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   42         <a href="jas-module.html">Module&nbsp;jas</a> ::
   43         Class&nbsp;SeriesRing
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   59 <!-- ==================== CLASS DESCRIPTION ==================== -->
   60 <h1 class="epydoc">Class SeriesRing</h1><p class="nomargin-top"><span class="codelink"><a href="jas-pysrc.html#SeriesRing">source&nbsp;code</a></span></p>
   61 <p>Represents a JAS power series ring: UnivPowerSeriesRing.</p>
   62   <p>Methods for univariate power series arithmetic.</p>
   63 
   64 <!-- ==================== INSTANCE METHODS ==================== -->
   65 <a name="section-InstanceMethods"></a>
   66 <table class="summary" border="1" cellpadding="3"
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   76          >hide private</a>]</span></td>
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   80 </tr>
   81 <tr>
   82     <td width="15%" align="right" valign="top" class="summary">
   83       <span class="summary-type">&nbsp;</span>
   84     </td><td class="summary">
   85       <table width="100%" cellpadding="0" cellspacing="0" border="0">
   86         <tr>
   87           <td><span class="summary-sig"><a name="__init__"></a><span class="summary-sig-name">__init__</span>(<span class="summary-sig-arg">self</span>,
   88         <span class="summary-sig-arg">ringstr</span>=<span class="summary-sig-default">&quot;&quot;</span>,
   89         <span class="summary-sig-arg">truncate</span>=<span class="summary-sig-default">None</span>,
   90         <span class="summary-sig-arg">ring</span>=<span class="summary-sig-default">None</span>,
   91         <span class="summary-sig-arg">cofac</span>=<span class="summary-sig-default">None</span>,
   92         <span class="summary-sig-arg">name</span>=<span class="summary-sig-default">&quot;z&quot;</span>)</span><br />
   93       Ring constructor.</td>
   94           <td align="right" valign="top">
   95             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.__init__">source&nbsp;code</a></span>
   96             
   97           </td>
   98         </tr>
   99       </table>
  100       
  101     </td>
  102   </tr>
  103 <tr>
  104     <td width="15%" align="right" valign="top" class="summary">
  105       <span class="summary-type">&nbsp;</span>
  106     </td><td class="summary">
  107       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  108         <tr>
  109           <td><span class="summary-sig"><a name="__str__"></a><span class="summary-sig-name">__str__</span>(<span class="summary-sig-arg">self</span>)</span><br />
  110       Create a string representation.</td>
  111           <td align="right" valign="top">
  112             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.__str__">source&nbsp;code</a></span>
  113             
  114           </td>
  115         </tr>
  116       </table>
  117       
  118     </td>
  119   </tr>
  120 <tr>
  121     <td width="15%" align="right" valign="top" class="summary">
  122       <span class="summary-type">&nbsp;</span>
  123     </td><td class="summary">
  124       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  125         <tr>
  126           <td><span class="summary-sig"><a name="gens"></a><span class="summary-sig-name">gens</span>(<span class="summary-sig-arg">self</span>)</span><br />
  127       Get the generators of the power series ring.</td>
  128           <td align="right" valign="top">
  129             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.gens">source&nbsp;code</a></span>
  130             
  131           </td>
  132         </tr>
  133       </table>
  134       
  135     </td>
  136   </tr>
  137 <tr>
  138     <td width="15%" align="right" valign="top" class="summary">
  139       <span class="summary-type">&nbsp;</span>
  140     </td><td class="summary">
  141       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  142         <tr>
  143           <td><span class="summary-sig"><a name="inject_variables"></a><span class="summary-sig-name">inject_variables</span>(<span class="summary-sig-arg">self</span>)</span><br />
  144       Inject generators as variables into the main global namespace</td>
  145           <td align="right" valign="top">
  146             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.inject_variables">source&nbsp;code</a></span>
  147             
  148           </td>
  149         </tr>
  150       </table>
  151       
  152     </td>
  153   </tr>
  154 <tr>
  155     <td width="15%" align="right" valign="top" class="summary">
  156       <span class="summary-type">&nbsp;</span>
  157     </td><td class="summary">
  158       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  159         <tr>
  160           <td><span class="summary-sig"><a name="one"></a><span class="summary-sig-name">one</span>(<span class="summary-sig-arg">self</span>)</span><br />
  161       Get the one of the power series ring.</td>
  162           <td align="right" valign="top">
  163             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.one">source&nbsp;code</a></span>
  164             
  165           </td>
  166         </tr>
  167       </table>
  168       
  169     </td>
  170   </tr>
  171 <tr>
  172     <td width="15%" align="right" valign="top" class="summary">
  173       <span class="summary-type">&nbsp;</span>
  174     </td><td class="summary">
  175       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  176         <tr>
  177           <td><span class="summary-sig"><a name="zero"></a><span class="summary-sig-name">zero</span>(<span class="summary-sig-arg">self</span>)</span><br />
  178       Get the zero of the power series ring.</td>
  179           <td align="right" valign="top">
  180             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.zero">source&nbsp;code</a></span>
  181             
  182           </td>
  183         </tr>
  184       </table>
  185       
  186     </td>
  187   </tr>
  188 <tr>
  189     <td width="15%" align="right" valign="top" class="summary">
  190       <span class="summary-type">&nbsp;</span>
  191     </td><td class="summary">
  192       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  193         <tr>
  194           <td><span class="summary-sig"><a name="random"></a><span class="summary-sig-name">random</span>(<span class="summary-sig-arg">self</span>,
  195         <span class="summary-sig-arg">n</span>)</span><br />
  196       Get a random power series.</td>
  197           <td align="right" valign="top">
  198             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.random">source&nbsp;code</a></span>
  199             
  200           </td>
  201         </tr>
  202       </table>
  203       
  204     </td>
  205   </tr>
  206 <tr>
  207     <td width="15%" align="right" valign="top" class="summary">
  208       <span class="summary-type">&nbsp;</span>
  209     </td><td class="summary">
  210       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  211         <tr>
  212           <td><span class="summary-sig"><a name="exp"></a><span class="summary-sig-name">exp</span>(<span class="summary-sig-arg">self</span>)</span><br />
  213       Get the exponential power series.</td>
  214           <td align="right" valign="top">
  215             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.exp">source&nbsp;code</a></span>
  216             
  217           </td>
  218         </tr>
  219       </table>
  220       
  221     </td>
  222   </tr>
  223 <tr>
  224     <td width="15%" align="right" valign="top" class="summary">
  225       <span class="summary-type">&nbsp;</span>
  226     </td><td class="summary">
  227       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  228         <tr>
  229           <td><span class="summary-sig"><a name="sin"></a><span class="summary-sig-name">sin</span>(<span class="summary-sig-arg">self</span>)</span><br />
  230       Get the sinus power series.</td>
  231           <td align="right" valign="top">
  232             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.sin">source&nbsp;code</a></span>
  233             
  234           </td>
  235         </tr>
  236       </table>
  237       
  238     </td>
  239   </tr>
  240 <tr>
  241     <td width="15%" align="right" valign="top" class="summary">
  242       <span class="summary-type">&nbsp;</span>
  243     </td><td class="summary">
  244       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  245         <tr>
  246           <td><span class="summary-sig"><a name="cos"></a><span class="summary-sig-name">cos</span>(<span class="summary-sig-arg">self</span>)</span><br />
  247       Get the cosinus power series.</td>
  248           <td align="right" valign="top">
  249             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.cos">source&nbsp;code</a></span>
  250             
  251           </td>
  252         </tr>
  253       </table>
  254       
  255     </td>
  256   </tr>
  257 <tr>
  258     <td width="15%" align="right" valign="top" class="summary">
  259       <span class="summary-type">&nbsp;</span>
  260     </td><td class="summary">
  261       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  262         <tr>
  263           <td><span class="summary-sig"><a name="tan"></a><span class="summary-sig-name">tan</span>(<span class="summary-sig-arg">self</span>)</span><br />
  264       Get the tangens power series.</td>
  265           <td align="right" valign="top">
  266             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.tan">source&nbsp;code</a></span>
  267             
  268           </td>
  269         </tr>
  270       </table>
  271       
  272     </td>
  273   </tr>
  274 <tr>
  275     <td width="15%" align="right" valign="top" class="summary">
  276       <span class="summary-type">&nbsp;</span>
  277     </td><td class="summary">
  278       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  279         <tr>
  280           <td><span class="summary-sig"><a href="jas.SeriesRing-class.html#create" class="summary-sig-name">create</a>(<span class="summary-sig-arg">self</span>,
  281         <span class="summary-sig-arg">ifunc</span>=<span class="summary-sig-default">None</span>,
  282         <span class="summary-sig-arg">jfunc</span>=<span class="summary-sig-default">None</span>,
  283         <span class="summary-sig-arg">clazz</span>=<span class="summary-sig-default">None</span>)</span><br />
  284       Create a power series with given generating function.</td>
  285           <td align="right" valign="top">
  286             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.create">source&nbsp;code</a></span>
  287             
  288           </td>
  289         </tr>
  290       </table>
  291       
  292     </td>
  293   </tr>
  294 <tr>
  295     <td width="15%" align="right" valign="top" class="summary">
  296       <span class="summary-type">&nbsp;</span>
  297     </td><td class="summary">
  298       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  299         <tr>
  300           <td><span class="summary-sig"><a href="jas.SeriesRing-class.html#fixPoint" class="summary-sig-name">fixPoint</a>(<span class="summary-sig-arg">self</span>,
  301         <span class="summary-sig-arg">psmap</span>)</span><br />
  302       Create a power series as fixed point of the given mapping.</td>
  303           <td align="right" valign="top">
  304             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.fixPoint">source&nbsp;code</a></span>
  305             
  306           </td>
  307         </tr>
  308       </table>
  309       
  310     </td>
  311   </tr>
  312 <tr>
  313     <td width="15%" align="right" valign="top" class="summary">
  314       <span class="summary-type">&nbsp;</span>
  315     </td><td class="summary">
  316       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  317         <tr>
  318           <td><span class="summary-sig"><a name="gcd"></a><span class="summary-sig-name">gcd</span>(<span class="summary-sig-arg">self</span>,
  319         <span class="summary-sig-arg">a</span>,
  320         <span class="summary-sig-arg">b</span>)</span><br />
  321       Compute the greatest common divisor of a and b.</td>
  322           <td align="right" valign="top">
  323             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.gcd">source&nbsp;code</a></span>
  324             
  325           </td>
  326         </tr>
  327       </table>
  328       
  329     </td>
  330   </tr>
  331 <tr>
  332     <td width="15%" align="right" valign="top" class="summary">
  333       <span class="summary-type">&nbsp;</span>
  334     </td><td class="summary">
  335       <table width="100%" cellpadding="0" cellspacing="0" border="0">
  336         <tr>
  337           <td><span class="summary-sig"><a name="fromPoly"></a><span class="summary-sig-name">fromPoly</span>(<span class="summary-sig-arg">self</span>,
  338         <span class="summary-sig-arg">a</span>)</span><br />
  339       Convert a GenPolynomial to a power series.</td>
  340           <td align="right" valign="top">
  341             <span class="codelink"><a href="jas-pysrc.html#SeriesRing.fromPoly">source&nbsp;code</a></span>
  342             
  343           </td>
  344         </tr>
  345       </table>
  346       
  347     </td>
  348   </tr>
  349 </table>
  350 <!-- ==================== METHOD DETAILS ==================== -->
  351 <a name="section-MethodDetails"></a>
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  361          class="privatelink" onclick="toggle_private();"
  362          >hide private</a>]</span></td>
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  368 <a name="create"></a>
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  375   <h3 class="epydoc"><span class="sig"><span class="sig-name">create</span>(<span class="sig-arg">self</span>,
  376         <span class="sig-arg">ifunc</span>=<span class="sig-default">None</span>,
  377         <span class="sig-arg">jfunc</span>=<span class="sig-default">None</span>,
  378         <span class="sig-arg">clazz</span>=<span class="sig-default">None</span>)</span>
  379   </h3>
  380   </td><td align="right" valign="top"
  381     ><span class="codelink"><a href="jas-pysrc.html#SeriesRing.create">source&nbsp;code</a></span>&nbsp;
  382     </td>
  383   </tr></table>
  384   
  385   <p>Create a power series with given generating function.</p>
  386   <p>ifunc(int i) must return a value which is used in 
  387   RingFactory.fromInteger(). jfunc(int i) must return a value of type 
  388   ring.coFac. clazz must implement the Coefficients abstract class.</p>
  389   <dl class="fields">
  390   </dl>
  391 </td></tr></table>
  392 </div>
  393 <a name="fixPoint"></a>
  394 <div>
  395 <table class="details" border="1" cellpadding="3"
  396        cellspacing="0" width="100%" bgcolor="white">
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  398   <table width="100%" cellpadding="0" cellspacing="0" border="0">
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  400   <h3 class="epydoc"><span class="sig"><span class="sig-name">fixPoint</span>(<span class="sig-arg">self</span>,
  401         <span class="sig-arg">psmap</span>)</span>
  402   </h3>
  403   </td><td align="right" valign="top"
  404     ><span class="codelink"><a href="jas-pysrc.html#SeriesRing.fixPoint">source&nbsp;code</a></span>&nbsp;
  405     </td>
  406   </tr></table>
  407   
  408   <p>Create a power series as fixed point of the given mapping.</p>
  409   <p>psmap must implement the UnivPowerSeriesMap interface.</p>
  410   <dl class="fields">
  411   </dl>
  412 </td></tr></table>
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