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

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

<short_description>Computes the S-polynomial of two Weyl polynomials.</short_description> | <short_description>Computes the S-polynomial of two Weyl polynomials.</short_description> |

## Latest revision as of 10:40, 7 October 2020

This article is about a function from ApCoCoA-1. |

## Weyl.WSPoly

Computes the S-polynomial of two 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