ApCoCoA-1:Weyl.WSPoly: Difference between revisions
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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.</short_description> | ||
<syntax> | <syntax> | ||
Weyl.WSPoly(F:POLY,G:POLY):POLY | Weyl.WSPoly(F:POLY,G:POLY):POLY | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
Computes the S-polynomial of F and G. | |||
<itemize> | |||
<item>@param <em>F</em> A Weyl polynomial in normal form.</item> | |||
<item>@param <em>G</em> A Weyl polynomial in normal form.</item> | |||
<item>@result The S-polynomial of F and G.</item> | |||
</itemize> | |||
<em>Note:</em> All polynomials that are not in normal form should be first converted in to normal form using <ref>Weyl.WNormalForm</ref>, otherwise you may get unexpected results. | |||
<example> | <example> | ||
W3::=ZZ/(7)[x[1..3],d[1..3]]; | W3::=ZZ/(7)[x[1..3],d[1..3]]; | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
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<types> | <types> | ||
<type>cocoaserver</type> | <type>cocoaserver</type> | ||
<type>poly</type> | |||
</types> | </types> | ||
<key>weyl.wspoly</key> | <key>weyl.wspoly</key> | ||
<key>wspoly</key> | |||
<wiki-category>Package_weyl</wiki-category> | <wiki-category>Package_weyl</wiki-category> | ||
</command> | </command> | ||
Revision as of 13:10, 23 April 2009
Weyl.WSPoly
Computes S-polynomial.
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 in to 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
