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>
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<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.
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<em>Note:</em> All polynomials that are not in normal form should be first converted into normal form using <ref>ApCoCoA-1:Weyl.WNormalForm|Weyl.WNormalForm</ref>, otherwise you may get unexpected results.
  
 
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     <seealso>
 
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       <see>Weyl.WNormalForm</see>
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       <see>ApCoCoA-1:Weyl.WNormalForm|Weyl.WNormalForm</see>
 
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     <key>wspoly</key>
 
     <key>wspoly</key>
     <wiki-category>Package_weyl</wiki-category>
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     <wiki-category>ApCoCoA-1:Package_weyl</wiki-category>
 
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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

Weyl.WNormalForm