Difference between revisions of "ApCoCoA-1:MatlabCoCoAModule"
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<table border="1"> | <table border="1"> | ||
<tr> | <tr> | ||
| − | <td> basering | + | <td> basering </td><td> A CoCoARing</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td> gens | + | <td> gens </td><td> an array of polynomials</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td> gBasis | + | <td> gBasis </td><td> the Groebner-Basis of a Module (Currently computation is not implemented)</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td> numBasisElements | + | <td> numBasisElements </td><td> The number of basis elements. If gBasis is not yet computed the number of generators is stored.</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td> numComponents | + | <td> numComponents </td><td> The number of components = size(Basis,2)</td> |
</tr> | </tr> | ||
</table> | </table> | ||
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<table border="1"> | <table border="1"> | ||
<tr> | <tr> | ||
| − | <td><b>Method</b> | + | <td><b>Method</b></td><td><b>Description</b></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td> display | + | <td> display</td><td> Is used by Matlab to print a CoCoAModule to the command window. E.g. when a command is not terminated by a ';'.</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td> get | + | <td> get</td><td> Returns the attributes of a module. Syntax: <br> |
| − | 'BaseRing': Returns the ring over which the polynomials in the generator list are defined. | + | get(moduleVar, 'Keyword'), where moduleVar is a CoCoAModule and 'Keyword' is one of the keywords:<br> |
| − | 'Gens': returns the generator array of CoCoAPoly's | + | 'BaseRing': Returns the ring over which the polynomials in the generator list are defined.<br> |
| − | 'GBasis': returns the GBasis of the Module if it has been computed. Otherwise [] is returned. | + | 'Gens': returns the generator array of CoCoAPoly's<br> |
| − | 'NumElements': Returns the number of basis elements. If gBasis is not yet computed the number of generators is returned. | + | 'GBasis': returns the GBasis of the Module if it has been computed. Otherwise [] is returned.<br> |
| − | 'NumComponents': Returns the number of components = size(Gens,2) | + | 'NumElements': Returns the number of basis elements. If gBasis is not yet computed the number of generators is returned.<br> |
| − | 'String': Returns the polynomial as a string. | + | 'NumComponents': Returns the number of components = size(Gens,2)<br> |
| + | 'String': Returns the polynomial as a string.<br> | ||
'Latex' will return a string using Latex syntax.</td> | 'Latex' will return a string using Latex syntax.</td> | ||
</tr> | </tr> | ||
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* Module generated by four polynomials. | * Module generated by four polynomials. | ||
<matlab> | <matlab> | ||
| − | p1 = CoCoAPoly( | + | p1 = CoCoAPoly('x^2-1'); |
| − | p2 = CoCoAPoly( | + | p2 = CoCoAPoly('y+x'); |
| − | p3 = CoCoAPoly( | + | p3 = CoCoAPoly('x^2y'); |
| − | p4 = CoCoAPoly( | + | p4 = CoCoAPoly('y'); |
myModule = CoCoAModule([p1 p2 ; p3 p4]); | myModule = CoCoAModule([p1 p2 ; p3 p4]); | ||
</matlab> | </matlab> | ||
[[Category:MatlabToolbox]] | [[Category:MatlabToolbox]] | ||
Latest revision as of 16:55, 19 June 2008
Introduction
The CoCoAModule class represents a module of polynomials over a given polynomial ring (See <a href="MatlabCoCoAPoly.html">Poly class</a>).
Constructor
The constructor for a CoCoAModule takes an array of polynomials. If no input is given the default module (1) over Q[x[1]] is returned Generators should be a MxN CoCoAPoly array.
Attributes
| basering | A CoCoARing |
| gens | an array of polynomials |
| gBasis | the Groebner-Basis of a Module (Currently computation is not implemented) |
| numBasisElements | The number of basis elements. If gBasis is not yet computed the number of generators is stored. |
| numComponents | The number of components = size(Basis,2) |
Methods
| Method | Description |
| display | Is used by Matlab to print a CoCoAModule to the command window. E.g. when a command is not terminated by a ';'. |
| get | Returns the attributes of a module. Syntax: get(moduleVar, 'Keyword'), where moduleVar is a CoCoAModule and 'Keyword' is one of the keywords: |
Examples
A collection of examples is provided in the file TestCoCoAModule.m. This file defines the function TestCoCoAModule which will run and display many examples. A few common examples are presented below.
- Module generated by four polynomials.
<matlab> p1 = CoCoAPoly('x^2-1'); p2 = CoCoAPoly('y+x'); p3 = CoCoAPoly('x^2y'); p4 = CoCoAPoly('y'); myModule = CoCoAModule([p1 p2 ; p3 p4]); </matlab>
