ApCoCoA-1:Weyl.WStandardForm: Difference between revisions
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New page: <command> <title>Weyl.WeylNormalForm</title> <short_description>Computes the Normal form of a Weyl polynomial. </short_description> <syntax> Weyl.WeylNormalForm(L:List):POLY </synt... |
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<command> | <command> | ||
<title>Weyl. | <title>Weyl.WStandardForm</title> | ||
<short_description>Computes the | <short_description>Computes the Standard form of a Weyl polynomial.</short_description> | ||
</short_description> | |||
<syntax> | <syntax> | ||
Weyl. | Weyl.WStandardForm(L:List):POLY | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
<itemize> | |||
<item>@param <em>L</em> A list of lists where each list represents a monomial of a Weyl polynomial.</item> | |||
<item>@result The result is a Weyl polynomial in standard form.</item> | |||
</itemize> | |||
<example> | <example> | ||
A2::=QQ[x[1..2],y[1..2]]; --Define | A2::=QQ[x[1..2],y[1..2]]; --Define appropriate ring | ||
Use A2; | Use A2; | ||
L:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3],[5]]; | L:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3],[5]]; | ||
Weyl. | Weyl.WStandardForm(L); | ||
------------------------------- | ------------------------------- | ||
-9x[1]^2x[2]^3y[2] - 27x[1]^2x[2]^2 + 2x[1]x[2]^2y[1] + 5 | -9x[1]^2x[2]^3y[2] - 27x[1]^2x[2]^2 + 2x[1]x[2]^2y[1] + 5 | ||
------------------------------- | |||
</example> | |||
<example> | |||
W3::=ZZ/(7)[x[1..3],d[1..3]]; | |||
Use W3; | |||
L2:=[[2d[1],d[2],d[3]],[3x[1],d[2],x[2]],[3d[3]^4,x[2]^3,x[3]^5],[5d[1]^3,x[1]^4],[3]]; | |||
Weyl.WStandardForm(L2); | |||
3x[2]^3x[3]^5d[3]^4 - 3x[2]^3x[3]^4d[3]^3 + 3x[2]^3x[3]^3d[3]^2 - 2x[1]^4d[1]^3 - x[2]^3x[3]^2d[3] - 3x[1]^3d[1]^2 + 3x[2]^3x[3] - 2x[1]^2d[1] + | |||
3x[1]x[2]d[2] + 2d[1]d[2]d[3] - 3x[1] + 3 | |||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<wiki-category> | |||
<key>Weyl.WStandardForm</key> | |||
<key>WStandardForm</key> | |||
<types> | |||
<type>polynomial</type> | |||
</types> | |||
<wiki-category>ApCoCoA-1:Package_weyl</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 10:40, 7 October 2020
| This article is about a function from ApCoCoA-1. |
Weyl.WStandardForm
Computes the Standard form of a Weyl polynomial.
Syntax
Weyl.WStandardForm(L:List):POLY
Description
@param L A list of lists where each list represents a monomial of a Weyl polynomial.
@result The result is a Weyl polynomial in standard form.
Example
A2::=QQ[x[1..2],y[1..2]]; --Define appropriate ring Use A2; L:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3],[5]]; Weyl.WStandardForm(L); ------------------------------- -9x[1]^2x[2]^3y[2] - 27x[1]^2x[2]^2 + 2x[1]x[2]^2y[1] + 5 -------------------------------
Example
W3::=ZZ/(7)[x[1..3],d[1..3]]; Use W3; L2:=[[2d[1],d[2],d[3]],[3x[1],d[2],x[2]],[3d[3]^4,x[2]^3,x[3]^5],[5d[1]^3,x[1]^4],[3]]; Weyl.WStandardForm(L2); 3x[2]^3x[3]^5d[3]^4 - 3x[2]^3x[3]^4d[3]^3 + 3x[2]^3x[3]^3d[3]^2 - 2x[1]^4d[1]^3 - x[2]^3x[3]^2d[3] - 3x[1]^3d[1]^2 + 3x[2]^3x[3] - 2x[1]^2d[1] + 3x[1]x[2]d[2] + 2d[1]d[2]d[3] - 3x[1] + 3 -------------------------------
