Difference between revisions of "ApCoCoA-1:Weyl.WStandardForm"

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{{Version|1}}
 
<command>
 
<command>
     <title>Weyl.WeylNormalForm</title>
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     <title>Weyl.WStandardForm</title>
     <short_description>Computes the Normal form of a Weyl polynomial.
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     <short_description>Computes the Standard form of a Weyl polynomial.</short_description>
</short_description>
 
 
<syntax>
 
<syntax>
Weyl.WeylNormalForm(L:List):POLY
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Weyl.WStandardForm(L:List):POLY
 
</syntax>
 
</syntax>
 
<description>
 
<description>
Input <em>L</em> is a list of lists where each list represents a monomial of a Weyl polynomial. The result is a Weyl polynomial in Normal form.
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<itemize>
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<item>@param <em>L</em> A list of lists where each list represents a monomial of a Weyl polynomial.</item>
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<item>@result The result is a Weyl polynomial in standard form.</item>
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</itemize>
  
 
<example>
 
<example>
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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.WeylNormalForm(L);
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Weyl.WStandardForm(L);
  
 
-------------------------------
 
-------------------------------
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Use W3;
 
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]];
 
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.WNormalForm(L2);
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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[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
 
3x[1]x[2]d[2] + 2d[1]d[2]d[3] - 3x[1] + 3
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</example>
 
</example>
 
</description>
 
</description>
<wiki-category>Package_weyl</wiki-category>
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<key>Weyl.WStandardForm</key>
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<key>WStandardForm</key>
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<types>
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<type>polynomial</type>
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</types>
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<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
-------------------------------