Difference between revisions of "ApCoCoA-1:Weyl.WStandardForm"
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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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| + | {{Version|1}} | ||
<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 -------------------------------
