faN is the factorization of N and L[i] is elllocalred(E, 
 1229 faN[i,1]); v is an obsolete field.
 1230 
 1231 
 1232   ***   at top-level: goto()
 1233   ***                 ^------
 1234   ***   not a function in function call
 1235 A function with that name existed in GP-1.39.15. Please update your script.
 1236 
 1237 This function no longer exists
 1238 
 1239 
 1240   ***   at top-level: hclassno()
 1241   ***                 ^----------
 1242   ***   not a function in function call
 1243 A function with that name existed in GP-1.39.15. Please update your script.
 1244 
 1245 New syntax: hclassno(x) ===> qfbhclassno(x)
 1246 
 1247 qfbhclassno(x): Hurwitz-Kronecker class number of x>0.
 1248 
 1249 
 1250   ***   at top-level: hell()
 1251   ***                 ^------
 1252   ***   not a function in function call
 1253 A function with that name existed in GP-1.39.15. Please update your script.
 1254 
 1255 New syntax: hell(e,x) ===> ellheight(e,x)
 1256 
 1257 ellheight(E,{P},{Q}): Faltings height of the curve E, resp. canonical height of 
 1258 the point P on elliptic curve E, resp. the value of the attached bilinear form 
 1259 at (P,Q).
 1260 
 1261 
 1262   ***   at top-level: hell2()
 1263   ***                 ^-------
 1264   ***   not a function in function call
 1265 A function with that name existed in GP-1.39.15. Please update your script.
 1266 
 1267 New syntax: hell2(e,x) ===> ellheight(e,x,1)
 1268 
 1269 ellheight(E,{P},{Q}): Faltings height of the curve E, resp. canonical height of 
 1270 the point P on elliptic curve E, resp. the value of the attached bilinear form 
 1271 at (P,Q).
 1272 
 1273 
 1274   ***   at top-level: hermite()
 1275   ***                 ^---------
 1276   ***   not a function in function call
 1277 A function with that name existed in GP-1.39.15. Please update your script.
 1278 
 1279 New syntax: hermite(x) ===> mathnf(x)
 1280 
 1281 mathnf(M,{flag=0}): (upper triangular) Hermite normal form of M, basis for the 
 1282 lattice formed by the columns of M. flag is optional whose value range from 0 
 1283 to 3 have a binary meaning. Bit 1: complete output, returns a 2-component 
 1284 vector [H,U] such that H is the HNF of M, and U is an invertible matrix such 
 1285 that MU=H. Bit 2: allow polynomial entries, otherwise assume that M is 
 1286 integral. These use a naive algorithm; larger values correspond to more 
 1287 involved algorithms and are restricted to integer matrices; flag = 4: returns 
 1288 [H,U] using LLL reduction along the way; flag = 5: return [H,U,P] where P is a 
 1289 permutation of row indices such that P applied to M U is H.
 1290 
 1291 
 1292   ***   at top-level: hermite2()
 1293   ***                 ^----------
 1294   ***   not a function in function call
 1295 A function with that name existed in GP-1.39.15. Please update your script.
 1296 
 1297 New syntax: hermite2(x) ===> mathnf(x,1)
 1298 
 1299 mathnf(M,{flag=0}): (upper triangular) Hermite normal form of M, basis for the 
 1300 lattice formed by the columns of M. flag is optional whose value range from 0 
 1301 to 3 have a binary meaning. Bit 1: complete output, returns a 2-component 
 1302 vector [H,U] such that H is the HNF of M, and U is an invertible matrix such 
 1303 that MU=H. Bit 2: allow polynomial entries, otherwise assume that M is 
 1304 integral. These use a naive algorithm; larger values correspond to more 
 1305 involved algorithms and are restricted to integer matrices; flag = 4: returns 
 1306 [H,U] using LLL reduction along the way; flag = 5: return [H,U,P] where P is a 
 1307 permutation of row indices such that P applied to M U is H.
 1308 
 1309 
 1310   ***   at top-level: hermitehavas()
 1311   ***                 ^--------------
 1312   ***   not a function in function call
 1313 A function with that name existed in GP-1.39.15. Please update your script.
 1314 
 1315 This function no longer exists
 1316 
 1317 
 1318   ***   at top-level: hermitemod()
 1319   ***                 ^------------
 1320   ***   not a function in function call
 1321 A function with that name existed in GP-1.39.15. Please update your script.
 1322 
 1323 New syntax: hermitemod(x,d) ===> mathnfmod(x,d)
 1324 
 1325 mathnfmod(x,d): (upper triangular) Hermite normal form of x, basis for the 
 1326 lattice formed by the columns of x, where d is a multiple of the nonzero 
 1327 determinant of this lattice.
 1328 
 1329 
 1330   ***   at top-level: hermitemodid()
 1331   ***                 ^--------------
 1332   ***   not a function in function call
 1333 A function with that name existed in GP-1.39.15. Please update your script.
 1334 
 1335 New syntax: hermitemodid(x,d) ===> mathnfmodid(x,d)
 1336 
 1337 mathnfmodid(x,d): (upper triangular) Hermite normal form of x concatenated with 
 1338 matdiagonal(d).
 1339 
 1340 
 1341   ***   at top-level: hermiteperm()
 1342   ***                 ^-------------
 1343   ***   not a function in function call
 1344 A function with that name existed in GP-1.39.15. Please update your script.
 1345 
 1346 New syntax: hermiteperm(x) ===> mathnf(x,3)
 1347 
 1348 mathnf(M,{flag=0}): (upper triangular) Hermite normal form of M, basis for the 
 1349 lattice formed by the columns of M. flag is optional whose value range from 0 
 1350 to 3 have a binary meaning. Bit 1: complete output, returns a 2-component 
 1351 vector [H,U] such that H is the HNF of M, and U is an invertible matrix such 
 1352 that MU=H. Bit 2: allow polynomial entries, otherwise assume that M is 
 1353 integral. These use a naive algorithm; larger values correspond to more 
 1354 involved algorithms and are restricted to integer matrices; flag = 4: returns 
 1355 [H,U] using LLL reduction along the way; flag = 5: return [H,U,P] where P is a 
 1356 permutation of row indices such that P applied to M U is H.
 1357 
 1358 
 1359   ***   at top-level: hess()
 1360   ***                 ^------
 1361   ***   not a function in function call
 1362 A function with that name existed in GP-1.39.15. Please update your script.
 1363 
 1364 New syntax: hess(x) ===> mathess(x)
 1365 
 1366 mathess(x): Hessenberg form of x.
 1367 
 1368 
 1369   ***   at top-level: hilb()
 1370   ***                 ^------
 1371   ***   not a function in function call
 1372 A function with that name existed in GP-1.39.15. Please update your script.
 1373 
 1374 New syntax: hilb(x,y) ===> hilbert(x,y)
 1375 
 1376 hilbert(x,y,{p}): Hilbert symbol at p of x,y.
 1377 
 1378 
 1379   ***   at top-level: hilbp()
 1380   ***                 ^-------
 1381   ***   not a function in function call
 1382 A function with that name existed in GP-1.39.15. Please update your script.
 1383 
 1384 New syntax: hilbp(x,y,p) ===> hilbert(x,y,p)
 1385 
 1386 hilbert(x,y,{p}): Hilbert symbol at p of x,y.
 1387 
 1388 
 1389   ***   at top-level: hvector()
 1390   ***                 ^---------
 1391   ***   not a function in function call
 1392 A function with that name existed in GP-1.39.15. Please update your script.
 1393 
 1394 New syntax: hvector(n,X,expr) ===> vector(n,X,expr)
 1395 
 1396 vector(n,{X},{expr=0}): row vector with n components of expression expr (X 
 1397 ranges from 1 to n). By default, fills with 0s.
 1398 
 1399 
 1400   ***   at top-level: i()
 1401   ***                 ^---
 1402   ***   not a function in function call
 1403 A function with that name existed in GP-1.39.15. Please update your script.
 1404 
 1405 New syntax: i ===> I
 1406 
 1407 I=I(): square root of -1.
 1408 
 1409 
 1410   ***   at top-level: idealaddmultone()
 1411   ***                 ^-----------------
 1412   ***   not a function in function call
 1413 A function with that name existed in GP-1.39.15. Please update your script.
 1414 
 1415 New syntax: idealaddmultone(nf,list) ===> idealaddtoone(nf,list)
 1416 
 1417 idealaddtoone(nf,x,{y}): if y is omitted, when the sum of the ideals in the 
 1418 number field K defined by nf and given in the vector x is equal to Z_K, gives a 
 1419 vector of elements of the corresponding ideals who sum to 1. Otherwise, x and y 
 1420 are ideals, and if they sum up to 1, find one element in each of them such that 
 1421 the sum is 1.
 1422 
 1423 
 1424   ***   at top-level: idealaddone()
 1425   ***                 ^-------------
 1426   ***   not a function in function call
 1427 A function with that name existed in GP-1.39.15. Please update your script.
 1428 
 1429 New syntax: idealaddone(nf,x,y) ===> idealaddtoone(nf,x,y)
 1430 
 1431 idealaddtoone(nf,x,{y}): if y is omitted, when the sum of the ideals in the 
 1432 number field K defined by nf and given in the vector x is equal to Z_K, gives a 
 1433 vector of elements of the corresponding ideals who sum to 1. Otherwise, x and y 
 1434 are ideals, and if they sum up to 1, find one element in each of them such that 
 1435 the sum is 1.
 1436 
 1437 
 1438   ***   at top-level: idealapprfact()
 1439   ***                 ^---------------
 1440   ***   not a function in function call
 1441 A function with that name existed in GP-1.39.15. Please update your script.
 1442 
 1443 New syntax: idealapprfact(nf,x) ===> idealappr(nf,x,1)
 1444 
 1445 idealappr(nf,x,{flag}): x being a fractional ideal, gives an element b such 
 1446 that v_p(b)=v_p(x) for all prime ideals p dividing x, and v_p(b)>=0 for all 
 1447 other p; x may also be a prime ideal factorization with possibly zero 
 1448 exponents. flag is deprecated (ignored), kept for backward compatibility.
 1449 
 1450 
 1451   ***   at top-level: idealdivexact()
 1452   ***                 ^---------------
 1453   ***   not a function in function call
 1454 A function with that name existed in GP-1.39.15. Please update your script.
 1455 
 1456 New syntax: idealdivexact(nf,x,y) ===> idealdiv(nf,x,y,1)
 1457 
 1458 idealdiv(nf,x,y,{flag=0}): quotient x/y of two ideals x and y in HNF in the 
 1459 number field nf. If (optional) flag is nonzero, the quotient is supposed to be 
 1460 an integral ideal (slightly faster).
 1461 
 1462 
 1463   ***   at top-level: idealhermite()
 1464   ***                 ^--------------
 1465   ***   not a function in function call
 1466 A function with that name existed in GP-1.39.15. Please update your script.
 1467 
 1468 New syntax: idealhermite(nf,x) ===> idealhnf(nf,x)
 1469 
 1470 idealhnf(nf,u,{v}): hermite normal form of the ideal u in the number field nf 
 1471 if v is omitted. If called as idealhnf(nf,u,v), the ideal is given as uZ_K + 
 1472 vZ_K in the number field K defined by nf.
 1473 
 1474 
 1475   ***   at top-level: idealhermite2()
 1476   ***                 ^---------------
 1477   ***   not a function in function call
 1478 A function with that name existed in GP-1.39.15. Please update your script.
 1479 
 1480 New syntax: idealhermite2(nf,x) ===> idealhnf(nf,x)
 1481 
 1482 idealhnf(nf,u,{v}): hermite normal form of the ideal u in the number field nf 
 1483 if v is omitted. If called as idealhnf(nf,u,v), the ideal is given as uZ_K + 
 1484 vZ_K in the number field K defined by nf.
 1485 
 1486 
 1487   ***   at top-level: idealinv2()
 1488   ***                 ^-----------
 1489   ***   not a function in function call
 1490 A function with that name existed in GP-1.39.15. Please update your script.
 1491 
 1492 New syntax: idealinv2(nf,x) ===> idealinv(nf,x,1)
 1493 
 1494 idealinv(nf,x): inverse of the ideal x in the number field nf.
 1495 
 1496 
 1497   ***   at top-level: ideallistarchgen()
 1498   ***                 ^------------------
 1499   ***   not a function in function call
 1500 A function with that name existed in GP-1.39.15. Please update your script.
 1501 
 1502 New syntax: ideallistarchgen(nf,list,arch) ===> ideallistarch(nf,list,arch)
 1503 
 1504 ideallistarch(nf,list,arch): list is a vector of vectors of bid's as output by 
 1505 ideallist. Return a vector of vectors with the same number of components as the 
 1506 original list. The leaves give information about moduli whose finite part is as 
 1507 in original list, in the same order, and Archimedean part is now arch. The 
 1508 information contained is of the same kind as was present in the input.
 1509 
 1510 
 1511   ***   at top-level: ideallistunit()
 1512   ***                 ^---------------
 1513   ***   not a function in function call
 1514 A function with that name existed in GP-1.39.15. Please update your script.
 1515 
 1516 New syntax: ideallistunit(nf,list) ===> ideallist(nf,list,2)
 1517 
 1518 ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all 
 1519 ideals of norm<=bound. If (optional) flag is present, its binary digits are 
 1520 toggles meaning 1: give generators; 2: add units; 4: give only the ideals and 
 1521 not the bid.
 1522 
 1523 
 1524   ***   at top-level: ideallistunitarch()
 1525   ***                 ^-------------------
 1526   ***   not a function in function call
 1527 A function with that name existed in GP-1.39.15. Please update your script.
 1528 
 1529 New syntax: ideallistunitarch ===> ideallistarch(nf,list,arch)
 1530 
 1531 ideallistarch(nf,list,arch): list is a vector of vectors of bid's as output by 
 1532 ideallist. Return a vector of vectors with the same number of components as the 
 1533 original list. The leaves give information about moduli whose finite part is as 
 1534 in original list, in the same order, and Archimedean part is now arch. The 
 1535 information contained is of the same kind as was present in the input.
 1536 
 1537 
 1538   ***   at top-level: ideallistunitarchgen()
 1539   ***                 ^----------------------
 1540   ***   not a function in function call
 1541 A function with that name existed in GP-1.39.15. Please update your script.
 1542 
 1543 New syntax: ideallistunitarchgen ===> ideallistarch(nf,list,arch)
 1544 
 1545 ideallistarch(nf,list,arch): list is a vector of vectors of bid's as output by 
 1546 ideallist. Return a vector of vectors with the same number of components as the 
 1547 original list. The leaves give information about moduli whose finite part is as 
 1548 in original list, in the same order, and Archimedean part is now arch. The 
 1549 information contained is of the same kind as was present in the input.
 1550 
 1551 
 1552   ***   at top-level: ideallistunitgen()
 1553   ***                 ^------------------
 1554   ***   not a function in function call
 1555 A function with that name existed in GP-1.39.15. Please update your script.
 1556 
 1557 New syntax: ideallistunitgen ===> ideallist(nf,list,3)
 1558 
 1559 ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all 
 1560 ideals of norm<=bound. If (optional) flag is present, its binary digits are 
 1561 toggles meaning 1: give generators; 2: add units; 4: give only the ideals and 
 1562 not the bid.
 1563 
 1564 
 1565   ***   at top-level: ideallistzstar()
 1566   ***                 ^----------------
 1567   ***   not a function in function call
 1568 A function with that name existed in GP-1.39.15. Please update your script.
 1569 
 1570 New syntax: ideallistzstar(nf,bound) ===> ideallist(nf,bound)
 1571 
 1572 ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all 
 1573 ideals of norm<=bound. If (optional) flag is present, its binary digits are 
 1574 toggles meaning 1: give generators; 2: add units; 4: give only the ideals and 
 1575 not the bid.
 1576 
 1577 
 1578   ***   at top-level: ideallistzstargen()
 1579   ***                 ^-------------------
 1580   ***   not a function in function call
 1581 A function with that name existed in GP-1.39.15. Please update your script.
 1582 
 1583 New syntax: ideallistzstargen(nf,bound) ===> ideallist(nf,bound,1)
 1584 
 1585 ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all 
 1586 ideals of norm<=bound. If (optional) flag is present, its binary digits are 
 1587 toggles meaning 1: give generators; 2: add units; 4: give only the ideals and 
 1588 not the bid.
 1589 
 1590 
 1591   ***   at top-level: ideallllred()
 1592   ***                 ^-------------
 1593   ***   not a function in function call
 1594 A function with that name existed in GP-1.39.15. Please update your script.
 1595 
 1596 New syntax: ideallllred(nf,x,vdir) ===> idealred(nf,x,vdir)
 1597 
 1598 idealred(nf,I,{v=0}): LLL reduction of the ideal I in the number field nf along 
 1599 direction v, in HNF.
 1600 
 1601 
 1602   ***   at top-level: idealmulred()
 1603   ***                 ^-------------
 1604   ***   not a function in function call
 1605 A function with that name existed in GP-1.39.15. Please update your script.
 1606 
 1607 New syntax: idealmulred(nf,x,y) ===> idealmul(nf,x,y,1)
 1608 
 1609 idealmul(nf,x,y,{flag=0}): product of the two ideals x and y in the number 
 1610 field nf. If (optional) flag is nonzero, reduce the result.
 1611 
 1612 
 1613   ***   at top-level: idealpowred()
 1614   ***                 ^-------------
 1615   ***   not a function in function call
 1616 A function with that name existed in GP-1.39.15. Please update your script.
 1617 
 1618 New syntax: idealpowred(nf,x,y) ===> idealpow(nf,x,y,1)
 1619 
 1620 idealpow(nf,x,k,{flag=0}): k-th power of the ideal x in HNF in the number field 
 1621 nf. If (optional) flag is nonzero, reduce the result.
 1622 
 1623 
 1624   ***   at top-level: idealtwoelt2()
 1625   ***                 ^--------------
 1626   ***   not a function in function call
 1627 A function with that name existed in GP-1.39.15. Please update your script.
 1628 
 1629 New syntax: idealtwoelt2(nf,x,a) ===> idealtwoelt(nf,x,a)
 1630 
 1631 idealtwoelt(nf,x,{a}): two-element representation of an ideal x in the number 
 1632 field nf. If (optional) a is nonzero, first element will be equal to a.
 1633 
 1634 
 1635   ***   at top-level: idmat()
 1636   ***                 ^-------
 1637   ***   not a function in function call
 1638 A function with that name existed in GP-1.39.15. Please update your script.
 1639 
 1640 New syntax: idmat(n) ===> matid(n)
 1641 
 1642 matid(n): identity matrix of order n.
 1643 
 1644 
 1645   ***   at top-level: image()
 1646   ***                 ^-------
 1647   ***   not a function in function call
 1648 A function with that name existed in GP-1.39.15. Please update your script.
 1649 
 1650 New syntax: image(x) ===> matimage(x)
 1651 
 1652 matimage(x,{flag=0}): basis of the image of the matrix x. flag is optional and 
 1653 can be set to 0 or 1, corresponding to two different algorithms.
 1654 
 1655 
 1656   ***   at top-level: image2()
 1657   ***                 ^--------
 1658   ***   not a function in function call
 1659 A function with that name existed in GP-1.39.15. Please update your script.
 1660 
 1661 New syntax: image2(x) ===> matimage(x,1)
 1662 
 1663 matimage(x,{flag=0}): basis of the image of the matrix x. flag is optional and 
 1664 can be set to 0 or 1, corresponding to two different algorithms.
 1665 
 1666 
 1667   ***   at top-level: imagecompl()
 1668   ***                 ^------------
 1669   ***   not a function in function call
 1670 A function with that name existed in GP-1.39.15. Please update your script.
 1671 
 1672 New syntax: imagecompl(x) ===> matimagecompl(x)
 1673 
 1674 matimagecompl(x): vector of column indices not corresponding to the indices 
 1675 given by the function matimage.
 1676 
 1677 
 1678   ***   at top-level: incgam1()
 1679   ***                 ^---------
 1680   ***   not a function in function call
 1681 A function with that name existed in GP-1.39.15. Please update your script.
 1682 
 1683 This function no longer exists
 1684 
 1685 
 1686   ***   at top-level: incgam2()
 1687   ***                 ^---------
 1688   ***   not a function in function call
 1689 A function with that name existed in GP-1.39.15. Please update your script.
 1690 
 1691 This function no longer exists
 1692 
 1693 
 1694   ***   at top-level: incgam3()
 1695   ***                 ^---------
 1696   ***   not a function in function call
 1697 A function with that name existed in GP-1.39.15. Please update your script.
 1698 
 1699 This function no longer exists
 1700 
 1701 
 1702   ***   at top-level: incgam4()
 1703   ***                 ^---------
 1704   ***   not a function in function call
 1705 A function with that name existed in GP-1.39.15. Please update your script.
 1706 
 1707 New syntax: incgam4(s,x,y) ===> incgam(s,x,y)
 1708 
 1709 incgam(s,x,{g}): incomplete gamma function. g is optional and is the 
 1710 precomputed value of gamma(s).
 1711 
 1712 
 1713   ***   at top-level: indexrank()
 1714   ***                 ^-----------
 1715   ***   not a function in function call
 1716 A function with that name existed in GP-1.39.15. Please update your script.
 1717 
 1718 New syntax: indexrank(x) ===> matindexrank(x)
 1719 
 1720 matindexrank(M): gives two extraction vectors (rows and columns) for the matrix 
 1721 M such that the extracted matrix is square of maximal rank.
 1722 
 1723 
 1724   ***   at top-level: indsort()
 1725   ***                 ^---------
 1726   ***   not a function in function call
 1727 A function with that name existed in GP-1.39.15. Please update your script.
 1728 
 1729 New syntax: indsort(x) ===> vecsort(x,,1)
 1730 
 1731 vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in 
 1732 ascending order, according to the comparison function cmpf, if not omitted. (If 
 1733 cmpf is an integer k, sort according to the value of the k-th component of each 
 1734 entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return 
 1735 the permutation instead of the permuted vector, 4: use descending instead of 
 1736 ascending order, 8: remove duplicate entries.
 1737 
 1738 
 1739   ***   at top-level: initalg()
 1740   ***                 ^---------
 1741   ***   not a function in function call
 1742 A function with that name existed in GP-1.39.15. Please update your script.
 1743 
 1744 New syntax: initalg(pol) ===> nfinit(pol)
 1745 
 1746 nfinit(pol,{flag=0}): pol being a nonconstant irreducible polynomial, gives the 
 1747 vector: [pol,[r1,r2],discf,index,[M,MC,T2,T,different] (see manual),r1+r2 first 
 1748 roots, integral basis, matrix of power basis in terms of integral basis, 
 1749 multiplication table of basis]. flag is optional and can be set to 0: default; 
 1750 1: do not compute different; 2: first use polred to find a simpler polynomial; 
 1751 3: outputs a two-element vector [nf,Mod(a,P)], where nf is as in 2 and Mod(a,P) 
 1752 is a polmod equal to Mod(x,pol) and P=nf.pol.
 1753 
 1754 
 1755   ***   at top-level: initalgred()
 1756   ***                 ^------------
 1757   ***   not a function in function call
 1758 A function with that name existed in GP-1.39.15. Please update your script.
 1759 
 1760 New syntax: initalgred(x) ===> nfinit(x,2)
 1761 
 1762 nfinit(pol,{flag=0}): pol being a nonconstant irreducible polynomial, gives the 
 1763 vector: [pol,[r1,r2],discf,index,[M,MC,T2,T,different] (see manual),r1+r2 first 
 1764 roots, integral basis, matrix of power basis in terms of integral basis, 
 1765 multiplication table of basis]. flag is optional and can be set to 0: default; 
 1766 1: do not compute different; 2: first use polred to find a simpler polynomial; 
 1767 3: outputs a two-element vector [nf,Mod(a,P)], where nf is as in 2 and Mod(a,P) 
 1768 is a polmod equal to Mod(x,pol) and P=nf.pol.
 1769 
 1770 
 1771   ***   at top-level: initalgred2()
 1772   ***                 ^-------------
 1773   ***   not a function in function call
 1774 A function with that name existed in GP-1.39.15. Please update your script.
 1775 
 1776 New syntax: initalgred2(x) ===> nfinit(x,3)
 1777 
 1778 nfinit(pol,{flag=0}): pol being a nonconstant irreducible polynomial, gives the 
 1779 vector: [pol,[r1,r2],discf,index,[M,MC,T2,T,different] (see manual),r1+r2 first 
 1780 roots, integral basis, matrix of power basis in terms of integral basis, 
 1781 multiplication table of basis]. flag is optional and can be set to 0: default; 
 1782 1: do not compute different; 2: first use polred to find a simpler polynomial; 
 1783 3: outputs a two-element vector [nf,Mod(a,P)], where nf is as in 2 and Mod(a,P) 
 1784 is a polmod equal to Mod(x,pol) and P=nf.pol.
 1785 
 1786 
 1787   ***   at top-level: initell()
 1788   ***                 ^---------
 1789   ***   not a function in function call
 1790 A function with that name existed in GP-1.39.15. Please update your script.
 1791 
 1792 New syntax: initell(x) ===> ellinit(x)
 1793 
 1794 ellinit(x,{D=1}): let x be a vector [a1,a2,a3,a4,a6], or [a4,a6] if a1=a2=a3=0, 
 1795 defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6; x can also be 
 1796 a string, in which case the curve with matching name is retrieved from the 
 1797 elldata database, if available. This function initializes an elliptic curve 
 1798 over the domain D (inferred from coefficients if omitted).
 1799 
 1800 
 1801   ***   at top-level: initzeta()
 1802   ***                 ^----------
 1803   ***   not a function in function call
 1804 A function with that name existed in GP-1.39.15. Please update your script.
 1805 
 1806 This function no longer exists
 1807 
 1808 
 1809   ***   at top-level: integ()
 1810   ***                 ^-------
 1811   ***   not a function in function call
 1812 A function with that name existed in GP-1.39.15. Please update your script.
 1813 
 1814 New syntax: integ(x,y) ===> intformal(x,y)
 1815 
 1816 intformal(x,{v}): formal integration of x with respect to v, or to the main 
 1817 variable of x if v is omitted.
 1818 
 1819 
 1820   ***   at top-level: intersect()
 1821   ***                 ^-----------
 1822   ***   not a function in function call
 1823 A function with that name existed in GP-1.39.15. Please update your script.
 1824 
 1825 New syntax: intersect(x,y) ===> matintersect(x,y)
 1826 
 1827 matintersect(x,y): intersection of the vector spaces whose bases are the 
 1828 columns of x and y.
 1829 
 1830 
 1831   ***   at top-level: intgen()
 1832   ***                 ^--------
 1833   ***   not a function in function call
 1834 A function with that name existed in GP-1.39.15. Please update your script.
 1835 
 1836 New syntax: intgen(x=a,b,s) ===> intnum(x=a,b,s,1)
 1837 
 1838 intnum(X=a,b,expr,{tab}): numerical integration of expr from a to b with 
 1839 respect to X. Plus/minus infinity is coded as +oo/-oo. Finally tab is either 
 1840 omitted (let the program choose the integration step), a nonnegative integer m 
 1841 (divide integration step by 2^m), or data precomputed with intnuminit.
 1842 
 1843 
 1844   ***   at top-level: intinf()
 1845   ***                 ^--------
 1846   ***   not a function in function call
 1847 A function with that name existed in GP-1.39.15. Please update your script.
 1848 
 1849 New syntax: intinf(x=a,b,s) ===> intnum(x=a,b,s,2)
 1850 
 1851 intnum(X=a,b,expr,{tab}): numerical integration of expr from a to b with 
 1852 respect to X. Plus/minus infinity is coded as +oo/-oo. Finally tab is either 
 1853 omitted (let the program choose the integration step), a nonnegative integer m 
 1854 (divide integration step by 2^m), or data precomputed with intnuminit.
 1855 
 1856 
 1857   ***   at top-level: intopen()
 1858   ***                 ^---------
 1859   ***   not a function in function call
 1860 A function with that name existed in GP-1.39.15. Please update your script.
 1861 
 1862 New syntax: intopen(x=a,b,s) ===> intnum(x=a,b,s,3)
 1863 
 1864 intnum(X=a,b,expr,{tab}): numerical integration of expr from a to b with 
 1865 respect to X. Plus/minus infinity is coded as +oo/-oo. Finally tab is either 
 1866 omitted (let the program choose the integration step), a nonnegative integer m 
 1867 (divide integration step by 2^m), or data precomputed with intnuminit.
 1868 
 1869 
 1870   ***   at top-level: inverseimage()
 1871   ***                 ^--------------
 1872   ***   not a function in function call
 1873 A function with that name existed in GP-1.39.15. Please update your script.
 1874 
 1875 New syntax: inverseimage(x,y) ===> matinverseimage(x,y)
 1876 
 1877 matinverseimage(x,y): an element of the inverse image of the vector y by the 
 1878 matrix x if one exists, the empty vector otherwise.
 1879 
 1880 
 1881   ***   at top-level: isdiagonal()
 1882   ***                 ^------------
 1883   ***   not a function in function call
 1884 A function with that name existed in GP-1.39.15. Please update your script.
 1885 
 1886 New syntax: isdiagonal(x) ===> matisdiagonal(x)
 1887 
 1888 matisdiagonal(x): true(1) if x is a diagonal matrix, false(0) otherwise.
 1889 
 1890 
 1891   ***   at top-level: isfund()
 1892   ***                 ^--------
 1893   ***   not a function in function call
 1894 A function with that name existed in GP-1.39.15. Please update your script.
 1895 
 1896 New syntax: isfund(x) ===> isfundamental(x)
 1897 
 1898 isfundamental(D): true(1) if D is a fundamental discriminant (including 1), 
 1899 false(0) if not.
 1900 
 1901 
 1902   ***   at top-level: isideal()
 1903   ***                 ^---------
 1904   ***   not a function in function call
 1905 A function with that name existed in GP-1.39.15. Please update your script.
 1906 
 1907 New syntax: isideal(nf,x) ===> nfisideal(nf,x)
 1908 
 1909 nfisideal(nf,x): true(1) if x is an ideal in the number field nf, false(0) if 
 1910 not.
 1911 
 1912 
 1913   ***   at top-level: isincl()
 1914   ***                 ^--------
 1915   ***   not a function in function call
 1916 A function with that name existed in GP-1.39.15. Please update your script.
 1917 
 1918 New syntax: isincl(x,y) ===> nfisincl(x,y)
 1919 
 1920 nfisincl(f,g,{flag=0}): let f and g define number fields, either irreducible 
 1921 rational polynomials or number fields as output by nfinit; tests whether the 
 1922 number field f is isomorphic to a subfield of g. Return 0 if not, and otherwise 
 1923 all the embeddings (flag=0, default) or only one (flag=1).
 1924 
 1925 
 1926   ***   at top-level: isinclfast()
 1927   ***                 ^------------
 1928   ***   not a function in function call
 1929 A function with that name existed in GP-1.39.15. Please update your script.
 1930 
 1931 New syntax: isinclfast(nf1,nf2) ===> nfisincl(nf1,nf2,1)
 1932 
 1933 nfisincl(f,g,{flag=0}): let f and g define number fields, either irreducible 
 1934 rational polynomials or number fields as output by nfinit; tests whether the 
 1935 number field f is isomorphic to a subfield of g. Return 0 if not, and otherwise 
 1936 all the embeddings (flag=0, default) or only one (flag=1).
 1937 
 1938 
 1939   ***   at top-level: isirreducible()
 1940   ***                 ^---------------
 1941   ***   not a function in function call
 1942 A function with that name existed in GP-1.39.15. Please update your script.
 1943 
 1944 New syntax: isirreducible(x) ===> polisirreducible(x)
 1945 
 1946 polisirreducible(pol): true(1) if pol is an irreducible nonconstant polynomial, 
 1947 false(0) if pol is reducible or constant.
 1948 
 1949 
 1950   ***   at top-level: isisom()
 1951   ***                 ^--------
 1952   ***   not a function in function call
 1953 A function with that name existed in GP-1.39.15. Please update your script.
 1954 
 1955 New syntax: isisom(x,y) ===> nfisisom(x,y)
 1956 
 1957 nfisisom(f,g): as nfisincl but tests whether f is isomorphic to g.
 1958 
 1959 
 1960   ***   at top-level: isisomfast()
 1961   ***                 ^------------
 1962   ***   not a function in function call
 1963 A function with that name existed in GP-1.39.15. Please update your script.
 1964 
 1965 New syntax: isisomfast(x,y) ===> nfisisom(x,y)
 1966 
 1967 nfisisom(f,g): as nfisincl but tests whether f is isomorphic to g.
 1968 
 1969 
 1970   ***   at top-level: isoncurve()
 1971   ***                 ^-----------
 1972   ***   not a function in function call
 1973 A function with that name existed in GP-1.39.15. Please update your script.
 1974 
 1975 New syntax: isoncurve(e,x) ===> ellisoncurve(e,x)
 1976 
 1977 ellisoncurve(E,z): true(1) if z is on elliptic curve E, false(0) if not.
 1978 
 1979 
 1980   ***   at top-level: isprincipal()
 1981   ***                 ^-------------
 1982   ***   not a function in function call
 1983 A function with that name existed in GP-1.39.15. Please update your script.
 1984 
 1985 New syntax: isprincipal(bnf,x) ===> bnfisprincipal(bnf,x,0)
 1986 
 1987 bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where 
 1988 e is the vector of exponents on the class group generators and t is the 
 1989 generator of the resulting principal ideal. In particular x is principal if and 
 1990 only if e is the zero vector. flag is optional, whose binary digits mean 1: 
 1991 output [e,t] (only e if unset); 2: increase precision until alpha can be 
 1992 computed (do not insist if unset); 4: return alpha in factored form (compact 
 1993 representation).
 1994 
 1995 
 1996   ***   at top-level: isprincipalforce()
 1997   ***                 ^------------------
 1998   ***   not a function in function call
 1999 A function with that name existed in GP-1.39.15. Please update your script.
 2000 
 2001 New syntax: isprincipalforce(bnf,x) ===> bnfisprincipal(bnf,x,2)
 2002 
 2003 bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where 
 2004 e is the vector of exponents on the class group generators and t is the 
 2005 generator of the resulting principal ideal. In particular x is principal if and 
 2006 only if e is the zero vector. flag is optional, whose binary digits mean 1: 
 2007 output [e,t] (only e if unset); 2: increase precision until alpha can be 
 2008 computed (do not insist if unset); 4: return alpha in factored form (compact 
 2009 representation).
 2010 
 2011 
 2012   ***   at top-level: isprincipalgen()
 2013   ***                 ^----------------
 2014   ***   not a function in function call
 2015 A function with that name existed in GP-1.39.15. Please update your script.
 2016 
 2017 New syntax: isprincipalgen(bnf,x) ===> bnfisprincipal(bnf,x)
 2018 
 2019 bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where 
 2020 e is the vector of exponents on the class group generators and t is the 
 2021 generator of the resulting principal ideal. In particular x is principal if and 
 2022 only if e is the zero vector. flag is optional, whose binary digits mean 1: 
 2023 output [e,t] (only e if unset); 2: increase precision until alpha can be 
 2024 computed (do not insist if unset); 4: return alpha in factored form (compact 
 2025 representation).
 2026 
 2027 
 2028   ***   at top-level: isprincipalgenforce()
 2029   ***                 ^---------------------
 2030   ***   not a function in function call
 2031 A function with that name existed in GP-1.39.15. Please update your script.
 2032 
 2033 New syntax: isprincipalgenforce(bnf,x) ===> bnfisprincipal(bnf,x,3)
 2034 
 2035 bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where 
 2036 e is the vector of exponents on the class group generators and t is the 
 2037 generator of the resulting principal ideal. In particular x is principal if and 
 2038 only if e is the zero vector. flag is optional, whose binary digits mean 1: 
 2039 output [e,t] (only e if unset); 2: increase precision until alpha can be 
 2040 computed (do not insist if unset); 4: return alpha in factored form (compact 
 2041 representation).
 2042 
 2043 
 2044   ***   at top-level: isprincipalray()
 2045   ***                 ^----------------
 2046   ***   not a function in function call
 2047 A function with that name existed in GP-1.39.15. Please update your script.
 2048 
 2049 New syntax: isprincipalray(bnf,x) ===> bnrisprincipal(bnf,x)
 2050 
 2051 bnrisprincipal(bnr,x,{flag=1}): bnr being output by bnrinit and x being an 
 2052 ideal coprime to bnr.mod, returns [v,alpha], where v is the vector of exponents 
 2053 on the ray class group generators and alpha is the generator of the resulting 
 2054 principal ideal. If (optional) flag is set to 0, output only v.
 2055 
 2056 
 2057   ***   at top-level: isprincipalraygen()
 2058   ***                 ^-------------------
 2059   ***   not a function in function call
 2060   ***   at top-level: ispsp()
 2061   ***                 ^-------
 2062   ***   not a function in function call
 2063 A function with that name existed in GP-1.39.15. Please update your script.
 2064 
 2065 New syntax: ispsp(x) ===> ispseudoprime(x)
 2066 
 2067 ispseudoprime(x,{flag}): true(1) if x is a strong pseudoprime, false(0) if not. 
 2068 If flag is 0 or omitted, use BPSW test, otherwise use strong Rabin-Miller test 
 2069 for flag randomly chosen bases.
 2070 
 2071 
 2072   ***   at top-level: isqrt()
 2073   ***                 ^-------
 2074   ***   not a function in function call
 2075 A function with that name existed in GP-1.39.15. Please update your script.
 2076 
 2077 New syntax: isqrt(x) ===> sqrtint(x)
 2078 
 2079 sqrtint(x,{&r}): integer square root y of x, where x is a nonnegative integer. 
 2080 If r is present, set it to the remainder x^2 - y.
 2081 
 2082 
 2083   ***   at top-level: isset()
 2084   ***                 ^-------
 2085   ***   not a function in function call
 2086 A function with that name existed in GP-1.39.15. Please update your script.
 2087 
 2088 New syntax: isset(x) ===> setisset(x)
 2089 
 2090 setisset(x): true(1) if x is a set (row vector with strictly increasing 
 2091 entries), false(0) if not.
 2092 
 2093 
 2094   ***   at top-level: issqfree()
 2095   ***                 ^----------
 2096   ***   not a function in function call
 2097 A function with that name existed in GP-1.39.15. Please update your script.
 2098 
 2099 New syntax: issqfree(x) ===> issquarefree(x)
 2100 
 2101 issquarefree(x): true(1) if x is squarefree, false(0) if not.
 2102 
 2103 
 2104   ***   at top-level: isunit()
 2105   ***                 ^--------
 2106   ***   not a function in function call
 2107 A function with that name existed in GP-1.39.15. Please update your script.
 2108 
 2109 New syntax: isunit(bnf,x) ===> bnfisunit(bnf,x)
 2110 
 2111 bnfisunit(bnf,x, {U}): bnf being output by bnfinit, give the column vector of 
 2112 exponents of x on the fundamental units and the roots of unity if x is a unit, 
 2113 the empty vector otherwise. If U is present, as given by bnfunits, decompose x 
 2114 on the attached S-units generators.
 2115 
 2116 
 2117   ***   at top-level: jacobi()
 2118   ***                 ^--------
 2119   ***   not a function in function call
 2120 A function with that name existed in GP-1.39.15. Please update your script.
 2121 
 2122 New syntax: jacobi(x) ===> qfjacobi(x)
 2123 
 2124 qfjacobi(A): eigenvalues and orthogonal matrix of eigenvectors of the real 
 2125 symmetric matrix A.
 2126 
 2127 
 2128   ***   at top-level: jbesselh()
 2129   ***                 ^----------
 2130   ***   not a function in function call
 2131 A function with that name existed in GP-1.39.15. Please update your script.
 2132 
 2133 New syntax: jbesselh(n,x) ===> besseljh(n,x)
 2134 
 2135 besseljh(n,x): J-bessel function of index n+1/2 and argument x, where n is a 
 2136 nonnegative integer.
 2137 
 2138 
 2139   ***   at top-level: jell()
 2140   ***                 ^------
 2141   ***   not a function in function call
 2142 A function with that name existed in GP-1.39.15. Please update your script.
 2143 
 2144 New syntax: jell(x) ===> ellj(x)
 2145 
 2146 ellj(x): elliptic j invariant of x.
 2147 
 2148 
 2149   ***   at top-level: karamul()
 2150   ***                 ^---------
 2151   ***   not a function in function call
 2152 A function with that name existed in GP-1.39.15. Please update your script.
 2153 
 2154 This function no longer exists
 2155 
 2156 
 2157   ***   at top-level: kbessel()
 2158   ***                 ^---------
 2159   ***   not a function in function call
 2160 A function with that name existed in GP-1.39.15. Please update your script.
 2161 
 2162 New syntax: kbessel(nu,x) ===> besselk(nu,x)
 2163 
 2164 besselk(nu,x): K-bessel function of index nu and argument x.
 2165 
 2166 
 2167   ***   at top-level: kbessel2()
 2168   ***                 ^----------
 2169   ***   not a function in function call
 2170 A function with that name existed in GP-1.39.15. Please update your script.
 2171 
 2172 New syntax: kbessel2(nu,x) ===> besselk(nu,x)
 2173 
 2174 besselk(nu,x): K-bessel function of index nu and argument x.
 2175 
 2176 
 2177   ***   at top-level: ker()
 2178   ***                 ^-----
 2179   ***   not a function in function call
 2180 A function with that name existed in GP-1.39.15. Please update your script.
 2181 
 2182 New syntax: ker(x) ===> matker(x)
 2183 
 2184 matker(x,{flag=0}): basis of the kernel of the matrix x. flag is optional, and 
 2185 may be set to 0: default; nonzero: x is known to have integral entries.
 2186 
 2187 
 2188   ***   at top-level: keri()
 2189   ***                 ^------
 2190   ***   not a function in function call
 2191 A function with that name existed in GP-1.39.15. Please update your script.
 2192 
 2193 New syntax: keri(x) ===> matker(x,1)
 2194 
 2195 matker(x,{flag=0}): basis of the kernel of the matrix x. flag is optional, and 
 2196 may be set to 0: default; nonzero: x is known to have integral entries.
 2197 
 2198 
 2199   ***   at top-level: kerint()
 2200   ***                 ^--------
 2201   ***   not a function in function call
 2202 A function with that name existed in GP-1.39.15. Please update your script.
 2203 
 2204 New syntax: kerint(x) ===> matkerint(x)
 2205 
 2206 matkerint(x,{flag=0}): LLL-reduced Z-basis of the kernel of the matrix x with 
 2207 integral entries. flag is deprecated, and may be set to 0 or 1 for backward 
 2208 compatibility.
 2209 
 2210 
 2211   ***   at top-level: kerint1()
 2212   ***                 ^---------
 2213   ***   not a function in function call
 2214 A function with that name existed in GP-1.39.15. Please update your script.
 2215 
 2216 New syntax: kerint1(x) ===> matkerint(x,1)
 2217 
 2218 matkerint(x,{flag=0}): LLL-reduced Z-basis of the kernel of the matrix x with 
 2219 integral entries. flag is deprecated, and may be set to 0 or 1 for backward 
 2220 compatibility.
 2221 
 2222 
 2223   ***   at top-level: kerint2()
 2224   ***                 ^---------
 2225   ***   not a function in function call
 2226 A function with that name existed in GP-1.39.15. Please update your script.
 2227 
 2228 This function no longer exists
 2229 
 2230 
 2231   ***   at top-level: kro()
 2232   ***                 ^-----
 2233   ***   not a function in function call
 2234 A function with that name existed in GP-1.39.15. Please update your script.
 2235 
 2236 New syntax: kro(x,y) ===> kronecker(x,y)
 2237 
 2238 kronecker(x,y): kronecker symbol (x/y).
 2239 
 2240 
 2241   ***   at top-level: label()
 2242   ***                 ^-------
 2243   ***   not a function in function call
 2244 A function with that name existed in GP-1.39.15. Please update your script.
 2245 
 2246 This function no longer exists
 2247 
 2248 
 2249   ***   at top-level: lambdak()
 2250   ***                 ^---------
 2251   ***   not a function in function call
 2252 A function with that name existed in GP-1.39.15. Please update your script.
 2253 
 2254 This function no longer exists
 2255 
 2256 
 2257   ***   at top-level: laplace()
 2258   ***                 ^---------
 2259   ***   not a function in function call
 2260 A function with that name existed in GP-1.39.15. Please update your script.
 2261 
 2262 New syntax: laplace(x) ===> serlaplace(x)
 2263 
 2264 serlaplace(x): replaces the power series sum of a_n*x^n/n! by sum of a_n*x^n. 
 2265 For the reverse operation, use serconvol(x,exp(X)).
 2266 
 2267 
 2268   ***   at top-level: legendre()
 2269   ***                 ^----------
 2270   ***   not a function in function call
 2271 A function with that name existed in GP-1.39.15. Please update your script.
 2272 
 2273 New syntax: legendre(n) ===> pollegendre(n)
 2274 
 2275 pollegendre(n,{a='x},{flag=0}): legendre polynomial of degree n evaluated at a. 
 2276 If flag is 1, return [P_{n-1}(a), P_n(a)].
 2277 
 2278 
 2279   ***   at top-level: lexsort()
 2280   ***                 ^---------
 2281   ***   not a function in function call
 2282 A function with that name existed in GP-1.39.15. Please update your script.
 2283 
 2284 New syntax: lexsort(x) ===> vecsort(x,,2)
 2285 
 2286 vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in 
 2287 ascending order, according to the comparison function cmpf, if not omitted. (If 
 2288 cmpf is an integer k, sort according to the value of the k-th component of each 
 2289 entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return 
 2290 the permutation instead of the permuted vector, 4: use descending instead of 
 2291 ascending order, 8: remove duplicate entries.
 2292 
 2293 
 2294   ***   at top-level: lindep2()
 2295   ***                 ^---------
 2296   ***   not a function in function call
 2297 A function with that name existed in GP-1.39.15. Please update your script.
 2298 
 2299 New syntax: lindep2(x) ===> lindep(x,1)
 2300 
 2301 lindep(v,{flag=0}): integral linear dependencies between components of v. flag 
 2302 is optional, and can be 0: default, guess a suitable accuracy, or positive: 
 2303 accuracy to use for the computation, in decimal digits.
 2304 
 2305 
 2306   ***   at top-level: lll()
 2307   ***                 ^-----
 2308   ***   not a function in function call
 2309 A function with that name existed in GP-1.39.15. Please update your script.
 2310 
 2311 New syntax: lll(x) ===> qflll(x)
 2312 
 2313 qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the 
 2314 unimodular transformation matrix T such that x*T is LLL-reduced). flag is 
 2315 optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is 
 2316 integral, returns a partially reduced basis, 4: assumes x is integral, returns 
 2317 [K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same 
 2318 as 4 but x may have polynomial coefficients, 8: same as 0 but x may have 
 2319 polynomial coefficients.
 2320 
 2321 
 2322   ***   at top-level: lll1()
 2323   ***                 ^------
 2324   ***   not a function in function call
 2325 A function with that name existed in GP-1.39.15. Please update your script.
 2326 
 2327 This function no longer exists
 2328 
 2329 
 2330   ***   at top-level: lllgen()
 2331   ***                 ^--------
 2332   ***   not a function in function call
 2333 A function with that name existed in GP-1.39.15. Please update your script.
 2334 
 2335 New syntax: lllgen(x) ===> qflll(x,8)
 2336 
 2337 qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the 
 2338 unimodular transformation matrix T such that x*T is LLL-reduced). flag is 
 2339 optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is 
 2340 integral, returns a partially reduced basis, 4: assumes x is integral, returns 
 2341 [K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same 
 2342 as 4 but x may have polynomial coefficients, 8: same as 0 but x may have 
 2343 polynomial coefficients.
 2344 
 2345 
 2346   ***   at top-level: lllgram()
 2347   ***                 ^---------
 2348   ***   not a function in function call
 2349 A function with that name existed in GP-1.39.15. Please update your script.
 2350 
 2351 New syntax: lllgram(x) ===> qflllgram(x)
 2352 
 2353 qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G 
 2354 (gives the unimodular transformation matrix). flag is optional and can be 0: 
 2355 default,1: assumes x is integral, 4: assumes x is integral, returns [K,T], 
 2356 where K is the integer kernel of x and T the LLL reduced image, 5: same as 4 
 2357 but x may have polynomial coefficients, 8: same as 0 but x may have polynomial 
 2358 coefficients.
 2359 
 2360 
 2361   ***   at top-level: lllgram1()
 2362   ***                 ^----------
 2363   ***   not a function in function call
 2364 A function with that name existed in GP-1.39.15. Please update your script.
 2365 
 2366 This function no longer exists
 2367 
 2368 
 2369   ***   at top-level: lllgramgen()
 2370   ***                 ^------------
 2371   ***   not a function in function call
 2372 A function with that name existed in GP-1.39.15. Please update your script.
 2373 
 2374 New syntax: lllgramgen(x) ===> qflllgram(x,8)
 2375 
 2376 qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G 
 2377 (gives the unimodular transformation matrix). flag is optional and can be 0: 
 2378 default,1: assumes x is integral, 4: assumes x is integral, returns [K,T], 
 2379 where K is the integer kernel of x and T the LLL reduced image, 5: same as 4 
 2380 but x may have polynomial coefficients, 8: same as 0 but x may have polynomial 
 2381 coefficients.
 2382 
 2383 
 2384   ***   at top-level: lllgramint()
 2385   ***                 ^------------
 2386   ***   not a function in function call
 2387 A function with that name existed in GP-1.39.15. Please update your script.
 2388 
 2389 New syntax: lllgramint(x) ===> qflllgram(x,1)
 2390 
 2391 qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G 
 2392 (gives the unimodular transformation matrix). flag is optional and can be 0: 
 2393 default,1: assumes x is integral, 4: assumes x is integral, returns [K,T], 
 2394 where K is the integer kernel of x and T the LLL reduced image, 5: same as 4 
 2395 but x may have polynomial coefficients, 8: same as 0 but x may have polynomial 
 2396 coefficients.
 2397 
 2398 
 2399   ***   at top-level: lllgramkerim()
 2400   ***                 ^--------------
 2401   ***   not a function in function call
 2402 A function with that name existed in GP-1.39.15. Please update your script.
 2403 
 2404 New syntax: lllgramkerim(x) ===> qflllgram(x,4)
 2405 
 2406 qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G 
 2407 (gives the unimodular transformation matrix). flag is optional and can be 0: 
 2408 default,1: assumes x is integral, 4: assumes x is integral, returns [K,T], 
 2409 where K is the integer kernel of x and T the LLL reduced image, 5: same as 4 
 2410 but x may have polynomial coefficients, 8: same as 0 but x may have polynomial 
 2411 coefficients.
 2412 
 2413 
 2414   ***   at top-level: lllgramkerimgen()
 2415   ***                 ^-----------------
 2416   ***   not a function in function call
 2417 A function with that name existed in GP-1.39.15. Please update your script.
 2418 
 2419 New syntax: lllgramkerimgen(x) ===> qflllgram(x,5)
 2420 
 2421 qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G 
 2422 (gives the unimodular transformation matrix). flag is optional and can be 0: 
 2423 default,1: assumes x is integral, 4: assumes x is integral, returns [K,T], 
 2424 where K is the integer kernel of x and T the LLL reduced image, 5: same as 4 
 2425 but x may have polynomial coefficients, 8: same as 0 but x may have polynomial 
 2426 coefficients.
 2427 
 2428 
 2429   ***   at top-level: lllint()
 2430   ***                 ^--------
 2431   ***   not a function in function call
 2432 A function with that name existed in GP-1.39.15. Please update your script.
 2433 
 2434 New syntax: lllint(x) ===> qflll(x,1)
 2435 
 2436 qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the 
 2437 unimodular transformation matrix T such that x*T is LLL-reduced). flag is 
 2438 optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is 
 2439 integral, returns a partially reduced basis, 4: assumes x is integral, returns 
 2440 [K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same 
 2441 as 4 but x may have polynomial coefficients, 8: same as 0 but x may have 
 2442 polynomial coefficients.
 2443 
 2444 
 2445   ***   at top-level: lllintpartial()
 2446   ***                 ^---------------
 2447   ***   not a function in function call
 2448 A function with that name existed in GP-1.39.15. Please update your script.
 2449 
 2450 New syntax: lllintpartial(x) ===> qflll(x,2)
 2451 
 2452 qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the 
 2453 unimodular transformation matrix T such that x*T is LLL-reduced). flag is 
 2454 optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is 
 2455 integral, returns a partially reduced basis, 4: assumes x is integral, returns 
 2456 [K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same 
 2457 as 4 but x may have polynomial coefficients, 8: same as 0 but x may have 
 2458 polynomial coefficients.
 2459 
 2460 
 2461   ***   at top-level: lllkerim()
 2462   ***                 ^----------
 2463   ***   not a function in function call
 2464 A function with that name existed in GP-1.39.15. Please update your script.
 2465 
 2466 New syntax: lllkerim(x) ===> qflll(x,4)
 2467 
 2468 qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the 
 2469 unimodular transformation matrix T such that x*T is LLL-reduced). flag is 
 2470 optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is 
 2471 integral, returns a partially reduced basis, 4: assumes x is integral, returns 
 2472 [K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same 
 2473 as 4 but x may have polynomial coefficients, 8: same as 0 but x may have 
 2474 polynomial coefficients.
 2475 
 2476 
 2477   ***   at top-level: lllkerimgen()
 2478   ***                 ^-------------
 2479   ***   not a function in function call
 2480 A function with that name existed in GP-1.39.15. Please update your script.
 2481 
 2482 New syntax: lllkerimgen(x) ===> qflll(x,5)
 2483 
 2484 qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the 
 2485 unimodular transformation matrix T such that x*T is LLL-reduced). flag is 
 2486 optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is 
 2487 integral, returns a partially reduced basis, 4: assumes x is integral, returns 
 2488 [K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same 
 2489 as 4 but x may have polynomial coefficients, 8: same as 0 but x may have 
 2490 polynomial coefficients.
 2491 
 2492 
 2493   ***   at top-level: lllrat()
 2494   ***                 ^--------
 2495   ***   not a function in function call
 2496 A function with that name existed in GP-1.39.15. Please update your script.
 2497 
 2498 This function no longer exists
 2499 
 2500 
 2501   ***   at top-level: ln()
 2502   ***                 ^----
 2503   ***   not a function in function call
 2504 A function with that name existed in GP-1.39.15. Please update your script.
 2505 
 2506 New syntax: ln(x) ===> log(x)
 2507 
 2508 log(x): natural logarithm of x.
 2509 
 2510 
 2511   ***   at top-level: localred()
 2512   ***                 ^----------
 2513   ***   not a function in function call
 2514 A function with that name existed in GP-1.39.15. Please update your script.
 2515 
 2516 New syntax: localred(e) ===> elllocalred(e)
 2517 
 2518 elllocalred(E,{p}): E being an elliptic curve, returns [f,kod,[u,r,s,t],c], 
 2519 where f is the conductor's exponent, kod is the Kodaira type for E at p, 
 2520 [u,r,s,t] is the change of variable needed to make E minimal at p, and c is the 
 2521 local Tamagawa number c_p.
 2522 
 2523 
 2524   ***   at top-level: logagm()
 2525   ***                 ^--------
 2526   ***   not a function in function call
 2527 A function with that name existed in GP-1.39.15. Please update your script.
 2528 
 2529 New syntax: logagm(x) ===> log(x,1)
 2530 
 2531 log(x): natural logarithm of x.
 2532 
 2533 
 2534   ***   at top-level: lseriesell()
 2535   ***                 ^------------
 2536   ***   not a function in function call
 2537 A function with that name existed in GP-1.39.15. Please update your script.
 2538 
 2539 New syntax: lseriesell(e,s,N,A) ===> elllseries(e,s,A)
 2540 
 2541 elllseries(E,s,{A=1}): L-series at s of the elliptic curve E, where A a cut-off 
 2542 point close to 1.
 2543 
 2544 
 2545   ***   at top-level: makebigbnf()
 2546   ***                 ^------------
 2547   ***   not a function in function call
 2548 A function with that name existed in GP-1.39.15. Please update your script.
 2549 
 2550 New syntax: makebigbnf(sbnf) ===> bnfinit(sbnf)
 2551 
 2552 bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in 
 2553 ideal and unit group computations, including fundamental units if they are not 
 2554 too large. flag and tech are both optional. flag can be any of 0: default, 1: 
 2555 include all data in algebraic form (compact units). See manual for details 
 2556 about tech.
 2557 
 2558 
 2559   ***   at top-level: mat()
 2560   ***                 ^-----
 2561   ***   not a function in function call
 2562 A function with that name existed in GP-1.39.15. Please update your script.
 2563 
 2564 New syntax: mat(x) ===> Mat(x)
 2565 
 2566 Mat({x=[]}): transforms any GEN x into a matrix. Empty matrix if x is omitted.
 2567 
 2568 
 2569   ***   at top-level: matextract()
 2570   ***                 ^------------
 2571   ***   not a function in function call
 2572 A function with that name existed in GP-1.39.15. Please update your script.
 2573 
 2574 New syntax: matextract(x,y,z) ===> vecextract(x,y,z)
 2575 
 2576 vecextract(x,y,{z}): extraction of the components of the matrix or vector x 
 2577 according to y and z. If z is omitted, y represents columns, otherwise y 
 2578 corresponds to rows and z to columns. y and z can be vectors (of indices), 
 2579 strings (indicating ranges as in "1..10") or masks (integers whose binary 
 2580 representation indicates the indices to extract, from left to right 1, 2, 4, 8, 
 2581 etc.).
 2582 
 2583 
 2584   ***   at top-level: mathell()
 2585   ***                 ^---------
 2586   ***   not a function in function call
 2587 A function with that name existed in GP-1.39.15. Please update your script.
 2588 
 2589 New syntax: mathell(e,x) ===> ellheightmatrix(e,x)
 2590 
 2591 ellheightmatrix(E,x): gives the height matrix for vector of points x on 
 2592 elliptic curve E.
 2593 
 2594 
 2595   ***   at top-level: matrixqz2()
 2596   ***                 ^-----------
 2597   ***   not a function in function call
 2598 A function with that name existed in GP-1.39.15. Please update your script.
 2599 
 2600 New syntax: matrixqz2(x,p) ===> matrixqz(x,-1)
 2601 
 2602 matrixqz(A,{p=0}): if p>=0, transforms the rational or integral mxn (m>=n) 
 2603 matrix A into an integral matrix with gcd of maximal determinants coprime to p. 
 2604 If p=-1, finds a basis of the intersection with Z^n of the lattice spanned by 
 2605 the columns of A. If p=-2, finds a basis of the intersection with Z^n of the 
 2606 Q-vector space spanned by the columns of A.
 2607 
 2608 
 2609   ***   at top-level: matrixqz3()
 2610   ***                 ^-----------
 2611   ***   not a function in function call
 2612 A function with that name existed in GP-1.39.15. Please update your script.
 2613 
 2614 New syntax: matrixqz3(x,p) ===> matrixqz(x,-2)
 2615 
 2616 matrixqz(A,{p=0}): if p>=0, transforms the rational or integral mxn (m>=n) 
 2617 matrix A into an integral matrix with gcd of maximal determinants coprime to p. 
 2618 If p=-1, finds a basis of the intersection with Z^n of the lattice spanned by 
 2619 the columns of A. If p=-2, finds a basis of the intersection with Z^n of the 
 2620 Q-vector space spanned by the columns of A.
 2621 
 2622 
 2623   ***   at top-level: minideal()
 2624   ***                 ^----------
 2625   ***   not a function in function call
 2626 A function with that name existed in GP-1.39.15. Please update your script.
 2627 
 2628 New syntax: minideal(nf,ix,vdir) ===> idealmin(nf,ix,vdir)
 2629 
 2630 idealmin(nf,ix,{vdir}): pseudo-minimum of the ideal ix in the direction vdir in 
 2631 the number field nf.
 2632 
 2633 
 2634   ***   at top-level: minim()
 2635   ***                 ^-------
 2636   ***   not a function in function call
 2637 A function with that name existed in GP-1.39.15. Please update your script.
 2638 
 2639 New syntax: minim(x,bound,maxnum) ===> qfminim(x,bound,maxnum)
 2640 
 2641 qfminim(x,{B},{m},{flag=0}): x being a square and symmetric matrix representing 
 2642 a positive definite quadratic form, this function deals with the vectors of x 
 2643 whose norm is less than or equal to B, enumerated using the Fincke-Pohst 
 2644 algorithm, storing at most m vectors (no limit if m is omitted). The function 
 2645 searches for the minimal nonzero vectors if B is omitted. The precise behavior 
 2646 depends on flag. 0: returns at most 2m vectors (unless m omitted), returns 
 2647 [N,M,V] where N is the number of vectors enumerated, M the maximum norm among 
 2648 these, and V lists half the vectors (the other half is given by -V). 1: ignores 
 2649 m and returns the first vector whose norm is less than B. 2: as 0 but uses a 
 2650 more robust, slower implementation
 2651 
 2652 
 2653   ***   at top-level: minim2()
 2654   ***                 ^--------
 2655   ***   not a function in function call
 2656 A function with that name existed in GP-1.39.15. Please update your script.
 2657 
 2658 New syntax: minim2(x,bound) ===> qfminim(x,bound,,1)
 2659 
 2660 qfminim(x,{B},{m},{flag=0}): x being a square and symmetric matrix representing 
 2661 a positive definite quadratic form, this function deals with the vectors of x 
 2662 whose norm is less than or equal to B, enumerated using the Fincke-Pohst 
 2663 algorithm, storing at most m vectors (no limit if m is omitted). The function 
 2664 searches for the minimal nonzero vectors if B is omitted. The precise behavior 
 2665 depends on flag. 0: returns at most 2m vectors (unless m omitted), returns 
 2666 [N,M,V] where N is the number of vectors enumerated, M the maximum norm among 
 2667 these, and V lists half the vectors (the other half is given by -V). 1: ignores 
 2668 m and returns the first vector whose norm is less than B. 2: as 0 but uses a 
 2669 more robust, slower implementation
 2670 
 2671 
 2672   ***   at top-level: mod()
 2673   ***                 ^-----
 2674   ***   not a function in function call
 2675 A function with that name existed in GP-1.39.15. Please update your script.
 2676 
 2677 New syntax: mod(x,y) ===> Mod(x,y)
 2678 
 2679 Mod(a,b): create 'a modulo b'.
 2680 
 2681 
 2682   ***   at top-level: modp()
 2683   ***                 ^------
 2684   ***   not a function in function call
 2685 A function with that name existed in GP-1.39.15. Please update your script.
 2686 
 2687 New syntax: modp(x,y,p) ===> Mod(x,y)
 2688 
 2689 Mod(a,b): create 'a modulo b'.
 2690 
 2691 
 2692   ***   at top-level: modulargcd()
 2693   ***                 ^------------
 2694   ***   not a function in function call
 2695 A function with that name existed in GP-1.39.15. Please update your script.
 2696 
 2697 New syntax: modulargcd(x,y) ===> gcd(x,y,1)
 2698 
 2699 gcd(x,{y}): greatest common divisor of x and y.
 2700 
 2701 
 2702   ***   at top-level: mu()
 2703   ***                 ^----
 2704   ***   not a function in function call
 2705 A function with that name existed in GP-1.39.15. Please update your script.
 2706 
 2707 New syntax: mu(n) ===> moebius(n)
 2708 
 2709 moebius(x): Moebius function of x.
 2710 
 2711 
 2712   ***   at top-level: nfdiv()
 2713   ***                 ^-------
 2714   ***   not a function in function call
 2715 A function with that name existed in GP-1.39.15. Please update your script.
 2716 
 2717 New syntax: nfdiv(nf,a,b) ===> nfeltdiv(nf,a,b)
 2718 
 2719 nfeltdiv(nf,x,y): element x/y in nf.
 2720 
 2721 
 2722   ***   at top-level: nfdiveuc()
 2723   ***                 ^----------
 2724   ***   not a function in function call
 2725 A function with that name existed in GP-1.39.15. Please update your script.
 2726 
 2727 New syntax: nfdiveuc(nf,a,b) ===> nfeltdiveuc(nf,a,b)
 2728 
 2729 nfeltdiveuc(nf,x,y): gives algebraic integer q such that x-qy is small.
 2730 
 2731 
 2732   ***   at top-level: nfdivres()
 2733   ***                 ^----------
 2734   ***   not a function in function call
 2735 A function with that name existed in GP-1.39.15. Please update your script.
 2736 
 2737 New syntax: nfdivres(nf,a,b) ===> nfeltdivrem(nf,a,b)
 2738 
 2739 nfeltdivrem(nf,x,y): gives [q,r] such that r=x-qy is small.
 2740 
 2741 
 2742   ***   at top-level: nfhermite()
 2743   ***                 ^-----------
 2744   ***   not a function in function call
 2745 A function with that name existed in GP-1.39.15. Please update your script.
 2746 
 2747 New syntax: nfhermite(nf,x) ===> nfhnf(nf,x)
 2748 
 2749 nfhnf(nf,x,{flag=0}): if x=[A,I], gives a pseudo-basis [B,J] of the module sum 
 2750 A_jI_j. If flag is nonzero, return [[B,J], U], where U is the transformation 
 2751 matrix such that AU = [0|B].
 2752 
 2753 
 2754   ***   at top-level: nfhermitemod()
 2755   ***                 ^--------------
 2756   ***   not a function in function call
 2757 A function with that name existed in GP-1.39.15. Please update your script.
 2758 
 2759 New syntax: nfhermitemod(nf,x,detx) ===> nfhnfmod(nf,x,detx)
 2760 
 2761 nfhnfmod(nf,x,detx): if x=[A,I], and detx is a multiple of the ideal 
 2762 determinant of x, gives a pseudo-basis of the module sum A_jI_j.
 2763 
 2764 
 2765   ***   at top-level: nfmod()
 2766   ***                 ^-------
 2767   ***   not a function in function call
 2768 A function with that name existed in GP-1.39.15. Please update your script.
 2769 
 2770 New syntax: nfmod(nf,a,b) ===> nfeltmod(nf,a,b)
 2771 
 2772 nfeltmod(nf,x,y): gives r such that r=x-qy is small with q algebraic integer.
 2773 
 2774 
 2775   ***   at top-level: nfmul()
 2776   ***                 ^-------
 2777   ***   not a function in function call
 2778 A function with that name existed in GP-1.39.15. Please update your script.
 2779 
 2780 New syntax: nfmul(nf,a,b) ===> nfeltmul(nf,a,b)
 2781 
 2782 nfeltmul(nf,x,y): element x.y in nf.
 2783 
 2784 
 2785   ***   at top-level: nfpow()
 2786   ***                 ^-------
 2787   ***   not a function in function call
 2788 A function with that name existed in GP-1.39.15. Please update your script.
 2789 
 2790 New syntax: nfpow(nf,a,k) ===> nfeltpow(nf,a,k)
 2791 
 2792 nfeltpow(nf,x,k): element x^k in nf.
 2793 
 2794 
 2795   ***   at top-level: nfreduce()
 2796   ***                 ^----------
 2797   ***   not a function in function call
 2798 A function with that name existed in GP-1.39.15. Please update your script.
 2799 
 2800 New syntax: nfreduce(nf,a,id) ===> nfeltreduce(nf,a,id)
 2801 
 2802 nfeltreduce(nf,a,id): gives r such that a-r is in the ideal id and r is small.
 2803 
 2804 
 2805   ***   at top-level: nfsmith()
 2806   ***                 ^---------
 2807   ***   not a function in function call
 2808 A function with that name existed in GP-1.39.15. Please update your script.
 2809 
 2810 New syntax: nfsmith(nf,x) ===> nfsnf(nf,x)
 2811 
 2812 nfsnf(nf,x,{flag=0}): if x=[A,I,J], outputs D=[d_1,...d_n] Smith normal form of 
 2813 x. If flag is nonzero return [D,U,V], where UAV = Id.
 2814 
 2815 
 2816   ***   at top-level: nfval()
 2817   ***                 ^-------
 2818   ***   not a function in function call
 2819 A function with that name existed in GP-1.39.15. Please update your script.
 2820 
 2821 New syntax: nfval(nf,a,pr) ===> nfeltval(nf,a,pr)
 2822 
 2823 nfeltval(nf,x,pr,{&y}): valuation of element x at the prime pr as output by 
 2824 idealprimedec.
 2825 
 2826 
 2827   ***   at top-level: nucomp()
 2828   ***                 ^--------
 2829   ***   not a function in function call
 2830 A function with that name existed in GP-1.39.15. Please update your script.
 2831 
 2832 New syntax: nucomp(x,y,l) ===> qfbnucomp(x,y,l)
 2833 
 2834 qfbnucomp(x,y,L): composite of primitive positive definite quadratic forms x 
 2835 and y using nucomp and nudupl, where L=[|D/4|^(1/4)] is precomputed.
 2836 
 2837 
 2838   ***   at top-level: numer()
 2839   ***                 ^-------
 2840   ***   not a function in function call
 2841 A function with that name existed in GP-1.39.15. Please update your script.
 2842 
 2843 New syntax: numer(x) ===> numerator(x)
 2844 
 2845 numerator(f,{D}): numerator of f.
 2846 
 2847 
 2848   ***   at top-level: nupow()
 2849   ***                 ^-------
 2850   ***   not a function in function call
 2851 A function with that name existed in GP-1.39.15. Please update your script.
 2852 
 2853 New syntax: nupow(x,n) ===> qfbnupow(x,n)
 2854 
 2855 qfbnupow(x,n,{L}): n-th power of primitive positive definite quadratic form x 
 2856 using nucomp and nudupl.
 2857 
 2858 
 2859   ***   at top-level: o()
 2860   ***                 ^---
 2861   ***   not a function in function call
 2862 A function with that name existed in GP-1.39.15. Please update your script.
 2863 
 2864 New syntax: o(x) ===> O(x)
 2865 
 2866 O(p^e): p-adic or power series zero with precision given by e.
 2867 
 2868 
 2869   ***   at top-level: ordell()
 2870   ***                 ^--------
 2871   ***   not a function in function call
 2872 A function with that name existed in GP-1.39.15. Please update your script.
 2873 
 2874 New syntax: ordell(e,x) ===> ellordinate(e,x)
 2875 
 2876 ellordinate(E,x): y-coordinates corresponding to x-ordinate x on elliptic curve 
 2877 E.
 2878 
 2879 
 2880   ***   at top-level: order()
 2881   ***                 ^-------
 2882   ***   not a function in function call
 2883 A function with that name existed in GP-1.39.15. Please update your script.
 2884 
 2885 New syntax: order(x) ===> znorder(x)
 2886 
 2887 znorder(x,{o}): order of the integermod x in (Z/nZ)*. Optional o represents a 
 2888 multiple of the order of the element.
 2889 
 2890 
 2891   ***   at top-level: orderell()
 2892   ***                 ^----------
 2893   ***   not a function in function call
 2894 A function with that name existed in GP-1.39.15. Please update your script.
 2895 
 2896 New syntax: orderell(e,x) ===> ellorder(e,x)
 2897 
 2898 ellorder(E,z,{o}): order of the point z on the elliptic curve E over a number 
 2899 field or a finite field, 0 if nontorsion. The parameter o, if present, 
 2900 represents a nonzero multiple of the order of z.
 2901 
 2902 
 2903   ***   at top-level: ordred()
 2904   ***                 ^--------
 2905   ***   not a function in function call
 2906 A function with that name existed in GP-1.39.15. Please update your script.
 2907 
 2908 New syntax: ordred(x) ===> polredord(x)
 2909 
 2910 polredord(x): this function is obsolete, use polredbest.
 2911 
 2912 
 2913   ***   at top-level: pascal()
 2914   ***                 ^--------
 2915   ***   not a function in function call
 2916 A function with that name existed in GP-1.39.15. Please update your script.
 2917 
 2918 New syntax: pascal(n) ===> matpascal(n)
 2919 
 2920 matpascal(n,{q}): Pascal triangle of order n if q is omitted. q-Pascal triangle 
 2921 otherwise.
 2922 
 2923 
 2924   ***   at top-level: perf()
 2925   ***                 ^------
 2926   ***   not a function in function call
 2927 A function with that name existed in GP-1.39.15. Please update your script.
 2928 
 2929 New syntax: perf(a) ===> qfperfection(a)
 2930 
 2931 qfperfection(G): rank of matrix of xx~ for x minimal vectors of a gram matrix 
 2932 G.
 2933 
 2934 
 2935   ***   at top-level: permutation()
 2936   ***                 ^-------------
 2937   ***   not a function in function call
 2938 A function with that name existed in GP-1.39.15. Please update your script.
 2939 
 2940 New syntax: permutation(n,k) ===> numtoperm(n,k)
 2941 
 2942 numtoperm(n,k): permutation number k (mod n!) of n letters (n C-integer).
 2943 
 2944 
 2945   ***   at top-level: permutation2num()
 2946   ***                 ^-----------------
 2947   ***   not a function in function call
 2948 A function with that name existed in GP-1.39.15. Please update your script.
 2949 
 2950 New syntax: permutation2num(vect) ===> permtonum(vect)
 2951 
 2952 permtonum(x): ordinal (between 0 and n!-1) of permutation x.
 2953 
 2954 
 2955   ***   at top-level: pf()
 2956   ***                 ^----
 2957   ***   not a function in function call
 2958 A function with that name existed in GP-1.39.15. Please update your script.
 2959 
 2960 New syntax: pf(x,p) ===> qfbprimeform(x,p)
 2961 
 2962 qfbprimeform(x,p): returns the prime form of discriminant x, whose first 
 2963 coefficient is p.
 2964 
 2965 
 2966   ***   at top-level: phi()
 2967   ***                 ^-----
 2968   ***   not a function in function call
 2969 A function with that name existed in GP-1.39.15. Please update your script.
 2970 
 2971 New syntax: phi(x) ===> eulerphi(x)
 2972 
 2973 eulerphi(x): Euler's totient function of x.
 2974 
 2975 
 2976   ***   at top-level: pi()
 2977   ***                 ^----
 2978   ***   not a function in function call
 2979 A function with that name existed in GP-1.39.15. Please update your script.
 2980 
 2981 New syntax: pi ===> Pi
 2982 
 2983 Pi=Pi(): the constant pi, with current precision.
 2984 
 2985 
 2986   ***   at top-level: pnqn()
 2987   ***                 ^------
 2988   ***   not a function in function call
 2989 A function with that name existed in GP-1.39.15. Please update your script.
 2990 
 2991 New syntax: pnqn(x) ===> contfracpnqn(x)
 2992 
 2993 contfracpnqn(x, {n=-1}): [p_n,p_{n-1}; q_n,q_{n-1}] corresponding to the 
 2994 continued fraction x. If n >= 0 is present, returns all convergents from 
 2995 p_0/q_0 up to p_n/q_n.
 2996 
 2997 
 2998   ***   at top-level: pointell()
 2999   ***                 ^----------
 3000   ***   not a function in function call
 3001 A function with that name existed in GP-1.39.15. Please update your script.
 3002 
 3003 New syntax: pointell(e,z) ===> ellztopoint(e,z)
 3004 
 3005 ellztopoint(E,z): inverse of ellpointtoz. Returns the coordinates of point P on 
 3006 the curve E corresponding to a complex or p-adic z.
 3007 
 3008 
 3009   ***   at top-level: polint()
 3010   ***                 ^--------
 3011   ***   not a function in function call
 3012 A function with that name existed in GP-1.39.15. Please update your script.
 3013 
 3014 New syntax: polint(xa,ya,x) ===> polinterpolate(xa,ya,p)
 3015 
 3016 polinterpolate(X,{Y},{t = 'x},{&e}): polynomial interpolation at t according to 
 3017 data vectors X, Y, i.e., given P of minimal degree such that P(X[i]) = Y[i] for 
 3018 all i, return P(t). If Y is omitted, take P such that P(i) = X[i]. If present 
 3019 and t is numeric, e will contain an error estimate on the returned value 
 3020 (Neville's algorithm).
 3021 
 3022 
 3023   ***   at top-level: polred2()
 3024   ***                 ^---------
 3025   ***   not a function in function call
 3026 A function with that name existed in GP-1.39.15. Please update your script.
 3027 
 3028 New syntax: polred2(x) ===> polred(x,2)
 3029 
 3030 polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T 
 3031 (gives minimal polynomials only). The following binary digits of (optional) 
 3032 flag are significant 1: partial reduction, 2: gives also elements.
 3033 
 3034 
 3035   ***   at top-level: polredabs2()
 3036   ***                 ^------------
 3037   ***   not a function in function call
 3038 A function with that name existed in GP-1.39.15. Please update your script.
 3039 
 3040 New syntax: polredabs2(x) ===> polredabs(x,1)
 3041 
 3042 polredabs(T,{flag=0}): a smallest generating polynomial of the number field for 
 3043 the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is 
 3044 optional, whose binary digit mean 1: give the element whose characteristic 
 3045 polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm 
 3046 (give only one of P(x) and P(-x)).
 3047 
 3048 
 3049   ***   at top-level: polredabsall()
 3050   ***                 ^--------------
 3051   ***   not a function in function call
 3052 A function with that name existed in GP-1.39.15. Please update your script.
 3053 
 3054 New syntax: polredabsall(x) ===> polredabs(x,4)
 3055 
 3056 polredabs(T,{flag=0}): a smallest generating polynomial of the number field for 
 3057 the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is 
 3058 optional, whose binary digit mean 1: give the element whose characteristic 
 3059 polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm 
 3060 (give only one of P(x) and P(-x)).
 3061 
 3062 
 3063   ***   at top-level: polredabsfast()
 3064   ***                 ^---------------
 3065   ***   not a function in function call
 3066 A function with that name existed in GP-1.39.15. Please update your script.
 3067 
 3068 New syntax: polredabsfast(x) ===> polredabs(x,8)
 3069 
 3070 polredabs(T,{flag=0}): a smallest generating polynomial of the number field for 
 3071 the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is 
 3072 optional, whose binary digit mean 1: give the element whose characteristic 
 3073 polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm 
 3074 (give only one of P(x) and P(-x)).
 3075 
 3076 
 3077   ***   at top-level: polredabsnored()
 3078   ***                 ^----------------
 3079   ***   not a function in function call
 3080 A function with that name existed in GP-1.39.15. Please update your script.
 3081 
 3082 New syntax: polredabsnored(x) ===> polredabs(x,2)
 3083 
 3084 polredabs(T,{flag=0}): a smallest generating polynomial of the number field for 
 3085 the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is 
 3086 optional, whose binary digit mean 1: give the element whose characteristic 
 3087 polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm 
 3088 (give only one of P(x) and P(-x)).
 3089 
 3090 
 3091   ***   at top-level: polvar()
 3092   ***                 ^--------
 3093   ***   not a function in function call
 3094 A function with that name existed in GP-1.39.15. Please update your script.
 3095 
 3096 New syntax: polvar(x) ===> variable(x)
 3097 
 3098 variable({x}): main variable of object x. Gives p for p-adic x, 0 if no 
 3099 variable can be attached to x. Returns the list of user variables if x is 
 3100 omitted.
 3101 
 3102 
 3103   ***   at top-level: poly()
 3104   ***                 ^------
 3105   ***   not a function in function call
 3106 A function with that name existed in GP-1.39.15. Please update your script.
 3107 
 3108 New syntax: poly(x,v) ===> Pol(x,v)
 3109 
 3110 Pol(t,{v='x}): convert t (usually a vector or a power series) into a polynomial 
 3111 with variable v, starting with the leading coefficient.
 3112 
 3113 
 3114   ***   at top-level: polylogd()
 3115   ***                 ^----------
 3116   ***   not a function in function call
 3117 A function with that name existed in GP-1.39.15. Please update your script.
 3118 
 3119 New syntax: polylogd(m,x) ===> polylog(m,x,1)
 3120 
 3121 polylog(m,x,{flag=0}): m-th polylogarithm of x. flag is optional, and can be 0: 
 3122 default, 1: D_m~-modified m-th polylog of x, 2: D_m-modified m-th polylog of x, 
 3123 3: P_m-modified m-th polylog of x.
 3124 
 3125 
 3126   ***   at top-level: polylogdold()
 3127   ***                 ^-------------
 3128   ***   not a function in function call
 3129 A function with that name existed in GP-1.39.15. Please update your script.
 3130 
 3131 New syntax: polylogdold(m,x) ===> polylog(m,x,2)
 3132 
 3133 polylog(m,x,{flag=0}): m-th polylogarithm of x. flag is optional, and can be 0: 
 3134 default, 1: D_m~-modified m-th polylog of x, 2: D_m-modified m-th polylog of x, 
 3135 3: P_m-modified m-th polylog of x.
 3136 
 3137 
 3138   ***   at top-level: polylogp()
 3139   ***                 ^----------
 3140   ***   not a function in function call
 3141 A function with that name existed in GP-1.39.15. Please update your script.
 3142 
 3143 New syntax: polylogp(m,x) ===> polylog(m,x,3)
 3144 
 3145 polylog(m,x,{flag=0}): m-th polylogarithm of x. flag is optional, and can be 0: 
 3146 default, 1: D_m~-modified m-th polylog of x, 2: D_m-modified m-th polylog of x, 
 3147 3: P_m-modified m-th polylog of x.
 3148 
 3149 
 3150   ***   at top-level: polyrev()
 3151   ***                 ^---------
 3152   ***   not a function in function call
 3153 A function with that name existed in GP-1.39.15. Please update your script.
 3154 
 3155 New syntax: polyrev(x,v) ===> Polrev(x,v)
 3156 
 3157 Polrev(t,{v='x}): convert t (usually a vector or a power series) into a 
 3158 polynomial with variable v, starting with the constant term.
 3159 
 3160 
 3161   ***   at top-level: polzag()
 3162   ***                 ^--------
 3163   ***   not a function in function call
 3164 A function with that name existed in GP-1.39.15. Please update your script.
 3165 
 3166 New syntax: polzag(n,m) ===> polzagier(n,m)
 3167 
 3168 polzagier(n,m): Zagier's polynomials of index n,m.
 3169 
 3170 
 3171   ***   at top-level: powell()
 3172   ***                 ^--------
 3173   ***   not a function in function call
 3174 A function with that name existed in GP-1.39.15. Please update your script.
 3175 
 3176 New syntax: powell(e,x,n) ===> ellmul(e,x,n)
 3177 
 3178 ellmul(E,z,n): n times the point z on elliptic curve E (n in Z).
 3179 
 3180 
 3181   ***   at top-level: powrealraw()
 3182   ***                 ^------------
 3183   ***   not a function in function call
 3184 A function with that name existed in GP-1.39.15. Please update your script.
 3185 
 3186 New syntax: powrealraw(x,n) ===> qfbpowraw(x,n)
 3187 
 3188 qfbpowraw(x,n): n-th power without reduction of the binary quadratic form x.
 3189 
 3190 
 3191   ***   at top-level: prec()
 3192   ***                 ^------
 3193   ***   not a function in function call
 3194 A function with that name existed in GP-1.39.15. Please update your script.
 3195 
 3196 New syntax: prec(x,n) ===> precision(x,n)
 3197 
 3198 precision(x,{n}): if n is present, return x at precision n. If n is omitted, 
 3199 return real precision of object x.
 3200 
 3201 
 3202   ***   at top-level: primedec()
 3203   ***                 ^----------
 3204   ***   not a function in function call
 3205 A function with that name existed in GP-1.39.15. Please update your script.
 3206 
 3207 New syntax: primedec(nf,p) ===> idealprimedec(nf,p)
 3208 
 3209 idealprimedec(nf,p,{f=0}): prime ideal decomposition of the prime number p in 
 3210 the number field nf as a vector of prime ideals. If f is present and nonzero, 
 3211 restrict the result to primes of residue degree <= f.
 3212 
 3213 
 3214   ***   at top-level: primroot()
 3215   ***                 ^----------
 3216   ***   not a function in function call
 3217 A function with that name existed in GP-1.39.15. Please update your script.
 3218 
 3219 New syntax: primroot(n) ===> znprimroot(n)
 3220 
 3221 znprimroot(n): returns a primitive root of n when it exists.
 3222 
 3223 
 3224   ***   at top-level: principalideal()
 3225   ***                 ^----------------
 3226   ***   not a function in function call
 3227 A function with that name existed in GP-1.39.15. Please update your script.
 3228 
 3229 This function no longer exists
 3230 
 3231 
 3232   ***   at top-level: principalidele()
 3233   ***                 ^----------------
 3234   ***   not a function in function call
 3235 A function with that name existed in GP-1.39.15. Please update your script.
 3236 
 3237 This function no longer exists
 3238 
 3239 
 3240   ***   at top-level: prodinf1()
 3241   ***                 ^----------
 3242   ***   not a function in function call
 3243 A function with that name existed in GP-1.39.15. Please update your script.
 3244 
 3245 New syntax: prodinf1(X=a,expr) ===> prodinf(X=a,expr,1)
 3246 
 3247 prodinf(X=a,expr,{flag=0}): infinite product (X goes from a to infinity) of 
 3248 real or complex expression. flag can be 0 (default) or 1, in which case compute 
 3249 the product of the 1+expr instead.
 3250 
 3251 
 3252   ***   at top-level: qfi()
 3253   ***                 ^-----
 3254   ***   not a function in function call
 3255 A function with that name existed in GP-1.39.15. Please update your script.
 3256 
 3257 New syntax: qfi(a,b,c) ===> Qfb(a,b,c)
 3258 
 3259 Qfb(a,b,c,{D=0.}): binary quadratic form a*x^2+b*x*y+c*y^2. D is optional (0.0 
 3260 by default) and initializes Shanks's distance if b^2-4*a*c>0.
 3261 
 3262 
 3263   ***   at top-level: qfr()
 3264   ***                 ^-----
 3265   ***   not a function in function call
 3266 A function with that name existed in GP-1.39.15. Please update your script.
 3267 
 3268 New syntax: qfr(a,b,c,d) ===> Qfb(a,b,c,d)
 3269 
 3270 Qfb(a,b,c,{D=0.}): binary quadratic form a*x^2+b*x*y+c*y^2. D is optional (0.0 
 3271 by default) and initializes Shanks's distance if b^2-4*a*c>0.
 3272 
 3273 
 3274 1546275796
 3275   ***   at top-level: rank()
 3276   ***                 ^------
 3277   ***   not a function in function call
 3278 A function with that name existed in GP-1.39.15. Please update your script.
 3279 
 3280 New syntax: rank(x) ===> matrank(x)
 3281 
 3282 matrank(x): rank of the matrix x.
 3283 
 3284 
 3285   ***   at top-level: rayclassno()
 3286   ***                 ^------------
 3287   ***   not a function in function call
 3288 A function with that name existed in GP-1.39.15. Please update your script.
 3289 
 3290 New syntax: rayclassno(bnf,x) ===> bnrclassno(bnf,x)
 3291 
 3292 bnrclassno(A,{B},{C}): relative degree of the class field defined by A,B,C. 
 3293 [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf,modulus], or 
 3294 [bnf,modulus,subgroup]. Faster than bnrinit if only the ray class number is 
 3295 wanted.
 3296 
 3297 
 3298   ***   at top-level: rayclassnolist()
 3299   ***                 ^----------------
 3300   ***   not a function in function call
 3301 A function with that name existed in GP-1.39.15. Please update your script.
 3302 
 3303 New syntax: rayclassnolist(bnf,liste) ===> bnrclassnolist(bnf,liste)
 3304 
 3305 bnrclassnolist(bnf,list): if list is as output by ideallist or similar, gives 
 3306 list of corresponding ray class numbers.
 3307 
 3308 
 3309   ***   at top-level: recip()
 3310   ***                 ^-------
 3311   ***   not a function in function call
 3312 A function with that name existed in GP-1.39.15. Please update your script.
 3313 
 3314 New syntax: recip(x) ===> polrecip(x)
 3315 
 3316 polrecip(pol): reciprocal polynomial of pol.
 3317 
 3318 
 3319   ***   at top-level: redimag()
 3320   ***                 ^---------
 3321   ***   not a function in function call
 3322 A function with that name existed in GP-1.39.15. Please update your script.
 3323 
 3324 New syntax: redimag(x) ===> qfbred(x)
 3325 
 3326 qfbred(x,{flag=0},{d},{isd},{sd}): reduction of the binary quadratic form x. 
 3327 All other args. are optional. The arguments d, isd and sd, if present, supply 
 3328 the values of the discriminant, floor(sqrt(d)) and sqrt(d) respectively. If 
 3329 d<0, its value is not used and all references to Shanks's distance hereafter 
 3330 are meaningless. flag can be any of 0: default, uses Shanks's distance function 
 3331 d; 1: use d, do a single reduction step; 2: do not use d; 3: do not use d, 
 3332 single reduction step.
 3333 
 3334 
 3335   ***   at top-level: redreal()
 3336   ***                 ^---------
 3337   ***   not a function in function call
 3338 A function with that name existed in GP-1.39.15. Please update your script.
 3339 
 3340 New syntax: redreal(x) ===> qfbred(x)
 3341 
 3342 qfbred(x,{flag=0},{d},{isd},{sd}): reduction of the binary quadratic form x. 
 3343 All other args. are optional. The arguments d, isd and sd, if present, supply 
 3344 the values of the discriminant, floor(sqrt(d)) and sqrt(d) respectively. If 
 3345 d<0, its value is not used and all references to Shanks's distance hereafter 
 3346 are meaningless. flag can be any of 0: default, uses Shanks's distance function 
 3347 d; 1: use d, do a single reduction step; 2: do not use d; 3: do not use d, 
 3348 single reduction step.
 3349 
 3350 
 3351   ***   at top-level: redrealnod()
 3352   ***                 ^------------
 3353   ***   not a function in function call
 3354 A function with that name existed in GP-1.39.15. Please update your script.
 3355 
 3356 New syntax: redrealnod(x,d) ===> qfbred(x,2,,d)
 3357 
 3358 qfbred(x,{flag=0},{d},{isd},{sd}): reduction of the binary quadratic form x. 
 3359 All other args. are optional. The arguments d, isd and sd, if present, supply 
 3360 the values of the discriminant, floor(sqrt(d)) and sqrt(d) respectively. If 
 3361 d<0, its value is not used and all references to Shanks's distance hereafter 
 3362 are meaningless. flag can be any of 0: default, uses Shanks's distance function 
 3363 d; 1: use d, do a single reduction step; 2: do not use d; 3: do not use d, 
 3364 single reduction step.
 3365 
 3366 
 3367   ***   at top-level: reduceddisc()
 3368   ***                 ^-------------
 3369   ***   not a function in function call
 3370 A function with that name existed in GP-1.39.15. Please update your script.
 3371 
 3372 New syntax: reduceddisc(f) ===> poldiscreduced(f)
 3373 
 3374 poldiscreduced(f): vector of elementary divisors of Z[a]/f'(a)Z[a], where a is 
 3375 a root of the polynomial f.
 3376 
 3377 
 3378   ***   at top-level: regula()
 3379   ***                 ^--------
 3380   ***   not a function in function call
 3381 A function with that name existed in GP-1.39.15. Please update your script.
 3382 
 3383 New syntax: regula(x) ===> quadregulator(x)
 3384 
 3385 quadregulator(x): regulator of the real quadratic field of discriminant x.
 3386 
 3387 
 3388   ***   at top-level: reorder()
 3389   ***                 ^---------
 3390   ***   not a function in function call
 3391 A function with that name existed in GP-1.39.15. Please update your script.
 3392 
 3393 This function no longer exists
 3394 
 3395 
 3396   ***   at top-level: resultant()
 3397   ***                 ^-----------
 3398   ***   not a function in function call
 3399 A function with that name existed in GP-1.39.15. Please update your script.
 3400 
 3401 New syntax: resultant(x,y) ===> polresultant(x,y)
 3402 
 3403 polresultant(x,y,{v},{flag=0}): resultant of the polynomials x and y, with 
 3404 respect to the main variables of x and y if v is omitted, with respect to the 
 3405 variable v otherwise. flag is optional, and can be 0: default, uses either the 
 3406 subresultant algorithm, a modular algorithm or Sylvester's matrix, depending on 
 3407 the inputs; 1 uses Sylvester's matrix (should always be slower than the 
 3408 default).
 3409 
 3410 
 3411   ***   at top-level: resultant2()
 3412   ***                 ^------------
 3413   ***   not a function in function call
 3414 A function with that name existed in GP-1.39.15. Please update your script.
 3415 
 3416 New syntax: resultant2(x,y) ===> polresultant(x,y,1)
 3417 
 3418 polresultant(x,y,{v},{flag=0}): resultant of the polynomials x and y, with 
 3419 respect to the main variables of x and y if v is omitted, with respect to the 
 3420 variable v otherwise. flag is optional, and can be 0: default, uses either the 
 3421 subresultant algorithm, a modular algorithm or Sylvester's matrix, depending on 
 3422 the inputs; 1 uses Sylvester's matrix (should always be slower than the 
 3423 default).
 3424 
 3425 
 3426   ***   at top-level: reverse()
 3427   ***                 ^---------
 3428   ***   not a function in function call
 3429 A function with that name existed in GP-1.39.15. Please update your script.
 3430 
 3431 New syntax: reverse(x) ===> serreverse(x)
 3432 
 3433 serreverse(s): reversion of the power series s.
 3434 
 3435 
 3436   ***   at top-level: rhoreal()
 3437   ***                 ^---------
 3438   ***   not a function in function call
 3439 A function with that name existed in GP-1.39.15. Please update your script.
 3440 
 3441 New syntax: rhoreal(x) ===> qfbred(x,1)
 3442 
 3443 qfbred(x,{flag=0},{d},{isd},{sd}): reduction of the binary quadratic form x. 
 3444 All other args. are optional. The arguments d, isd and sd, if present, supply 
 3445 the values of the discriminant, floor(sqrt(d)) and sqrt(d) respectively. If 
 3446 d<0, its value is not used and all references to Shanks's distance hereafter 
 3447 are meaningless. flag can be any of 0: default, uses Shanks's distance function 
 3448 d; 1: use d, do a single reduction step; 2: do not use d; 3: do not use d, 
 3449 single reduction step.
 3450 
 3451 
 3452   ***   at top-level: rhorealnod()
 3453   ***                 ^------------
 3454   ***   not a function in function call
 3455 A function with that name existed in GP-1.39.15. Please update your script.
 3456 
 3457 New syntax: rhorealnod(x,d) ===> qfbred(x,3,,d)
 3458 
 3459 qfbred(x,{flag=0},{d},{isd},{sd}): reduction of the binary quadratic form x. 
 3460 All other args. are optional. The arguments d, isd and sd, if present, supply 
 3461 the values of the discriminant, floor(sqrt(d)) and sqrt(d) respectively. If 
 3462 d<0, its value is not used and all references to Shanks's distance hereafter 
 3463 are meaningless. flag can be any of 0: default, uses Shanks's distance function 
 3464 d; 1: use d, do a single reduction step; 2: do not use d; 3: do not use d, 
 3465 single reduction step.
 3466 
 3467 
 3468   ***   at top-level: rndtoi()
 3469   ***                 ^--------
 3470   ***   not a function in function call
 3471 A function with that name existed in GP-1.39.15. Please update your script.
 3472 
 3473 New syntax: rndtoi(x) ===> round(x,&e)
 3474 
 3475 round(x,{&e}): take the nearest integer to all the coefficients of x. If e is 
 3476 present, do not take into account loss of integer part precision, and set e = 
 3477 error estimate in bits.
 3478 
 3479 
 3480   ***   at top-level: rnfdiscf()
 3481   ***                 ^----------
 3482   ***   not a function in function call
 3483 A function with that name existed in GP-1.39.15. Please update your script.
 3484 
 3485 New syntax: rnfdiscf(nf,pol) ===> rnfdisc(nf,pol)
 3486 
 3487 rnfdisc(nf,T): given a polynomial T with coefficients in nf, gives a 
 3488 2-component vector [D,d], where D is the relative ideal discriminant, and d is 
 3489 the relative discriminant in nf^*/nf*^2.
 3490 
 3491 
 3492   ***   at top-level: rnfequation2()
 3493   ***                 ^--------------
 3494   ***   not a function in function call
 3495 A function with that name existed in GP-1.39.15. Please update your script.
 3496 
 3497 New syntax: rnfequation2(nf,pol) ===> rnfequation(nf,pol,1)
 3498 
 3499 rnfequation(nf,pol,{flag=0}): given a pol with coefficients in nf, gives an 
 3500 absolute equation z of the number field defined by pol. flag is optional, and 
 3501 can be 0: default, or nonzero, gives [z,al,k], where z defines the absolute 
 3502 equation L/Q as in the default behavior, al expresses as an element of L a root 
 3503 of the polynomial defining the base field nf, and k is a small integer such 
 3504 that t = b + k al is a root of z, for b a root of pol.
 3505 
 3506 
 3507   ***   at top-level: rnfhermitebasis()
 3508   ***                 ^-----------------
 3509   ***   not a function in function call
 3510 A function with that name existed in GP-1.39.15. Please update your script.
 3511 
 3512 New syntax: rnfhermitebasis(bnf,order) ===> rnfhnfbasis(bnf,order)
 3513 
 3514 rnfhnfbasis(bnf,x): given an order x as output by rnfpseudobasis, gives either 
 3515 a true HNF basis of the order if it exists, zero otherwise.
 3516 
 3517 
 3518   ***   at top-level: rootmod()
 3519   ***                 ^---------
 3520   ***   not a function in function call
 3521 A function with that name existed in GP-1.39.15. Please update your script.
 3522 
 3523 New syntax: rootmod(x,p) ===> polrootsmod(x,p)
 3524 
 3525 polrootsmod(f,{D}): roots of the polynomial f over the finite field defined by 
 3526 the domain D.
 3527 
 3528 
 3529   ***   at top-level: rootmod2()
 3530   ***                 ^----------
 3531   ***   not a function in function call
 3532 A function with that name existed in GP-1.39.15. Please update your script.
 3533 
 3534 New syntax: rootmod2(x,p) ===> polrootsmod(x,p)
 3535 
 3536 polrootsmod(f,{D}): roots of the polynomial f over the finite field defined by 
 3537 the domain D.
 3538 
 3539 
 3540   ***   at top-level: rootpadic()
 3541   ***                 ^-----------
 3542   ***   not a function in function call
 3543 A function with that name existed in GP-1.39.15. Please update your script.
 3544 
 3545 New syntax: rootpadic(x,p,r) ===> polrootspadic(x,p,r)
 3546 
 3547 polrootspadic(f,p,r): p-adic roots of the polynomial f to precision r.
 3548 
 3549 
 3550   ***   at top-level: roots()
 3551   ***                 ^-------
 3552   ***   not a function in function call
 3553 A function with that name existed in GP-1.39.15. Please update your script.
 3554 
 3555 New syntax: roots(x) ===> polroots(x)
 3556 
 3557 polroots(T): complex roots of the polynomial T using Schonhage's method, as 
 3558 modified by Gourdon.
 3559 
 3560 
 3561   ***   too few arguments: rootsof1()
 3562   ***                               ^-
 3563   ***   at top-level: rootsold()
 3564   ***                 ^----------
 3565   ***   not a function in function call
 3566 A function with that name existed in GP-1.39.15. Please update your script.
 3567 
 3568 This function no longer exists
 3569 
 3570 
 3571   ***   at top-level: rounderror()
 3572   ***                 ^------------
 3573   ***   not a function in function call
 3574 A function with that name existed in GP-1.39.15. Please update your script.
 3575 
 3576 New syntax: rounderror(x) ===> round(x,&e)
 3577 
 3578 round(x,{&e}): take the nearest integer to all the coefficients of x. If e is 
 3579 present, do not take into account loss of integer part precision, and set e = 
 3580 error estimate in bits.
 3581 
 3582 
 3583   ***   at top-level: series()
 3584   ***                 ^--------
 3585   ***   not a function in function call
 3586 A function with that name existed in GP-1.39.15. Please update your script.
 3587 
 3588 New syntax: series(x,v) ===> Ser(x,v)
 3589 
 3590 Ser(s,{v='x},{d=seriesprecision}): convert s into a power series with variable 
 3591 v and precision d, starting with the constant coefficient.
 3592 
 3593 
 3594   ***   at top-level: set()
 3595   ***                 ^-----
 3596   ***   not a function in function call
 3597 A function with that name existed in GP-1.39.15. Please update your script.
 3598 
 3599 New syntax: set(x) ===> Set(x)
 3600 
 3601 Set({x=[]}): convert x into a set, i.e. a row vector with strictly increasing 
 3602 coefficients. Empty set if x is omitted.
 3603 
 3604 
 3605   ***   at top-level: sigmak()
 3606   ***                 ^--------
 3607   ***   not a function in function call
 3608 A function with that name existed in GP-1.39.15. Please update your script.
 3609 
 3610 New syntax: sigmak(k,x) ===> sigma(x,k)
 3611 
 3612 sigma(x,{k=1}): sum of the k-th powers of the divisors of x. k is optional and 
 3613 if omitted is assumed to be equal to 1.
 3614 
 3615 
 3616   ***   at top-level: signat()
 3617   ***                 ^--------
 3618   ***   not a function in function call
 3619 A function with that name existed in GP-1.39.15. Please update your script.
 3620 
 3621 New syntax: signat(x) ===> qfsign(x)
 3622 
 3623 qfsign(x): signature of the symmetric matrix x.
 3624 
 3625 
 3626   ***   at top-level: signunit()
 3627   ***                 ^----------
 3628   ***   not a function in function call
 3629 A function with that name existed in GP-1.39.15. Please update your script.
 3630 
 3631 New syntax: signunit(bnf) ===> bnfsignunit(bnf)
 3632 
 3633 bnfsignunit(bnf): matrix of signs of the real embeddings of the system of 
 3634 fundamental units found by bnfinit.
 3635 
 3636 
 3637   ***   at top-level: simplefactmod()
 3638   ***                 ^---------------
 3639   ***   not a function in function call
 3640 A function with that name existed in GP-1.39.15. Please update your script.
 3641 
 3642 New syntax: simplefactmod(x,p) ===> factormod(x,p,1)
 3643 
 3644 factormod(f,{D},{flag=0}): factors the polynomial f over the finite field 
 3645 defined by the domain D; flag is optional, and can be 0: default or 1: only the 
 3646 degrees of the irreducible factors are given.
 3647 
 3648 
 3649   ***   at top-level: size()
 3650   ***                 ^------
 3651   ***   not a function in function call
 3652 A function with that name existed in GP-1.39.15. Please update your script.
 3653 
 3654 New syntax: size(x) ===> sizedigit(x)
 3655 
 3656 sizedigit(x): rough upper bound for the number of decimal digits of (the 
 3657 components of) x. DEPRECATED.
 3658 
 3659 
 3660   ***   at top-level: smallbasis()
 3661   ***                 ^------------
 3662   ***   not a function in function call
 3663 A function with that name existed in GP-1.39.15. Please update your script.
 3664 
 3665 New syntax: smallbasis(x) ===> nfbasis(x,1)
 3666 
 3667 nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the 
 3668 polynomial T, using the round 4 algorithm. An argument [T,listP] is possible, 
 3669 where listP is a list of primes or a prime bound, to get an order which is 
 3670 maximal at certain primes only. If present, dK is set to the discriminant of 
 3671 the returned order.
 3672 
 3673 
 3674   ***   at top-level: smallbuchinit()
 3675   ***                 ^---------------
 3676   ***   not a function in function call
 3677 A function with that name existed in GP-1.39.15. Please update your script.
 3678 
 3679 This function no longer exists
 3680 
 3681 
 3682   ***   at top-level: smalldiscf()
 3683   ***                 ^------------
 3684   ***   not a function in function call
 3685 A function with that name existed in GP-1.39.15. Please update your script.
 3686 
 3687 New syntax: smalldiscf(x) ===> nfdisc(x,1)
 3688 
 3689 nfdisc(T): discriminant of the number field defined by the polynomial T. An 
 3690 argument [T,listP] is possible, where listP is a list of primes or a prime 
 3691 bound.
 3692 
 3693 
 3694   ***   at top-level: smallfact()
 3695   ***                 ^-----------
 3696   ***   not a function in function call
 3697 A function with that name existed in GP-1.39.15. Please update your script.
 3698 
 3699 New syntax: smallfact(x) ===> factor(x,0)
 3700 
 3701 factor(x,{D}): factorization of x over domain D. If x and D are both integers, 
 3702 return partial factorization, using primes < D.
 3703 
 3704 
 3705   ***   at top-level: smallinitell()
 3706   ***                 ^--------------
 3707   ***   not a function in function call
 3708 A function with that name existed in GP-1.39.15. Please update your script.
 3709 
 3710 New syntax: smallinitell(x) ===> ellinit(x,1)
 3711 
 3712 ellinit(x,{D=1}): let x be a vector [a1,a2,a3,a4,a6], or [a4,a6] if a1=a2=a3=0, 
 3713 defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6; x can also be 
 3714 a string, in which case the curve with matching name is retrieved from the 
 3715 elldata database, if available. This function initializes an elliptic curve 
 3716 over the domain D (inferred from coefficients if omitted).
 3717 
 3718 
 3719   ***   at top-level: smallpolred()
 3720   ***                 ^-------------
 3721   ***   not a function in function call
 3722 A function with that name existed in GP-1.39.15. Please update your script.
 3723 
 3724 New syntax: smallpolred(x) ===> polred(x,1)
 3725 
 3726 polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T 
 3727 (gives minimal polynomials only). The following binary digits of (optional) 
 3728 flag are significant 1: partial reduction, 2: gives also elements.
 3729 
 3730 
 3731   ***   at top-level: smallpolred2()
 3732   ***                 ^--------------
 3733   ***   not a function in function call
 3734 A function with that name existed in GP-1.39.15. Please update your script.
 3735 
 3736 New syntax: smallpolred2(x) ===> polred(x,3)
 3737 
 3738 polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T 
 3739 (gives minimal polynomials only). The following binary digits of (optional) 
 3740 flag are significant 1: partial reduction, 2: gives also elements.
 3741 
 3742 
 3743   ***   at top-level: smith()
 3744   ***                 ^-------
 3745   ***   not a function in function call
 3746 A function with that name existed in GP-1.39.15. Please update your script.
 3747 
 3748 New syntax: smith(x) ===> matsnf(x)
 3749 
 3750 matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix 
 3751 X, expressed as a vector d; X must have integer or polynomial entries. Binary 
 3752 digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the 
 3753 diagonal d is returned, 4: removes all information corresponding to entries 
 3754 equal to 1 in d.
 3755 
 3756 
 3757   ***   at top-level: smith2()
 3758   ***                 ^--------
 3759   ***   not a function in function call
 3760 A function with that name existed in GP-1.39.15. Please update your script.
 3761 
 3762 New syntax: smith2(x) ===> matsnf(x,1)
 3763 
 3764 matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix 
 3765 X, expressed as a vector d; X must have integer or polynomial entries. Binary 
 3766 digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the 
 3767 diagonal d is returned, 4: removes all information corresponding to entries 
 3768 equal to 1 in d.
 3769 
 3770 
 3771   ***   at top-level: smithclean()
 3772   ***                 ^------------
 3773   ***   not a function in function call
 3774 A function with that name existed in GP-1.39.15. Please update your script.
 3775 
 3776 New syntax: smithclean(x) ===> matsnf(x,4)
 3777 
 3778 matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix 
 3779 X, expressed as a vector d; X must have integer or polynomial entries. Binary 
 3780 digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the 
 3781 diagonal d is returned, 4: removes all information corresponding to entries 
 3782 equal to 1 in d.
 3783 
 3784 
 3785   ***   at top-level: smithpol()
 3786   ***                 ^----------
 3787   ***   not a function in function call
 3788 A function with that name existed in GP-1.39.15. Please update your script.
 3789 
 3790 New syntax: smithpol(x) ===> matsnf(x,2)
 3791 
 3792 matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix 
 3793 X, expressed as a vector d; X must have integer or polynomial entries. Binary 
 3794 digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the 
 3795 diagonal d is returned, 4: removes all information corresponding to entries 
 3796 equal to 1 in d.
 3797 
 3798 
 3799   ***   at top-level: sort()
 3800   ***                 ^------
 3801   ***   not a function in function call
 3802 A function with that name existed in GP-1.39.15. Please update your script.
 3803 
 3804 New syntax: sort(x) ===> vecsort(x)
 3805 
 3806 vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in 
 3807 ascending order, according to the comparison function cmpf, if not omitted. (If 
 3808 cmpf is an integer k, sort according to the value of the k-th component of each 
 3809 entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return 
 3810 the permutation instead of the permuted vector, 4: use descending instead of 
 3811 ascending order, 8: remove duplicate entries.
 3812 
 3813 
 3814   ***   at top-level: sqred()
 3815   ***                 ^-------
 3816   ***   not a function in function call
 3817 A function with that name existed in GP-1.39.15. Please update your script.
 3818 
 3819 New syntax: sqred(x) ===> qfgaussred(x)
 3820 
 3821 qfgaussred(q): square reduction of the (symmetric) matrix q (returns a square 
 3822 matrix whose i-th diagonal term is the coefficient of the i-th square in which 
 3823 the coefficient of the i-th variable is 1).
 3824 
 3825 
 3826   ***   at top-level: srgcd()
 3827   ***                 ^-------
 3828   ***   not a function in function call
 3829 A function with that name existed in GP-1.39.15. Please update your script.
 3830 
 3831 New syntax: srgcd(x,y) ===> gcd(x,y,2)
 3832 
 3833 gcd(x,{y}): greatest common divisor of x and y.
 3834 
 3835 
 3836   ***   at top-level: sturm()
 3837   ***                 ^-------
 3838   ***   not a function in function call
 3839 A function with that name existed in GP-1.39.15. Please update your script.
 3840 
 3841 New syntax: sturm(x) ===> polsturm(x)
 3842 
 3843 polsturm(T,{ab}): number of distinct real roots of the polynomial T (in the 
 3844 interval ab = [a,b] if present).
 3845 
 3846 
 3847   ***   at top-level: sturmpart()
 3848   ***                 ^-----------
 3849   ***   not a function in function call
 3850 A function with that name existed in GP-1.39.15. Please update your script.
 3851 
 3852 New syntax: sturmpart(x,a,b) ===> polsturm(x,a,b)
 3853 
 3854 polsturm(T,{ab}): number of distinct real roots of the polynomial T (in the 
 3855 interval ab = [a,b] if present).
 3856 
 3857 
 3858   ***   at top-level: subcyclo()
 3859   ***                 ^----------
 3860   ***   not a function in function call
 3861 A function with that name existed in GP-1.39.15. Please update your script.
 3862 
 3863 New syntax: subcyclo(p,d) ===> polsubcyclo(p,d)
 3864 
 3865 polsubcyclo(n,d,{v='x}): finds an equation (in variable v) for the d-th degree 
 3866 subfields of Q(zeta_n). Output is a polynomial, or a vector of polynomials if 
 3867 there are several such fields or none.
 3868 
 3869 
 3870   ***   at top-level: subell()
 3871   ***                 ^--------
 3872   ***   not a function in function call
 3873 A function with that name existed in GP-1.39.15. Please update your script.
 3874 
 3875 New syntax: subell(e,a,b) ===> ellsub(e,a,b)
 3876 
 3877 ellsub(E,z1,z2): difference of the points z1 and z2 on elliptic curve E.
 3878 
 3879 
 3880   ***   at top-level: sumalt2()
 3881   ***                 ^---------
 3882   ***   not a function in function call
 3883 A function with that name existed in GP-1.39.15. Please update your script.
 3884 
 3885 New syntax: sumalt2(X=a,expr) ===> sumalt(X=a,expr,1)
 3886 
 3887 sumalt(X=a,expr,{flag=0}): Cohen-Villegas-Zagier's acceleration of alternating 
 3888 series expr, X starting at a. flag is optional, and can be 0: default, or 1: 
 3889 uses a slightly different method using Zagier's polynomials.
 3890 
 3891 
 3892   ***   at top-level: sumpos2()
 3893   ***                 ^---------
 3894   ***   not a function in function call
 3895 A function with that name existed in GP-1.39.15. Please update your script.
 3896 
 3897 New syntax: sumpos2(X=a,expr) ===> sumpos(X=a,expr,1)
 3898 
 3899 sumpos(X=a,expr,{flag=0}): sum of positive (or negative) series expr, the 
 3900 formal variable X starting at a. flag is optional, and can be 0: default, or 1: 
 3901 uses a slightly different method using Zagier's polynomials.
 3902 
 3903 
 3904   ***   at top-level: supplement()
 3905   ***                 ^------------
 3906   ***   not a function in function call
 3907 A function with that name existed in GP-1.39.15. Please update your script.
 3908 
 3909 New syntax: supplement(x) ===> matsupplement(x)
 3910 
 3911 matsupplement(x): supplement the columns of the matrix x to an invertible 
 3912 matrix.
 3913 
 3914 
 3915   ***   at top-level: sylvestermatrix()
 3916   ***                 ^-----------------
 3917   ***   not a function in function call
 3918 A function with that name existed in GP-1.39.15. Please update your script.
 3919 
 3920 New syntax: sylvestermatrix(x,y) ===> polsylvestermatrix(x,y)
 3921 
 3922 polsylvestermatrix(x,y): forms the sylvester matrix attached to the two 
 3923 polynomials x and y. Warning: the polynomial coefficients are in columns, not 
 3924 in rows.
 3925 
 3926 
 3927   ***   at top-level: taniyama()
 3928   ***                 ^----------
 3929   ***   not a function in function call
 3930 A function with that name existed in GP-1.39.15. Please update your script.
 3931 
 3932 New syntax: taniyama(e) ===> elltaniyama(e)
 3933 
 3934 elltaniyama(E, {n = seriesprecision}): modular parametrization of elliptic 
 3935 curve E/Q.
 3936 
 3937 
 3938   ***   at top-level: tchebi()
 3939   ***                 ^--------
 3940   ***   not a function in function call
 3941 A function with that name existed in GP-1.39.15. Please update your script.
 3942 
 3943 New syntax: tchebi(n) ===> polchebyshev(n)
 3944 
 3945 polchebyshev(n,{flag=1},{a='x}): Chebyshev polynomial of the first (flag = 1) 
 3946 or second (flag = 2) kind, of degree n, evaluated at a.
 3947 
 3948 
 3949   ***   at top-level: teich()
 3950   ***                 ^-------
 3951   ***   not a function in function call
 3952 A function with that name existed in GP-1.39.15. Please update your script.
 3953 
 3954 New syntax: teich(x) ===> teichmuller(x)
 3955 
 3956 teichmuller(x,{tab}): Teichmuller character of p-adic number x. If x = [p,n], 
 3957 return the lifts of all teichmuller(i + O(p^n)) for i = 1, ..., p-1. Such a 
 3958 vector can be fed back to teichmuller, as the optional argument tab, to speed 
 3959 up later computations.
 3960 
 3961 
 3962   ***   at top-level: threetotwo()
 3963   ***                 ^------------
 3964   ***   not a function in function call
 3965 A function with that name existed in GP-1.39.15. Please update your script.
 3966 
 3967 This function no longer exists
 3968 
 3969 
 3970   ***   at top-level: threetotwo2()
 3971   ***                 ^-------------
 3972   ***   not a function in function call
 3973 A function with that name existed in GP-1.39.15. Please update your script.
 3974 
 3975 This function no longer exists
 3976 
 3977 
 3978   ***   at top-level: torsell()
 3979   ***                 ^---------
 3980   ***   not a function in function call
 3981 A function with that name existed in GP-1.39.15. Please update your script.
 3982 
 3983 New syntax: torsell(e) ===> elltors(e)
 3984 
 3985 elltors(E): torsion subgroup of elliptic curve E: order, structure, generators.
 3986 
 3987 
 3988   ***   at top-level: trans()
 3989   ***                 ^-------
 3990   ***   not a function in function call
 3991 A function with that name existed in GP-1.39.15. Please update your script.
 3992 
 3993 New syntax: trans(x) ===> mattranspose(x)
 3994 
 3995 mattranspose(x): x~ = transpose of x.
 3996 
 3997 
 3998   ***   at top-level: trunc()
 3999   ***                 ^-------
 4000   ***   not a function in function call
 4001 A function with that name existed in GP-1.39.15. Please update your script.
 4002 
 4003 New syntax: trunc(x) ===> truncate(x)
 4004 
 4005 truncate(x,{&e}): truncation of x; when x is a power series,take away the 
 4006 O(X^). If e is present, do not take into account loss of integer part 
 4007 precision, and set e = error estimate in bits.
 4008 
 4009 
 4010   ***   at top-level: tschirnhaus()
 4011   ***                 ^-------------
 4012   ***   not a function in function call
 4013 A function with that name existed in GP-1.39.15. Please update your script.
 4014 
 4015 New syntax: tschirnhaus(x) ===> poltschirnhaus(x)
 4016 
 4017 poltschirnhaus(x): random Tschirnhausen transformation of the polynomial x.
 4018 
 4019 
 4020   ***   at top-level: twototwo()
 4021   ***                 ^----------
 4022   ***   not a function in function call
 4023 A function with that name existed in GP-1.39.15. Please update your script.
 4024 
 4025 This function no longer exists
 4026 
 4027 
 4028   ***   at top-level: unit()
 4029   ***                 ^------
 4030   ***   not a function in function call
 4031 A function with that name existed in GP-1.39.15. Please update your script.
 4032 
 4033 New syntax: unit(x) ===> quadunit(x)
 4034 
 4035 quadunit(D,{v = 'w}): fundamental unit u of the quadratic field of discriminant 
 4036 D where D must be positive. If v is given, the variable name is used to display 
 4037 u, else 'w' is used.
 4038 
 4039 
 4040   ***   at top-level: vec()
 4041   ***                 ^-----
 4042   ***   not a function in function call
 4043 A function with that name existed in GP-1.39.15. Please update your script.
 4044 
 4045 New syntax: vec(x) ===> Vec(x)
 4046 
 4047 Vec(x, {n}): transforms the object x into a vector of dimension n.
 4048 
 4049 
 4050   ***   at top-level: vecindexsort()
 4051   ***                 ^--------------
 4052   ***   not a function in function call
 4053 A function with that name existed in GP-1.39.15. Please update your script.
 4054 
 4055 New syntax: vecindexsort(x) ===> vecsort(x,,1)
 4056 
 4057 vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in 
 4058 ascending order, according to the comparison function cmpf, if not omitted. (If 
 4059 cmpf is an integer k, sort according to the value of the k-th component of each 
 4060 entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return 
 4061 the permutation instead of the permuted vector, 4: use descending instead of 
 4062 ascending order, 8: remove duplicate entries.
 4063 
 4064 
 4065   ***   at top-level: veclexsort()
 4066   ***                 ^------------
 4067   ***   not a function in function call
 4068 A function with that name existed in GP-1.39.15. Please update your script.
 4069 
 4070 New syntax: veclexsort(x) ===> vecsort(x,,2)
 4071 
 4072 vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in 
 4073 ascending order, according to the comparison function cmpf, if not omitted. (If 
 4074 cmpf is an integer k, sort according to the value of the k-th component of each 
 4075 entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return 
 4076 the permutation instead of the permuted vector, 4: use descending instead of 
 4077 ascending order, 8: remove duplicate entries.
 4078 
 4079 
 4080   ***   at top-level: vvector()
 4081   ***                 ^---------
 4082   ***   not a function in function call
 4083 A function with that name existed in GP-1.39.15. Please update your script.
 4084 
 4085 New syntax: vvector(n,X,expr) ===> vectorv(n,X,expr)
 4086 
 4087 vectorv(n,{X},{expr=0}): column vector with n components of expression expr (X 
 4088 ranges from 1 to n). By default, fill with 0s.
 4089 
 4090 
 4091   ***   at top-level: weipell()
 4092   ***                 ^---------
 4093   ***   not a function in function call
 4094 A function with that name existed in GP-1.39.15. Please update your script.
 4095 
 4096 New syntax: weipell(e) ===> ellwp(e)
 4097 
 4098 ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P function 
 4099 attached to the lattice w, as given by ellperiods. Optional flag means 0 
 4100 (default), compute only P(z), 1 compute [P(z),P'(z)].
 4101 
 4102 
 4103   ***   at top-level: wf()
 4104   ***                 ^----
 4105   ***   not a function in function call
 4106 A function with that name existed in GP-1.39.15. Please update your script.
 4107 
 4108 New syntax: wf(x) ===> weber(x)
 4109 
 4110 weber(x,{flag=0}): one of Weber's f function of x. flag is optional, and can be 
 4111 0: default, function f(x)=exp(-i*Pi/24)*eta((x+1)/2)/eta(x), 1: function 
 4112 f1(x)=eta(x/2)/eta(x) 2: function f2(x)=sqrt(2)*eta(2*x)/eta(x). Note that j = 
 4113 (f^24-16)^3/f^24 = (f1^24+16)^3/f1^24 = (f2^24+16)^3/f2^24.
 4114 
 4115 
 4116   ***   at top-level: wf2()
 4117   ***                 ^-----
 4118   ***   not a function in function call
 4119 A function with that name existed in GP-1.39.15. Please update your script.
 4120 
 4121 New syntax: wf2(x) ===> weber(x,2)
 4122 
 4123 weber(x,{flag=0}): one of Weber's f function of x. flag is optional, and can be 
 4124 0: default, function f(x)=exp(-i*Pi/24)*eta((x+1)/2)/eta(x), 1: function 
 4125 f1(x)=eta(x/2)/eta(x) 2: function f2(x)=sqrt(2)*eta(2*x)/eta(x). Note that j = 
 4126 (f^24-16)^3/f^24 = (f1^24+16)^3/f1^24 = (f2^24+16)^3/f2^24.
 4127 
 4128 
 4129   ***   at top-level: zell()
 4130   ***                 ^------
 4131   ***   not a function in function call
 4132 A function with that name existed in GP-1.39.15. Please update your script.
 4133 
 4134 New syntax: zell(e,P) ===> ellpointtoz(e,P)
 4135 
 4136 ellpointtoz(E,P): lattice point z corresponding to the point P on the elliptic 
 4137 curve E.
 4138 
 4139 
 4140   ***   at top-level: zideallog()
 4141   ***                 ^-----------
 4142   ***   not a function in function call
 4143 A function with that name existed in GP-1.39.15. Please update your script.
 4144 
 4145 New syntax: zideallog(nf,x,bid) ===> ideallog(nf,x,bid)
 4146 
 4147 ideallog({nf},x,bid): if bid is a big ideal, as given by idealstar(nf,D,...), 
 4148 gives the vector of exponents on the generators bid.gen (even if these 
 4149 generators have not been explicitly computed).
 4150 
 4151 
 4152   ***   at top-level: zidealstar()
 4153   ***                 ^------------
 4154   ***   not a function in function call
 4155 A function with that name existed in GP-1.39.15. Please update your script.
 4156 
 4157 New syntax: zidealstar(nf,I) ===> idealstar(nf,I)
 4158 
 4159 idealstar({nf},N,{flag=1},{cycmod}): gives the structure of (Z_K/N)^*, where N 
 4160 is a modulus (an ideal in any form or a vector [f0, foo], where f0 is an ideal 
 4161 and foo is a {0,1}-vector with r1 components. If the positive integer cycmod is 
 4162 present, only compute the group modulo cycmod-th powers. flag is optional, and 
 4163 can be 0: structure as an abelian group [h,d,g] where h is the order, d the 
 4164 orders of the cyclic factors and g the generators; if flag=1 (default), gives a 
 4165 bid structure used in ideallog to compute discrete logarithms; underlying 
 4166 generators are well-defined but not explicitly computed, which saves time; if 
 4167 flag=2, same as with flag=1 except that the generators are also given. If nf is 
 4168 omitted, N must be an integer and we return the structure of (Z/NZ)^*.
 4169 
 4170 
 4171   ***   at top-level: zidealstarinit()
 4172   ***                 ^----------------
 4173   ***   not a function in function call
 4174 A function with that name existed in GP-1.39.15. Please update your script.
 4175 
 4176 New syntax: zidealstarinit(nf,id) ===> idealstar(nf,id,1)
 4177 
 4178 idealstar({nf},N,{flag=1},{cycmod}): gives the structure of (Z_K/N)^*, where N 
 4179 is a modulus (an ideal in any form or a vector [f0, foo], where f0 is an ideal 
 4180 and foo is a {0,1}-vector with r1 components. If the positive integer cycmod is 
 4181 present, only compute the group modulo cycmod-th powers. flag is optional, and 
 4182 can be 0: structure as an abelian group [h,d,g] where h is the order, d the 
 4183 orders of the cyclic factors and g the generators; if flag=1 (default), gives a 
 4184 bid structure used in ideallog to compute discrete logarithms; underlying 
 4185 generators are well-defined but not explicitly computed, which saves time; if 
 4186 flag=2, same as with flag=1 except that the generators are also given. If nf is 
 4187 omitted, N must be an integer and we return the structure of (Z/NZ)^*.
 4188 
 4189 
 4190   ***   at top-level: zidealstarinitgen()
 4191   ***                 ^-------------------
 4192   ***   not a function in function call
 4193 A function with that name existed in GP-1.39.15. Please update your script.
 4194 
 4195 New syntax: zidealstarinitgen(nf,id) ===> idealstar(nf,id,2)
 4196 
 4197 idealstar({nf},N,{flag=1},{cycmod}): gives the structure of (Z_K/N)^*, where N 
 4198 is a modulus (an ideal in any form or a vector [f0, foo], where f0 is an ideal 
 4199 and foo is a {0,1}-vector with r1 components. If the positive integer cycmod is 
 4200 present, only compute the group modulo cycmod-th powers. flag is optional, and 
 4201 can be 0: structure as an abelian group [h,d,g] where h is the order, d the 
 4202 orders of the cyclic factors and g the generators; if flag=1 (default), gives a 
 4203 bid structure used in ideallog to compute discrete logarithms; underlying 
 4204 generators are well-defined but not explicitly computed, which saves time; if 
 4205 flag=2, same as with flag=1 except that the generators are also given. If nf is 
 4206 omitted, N must be an integer and we return the structure of (Z/NZ)^*.
 4207 
 4208 
 4209   ***   at top-level: box()
 4210   ***                 ^-----
 4211   ***   not a function in function call
 4212 A function with that name existed in GP-1.39.15. Please update your script.
 4213 
 4214 New syntax: box(x,a) ===> plotbox(x,a)
 4215 
 4216 plotbox(w,x2,y2,{filled=0}): if the cursor is at position (x1,y1), draw a box 
 4217 with diagonal (x1,y1) and (x2,y2) in rectwindow w (cursor does not move). If 
 4218 filled=1, fill the box.
 4219 
 4220 
 4221   ***   at top-level: color()
 4222   ***                 ^-------
 4223   ***   not a function in function call
 4224 A function with that name existed in GP-1.39.15. Please update your script.
 4225 
 4226 New syntax: color(w,c) ===> plotcolor(w,c)
 4227 
 4228 plotcolor(w,c): in rectwindow w, set default color to c. Possible values for c 
 4229 are [R,G,B] values, a color name or an index in the graphcolormap default: 
 4230 factory settings are 1=black, 2=blue, 3=sienna, 4=red, 5=green, 6=grey, 
 4231 7=gainsborough. Return [R,G,B] value attached to color.
 4232 
 4233 
 4234   ***   at top-level: cursor()
 4235   ***                 ^--------
 4236   ***   not a function in function call
 4237 A function with that name existed in GP-1.39.15. Please update your script.
 4238 
 4239 New syntax: cursor(w) ===> plotcursor(w)
 4240 
 4241 plotcursor(w): current position of cursor in rectwindow w.
 4242 
 4243 
 4244   ***   at top-level: draw()
 4245   ***                 ^------
 4246   ***   not a function in function call
 4247 A function with that name existed in GP-1.39.15. Please update your script.
 4248 
 4249 New syntax: draw(list) ===> plotdraw(list)
 4250 
 4251 plotdraw(w, {flag=0}): draw rectwindow w. More generally, w can be of the form 
 4252 [w1,x1,y1, w2,x2,y2,etc.]: draw rectwindows wi at given xi,yi positions. If 
 4253 flag!=0, the xi,yi express fractions of the size of the current output device.
 4254 
 4255 
 4256   ***   at top-level: initrect()
 4257   ***                 ^----------
 4258   ***   not a function in function call
 4259   ***   at top-level: killrect()
 4260   ***                 ^----------
 4261   ***   not a function in function call
 4262   ***   at top-level: line()
 4263   ***                 ^------
 4264   ***   not a function in function call
 4265 A function with that name existed in GP-1.39.15. Please update your script.
 4266 
 4267 New syntax: line(w,x2,y2) ===> plotlines(w,x2,y2)
 4268 
 4269 plotlines(w,X,Y,{flag=0}): draws an open polygon in rectwindow w where X and Y 
 4270 contain the x (resp. y) coordinates of the vertices. If X and Y are both single 
 4271 values (i.e not vectors), draw the corresponding line (and move cursor). If 
 4272 (optional) flag is nonzero, close the polygon.
 4273 
 4274 
 4275   ***   at top-level: lines()
 4276   ***                 ^-------
 4277   ***   not a function in function call
 4278 A function with that name existed in GP-1.39.15. Please update your script.
 4279 
 4280 New syntax: lines(w,x2,y2) ===> plotlines(w,x2,y2)
 4281 
 4282 plotlines(w,X,Y,{flag=0}): draws an open polygon in rectwindow w where X and Y 
 4283 contain the x (resp. y) coordinates of the vertices. If X and Y are both single 
 4284 values (i.e not vectors), draw the corresponding line (and move cursor). If 
 4285 (optional) flag is nonzero, close the polygon.
 4286 
 4287 
 4288   ***   at top-level: move()
 4289   ***                 ^------
 4290   ***   not a function in function call
 4291 A function with that name existed in GP-1.39.15. Please update your script.
 4292 
 4293 New syntax: move(w,x,y) ===> plotmove(w,x,y)
 4294 
 4295 plotmove(w,x,y): move cursor to position x,y in rectwindow w.
 4296 
 4297 
 4298   ***   at top-level: ploth2()
 4299   ***                 ^--------
 4300   ***   not a function in function call
 4301 A function with that name existed in GP-1.39.15. Please update your script.
 4302 
 4303 New syntax: ploth2(X=a,b,expr) ===> ploth(X=a,b,expr,1)
 4304 
 4305 ploth(X=a,b,expr,{flag=0},{n=0}): plot of expression expr, X goes from a to b 
 4306 in high resolution. Both flag and n are optional. Binary digits of flag mean: 
 4307 1=Parametric, 2=Recursive, 4=no_Rescale, 8=no_X_axis, 16=no_Y_axis, 
 4308 32=no_Frame, 64=no_Lines (do not join points), 128=Points_too (plot both lines 
 4309 and points), 256=Splines (use cubic splines), 512=no_X_ticks, 1024= no_Y_ticks, 
 4310 2048=Same_ticks (plot all ticks with the same length), 4096=Complex (the two 
 4311 coordinates of each point are encoded as a complex number). n specifies number 
 4312 of reference points on the graph (0=use default value). Returns a vector for 
 4313 the bounding box.
 4314 
 4315 
 4316   ***   at top-level: plothmult()
 4317   ***                 ^-----------
 4318   ***   not a function in function call
 4319 A function with that name existed in GP-1.39.15. Please update your script.
 4320 
 4321 New syntax: plothmult(X=a,b,expr) ===> ploth(X=a,b,expr)
 4322 
 4323 ploth(X=a,b,expr,{flag=0},{n=0}): plot of expression expr, X goes from a to b 
 4324 in high resolution. Both flag and n are optional. Binary digits of flag mean: 
 4325 1=Parametric, 2=Recursive, 4=no_Rescale, 8=no_X_axis, 16=no_Y_axis, 
 4326 32=no_Frame, 64=no_Lines (do not join points), 128=Points_too (plot both lines 
 4327 and points), 256=Splines (use cubic splines), 512=no_X_ticks, 1024= no_Y_ticks, 
 4328 2048=Same_ticks (plot all ticks with the same length), 4096=Complex (the two 
 4329 coordinates of each point are encoded as a complex number). n specifies number 
 4330 of reference points on the graph (0=use default value). Returns a vector for 
 4331 the bounding box.
 4332 
 4333 
 4334   ***   at top-level: point()
 4335   ***                 ^-------
 4336   ***   not a function in function call
 4337 A function with that name existed in GP-1.39.15. Please update your script.
 4338 
 4339 New syntax: point(w,x,y) ===> plotpoints(w,x,y)
 4340 
 4341 plotpoints(w,X,Y): draws in rectwindow w the points whose x (resp y) 
 4342 coordinates are in X (resp Y). If X and Y are both single values (i.e not 
 4343 vectors), draw the corresponding point (and move cursor).
 4344 
 4345 
 4346   ***   at top-level: points()
 4347   ***                 ^--------
 4348   ***   not a function in function call
 4349 A function with that name existed in GP-1.39.15. Please update your script.
 4350 
 4351 New syntax: points(w,x,y) ===> plotpoints(w,x,y)
 4352 
 4353 plotpoints(w,X,Y): draws in rectwindow w the points whose x (resp y) 
 4354 coordinates are in X (resp Y). If X and Y are both single values (i.e not 
 4355 vectors), draw the corresponding point (and move cursor).
 4356 
 4357 
 4358   ***   at top-level: postdraw()
 4359   ***                 ^----------
 4360   ***   not a function in function call
 4361   ***   at top-level: postploth()
 4362   ***                 ^-----------
 4363   ***   not a function in function call
 4364   ***   at top-level: postploth2()
 4365   ***                 ^------------
 4366   ***   not a function in function call
 4367 A function with that name existed in GP-1.39.15. Please update your script.
 4368 
 4369 New syntax: postploth2(X=a,b,expr) ===> psploth(X=a,b,expr,1)
 4370 
 4371 psploth(X=a,b,expr,{flags=0},{n=0}): obsolete function.
 4372 
 4373 
 4374   ***   at top-level: postplothraw()
 4375   ***                 ^--------------
 4376   ***   not a function in function call
 4377   ***   at top-level: pprint()
 4378   ***                 ^--------
 4379   ***   not a function in function call
 4380 A function with that name existed in GP-1.39.15. Please update your script.
 4381 
 4382 This function no longer exists
 4383 
 4384 
 4385   ***   at top-level: pprint1()
 4386   ***                 ^---------
 4387   ***   not a function in function call
 4388 A function with that name existed in GP-1.39.15. Please update your script.
 4389 
 4390 This function no longer exists
 4391 
 4392 
 4393 
 4394   ***   at top-level: rbox()
 4395   ***                 ^------
 4396   ***   not a function in function call
 4397 A function with that name existed in GP-1.39.15. Please update your script.
 4398 
 4399 New syntax: rbox(w,dx,dy) ===> plotrbox(w,dx,dy)
 4400 
 4401 plotrbox(w,dx,dy,{filled}): if the cursor is at (x1,y1), draw a box with 
 4402 diagonal (x1,y1)-(x1+dx,y1+dy) in rectwindow w (cursor does not move). If 
 4403 filled=1, fill the box.
 4404 
 4405 
 4406   ***   at top-level: read()
 4407   ***                 ^------
 4408   *** read: You never gave me anything to read!.
 4409   ***   at top-level: rline()
 4410   ***                 ^-------
 4411   ***   not a function in function call
 4412 A function with that name existed in GP-1.39.15. Please update your script.
 4413 
 4414 New syntax: rline(w,dx,dy) ===> plotrline(w,dx,dy)
 4415 
 4416 plotrline(w,dx,dy): if the cursor is at (x1,y1), draw a line from (x1,y1) to 
 4417 (x1+dx,y1+dy) (and move the cursor) in the rectwindow w.
 4418 
 4419 
 4420   ***   at top-level: rlines()
 4421   ***                 ^--------
 4422   ***   not a function in function call
 4423 A function with that name existed in GP-1.39.15. Please update your script.
 4424 
 4425   ***   at top-level: rlines()
 4426   ***                 ^--------
 4427   ***   bug in whatnow, please report.
 4428   ***   at top-level: rmove()
 4429   ***                 ^-------
 4430   ***   not a function in function call
 4431 A function with that name existed in GP-1.39.15. Please update your script.
 4432 
 4433 New syntax: rmove(w,dx,dy) ===> plotrmove(w,dx,dy)
 4434 
 4435 plotrmove(w,dx,dy): move cursor to position (dx,dy) relative to the present 
 4436 position in the rectwindow w.
 4437 
 4438 
 4439   ***   at top-level: rpoint()
 4440   ***                 ^--------
 4441   ***   not a function in function call
 4442 A function with that name existed in GP-1.39.15. Please update your script.
 4443 
 4444 New syntax: rpoint(w,dx,dy) ===> plotrpoint(w,dx,dy)
 4445 
 4446 plotrpoint(w,dx,dy): draw a point (and move cursor) at position dx,dy relative 
 4447 to present position of the cursor in rectwindow w.
 4448 
 4449 
 4450   ***   at top-level: rpoints()
 4451   ***                 ^---------
 4452   ***   not a function in function call
 4453 A function with that name existed in GP-1.39.15. Please update your script.
 4454 
 4455   ***   at top-level: rpoints()
 4456   ***                 ^---------
 4457   ***   bug in whatnow, please report.
 4458   ***   at top-level: scale()
 4459   ***                 ^-------
 4460   ***   not a function in function call
 4461 A function with that name existed in GP-1.39.15. Please update your script.
 4462 
 4463 New syntax: scale(w,x1,x2,y1,y2) ===> plotscale(w,x1,x2,y1,y2)
 4464 
 4465 plotscale(w,x1,x2,y1,y2): scale the coordinates in rectwindow w so that x goes 
 4466 from x1 to x2 and y from y1 to y2 (y2<y1 is allowed).
 4467 
 4468 
 4469   ***   at top-level: setprecision()
 4470   ***                 ^--------------
 4471   ***   not a function in function call
 4472 A function with that name existed in GP-1.39.15. Please update your script.
 4473 
 4474 New syntax: setprecision(n) ===> default(realprecision,n)
 4475 
 4476 default({key},{val}): returns the current value of the default key. If val is 
 4477 present, set opt to val first. If no argument is given, print a list of all 
 4478 defaults as well as their values.
 4479 
 4480 
 4481   ***   at top-level: setserieslength()
 4482   ***                 ^-----------------
 4483   ***   not a function in function call
 4484 A function with that name existed in GP-1.39.15. Please update your script.
 4485 
 4486 New syntax: setserieslength(n) ===> default(seriesprecision,n)
 4487 
 4488 default({key},{val}): returns the current value of the default key. If val is 
 4489 present, set opt to val first. If no argument is given, print a list of all 
 4490 defaults as well as their values.
 4491 
 4492 
 4493   ***   at top-level: settype()
 4494   ***                 ^---------
 4495   ***   not a function in function call
 4496 A function with that name existed in GP-1.39.15. Please update your script.
 4497 
 4498 New syntax: settype(x,t) ===> type(x,t)
 4499 
 4500 type(x): return the type of the GEN x.
 4501 
 4502 
 4503   ***   at top-level: string()
 4504   ***                 ^--------
 4505   ***   not a function in function call
 4506 A function with that name existed in GP-1.39.15. Please update your script.
 4507 
 4508 New syntax: string(w,x) ===> plotstring(w,x)
 4509 
 4510 plotstring(w,x,{flags=0}): draw in rectwindow w the string corresponding to x. 
 4511 Bits 1 and 2 of flag regulate horizontal alignment: left if 0, right if 2, 
 4512 center if 1. Bits 4 and 8 regulate vertical alignment: bottom if 0, top if 8, 
 4513 v-center if 4. Can insert additional gap between point and string: horizontal 
 4514 if bit 16 is set, vertical if bit 32 is set.
 4515 
 4516 
 4517   ***   at top-level: texprint()
 4518   ***                 ^----------
 4519   ***   not a function in function call
 4520 A function with that name existed in GP-1.39.15. Please update your script.
 4521 
 4522 New syntax: texprint(x) ===> printtex(x)
 4523 
 4524 printtex({str}*): outputs its string arguments in TeX format.
 4525 
 4526 
 4527 Total time spent: 2