# Difference between revisions of "ApCoCoA-1:Weyl.WSPoly"

From ApCoCoAWiki

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<command> | <command> | ||

<title>Weyl.WSPoly</title> | <title>Weyl.WSPoly</title> | ||

− | <short_description>Computes S-polynomial.</short_description> | + | <short_description>Computes S-polynomial of Weyl polynomials.</short_description> |

<syntax> | <syntax> | ||

Weyl.WSPoly(F:POLY,G:POLY):POLY | Weyl.WSPoly(F:POLY,G:POLY):POLY | ||

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</itemize> | </itemize> | ||

− | <em>Note:</em> All polynomials that are not in normal form should be first converted | + | <em>Note:</em> All polynomials that are not in normal form should be first converted into normal form using <ref>Weyl.WNormalForm</ref>, otherwise you may get unexpected results. |

<example> | <example> |

## Revision as of 14:43, 28 April 2009

## Weyl.WSPoly

Computes S-polynomial of Weyl polynomials.

### Syntax

Weyl.WSPoly(F:POLY,G:POLY):POLY

### Description

Computes the S-polynomial of F and G.

@param

*F*A Weyl polynomial in normal form.@param

*G*A Weyl polynomial in normal form.@result The S-polynomial of F and G.

*Note:* All polynomials that are not in normal form should be first converted into normal form using Weyl.WNormalForm, otherwise you may get unexpected results.

#### Example

W3::=ZZ/(7)[x[1..3],d[1..3]]; Use W3; F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; F2:=-3x[2]d[2]^5d[3]^5+x[2]d[1]^3; F3:=-2d[1]^4d[2]^5-x[1]d[2]^7+x[3]^3d[3]^5; Weyl.WSPoly(F1,F2); x[2]d[1]^6 - 3x[2]^6 ------------------------------- Weyl.WSPoly(F2,F3); -3x[1]x[2]d[2]^7d[3]^5 + 3x[2]x[3]^3d[3]^10 + 3x[2]x[3]^2d[3]^9 - 2x[2]x[3]d[3]^8 - 2x[2]d[1]^7 - 2x[2]d[3]^7 ------------------------------- Weyl.WSPoly(F1,F3); -x[1]d[2]^7d[3]^5 + x[3]^3d[3]^10 + x[3]^2d[3]^9 - 3x[3]d[3]^8 - 3d[3]^7 - 2x[2]^5d[1] ------------------------------- Weyl.WSPoly(F3,F1); x[1]d[2]^7d[3]^5 - x[3]^3d[3]^10 - x[3]^2d[3]^9 + 3x[3]d[3]^8 + 3d[3]^7 + 2x[2]^5d[1] -------------------------------

### See also