Difference between revisions of "ApCoCoA-1:Weyl.WStandardForm"
From ApCoCoAWiki
m (ApCoCoA:Weyl.WeylNormalForm moved to ApCoCoA:Weyl.WNormalForm: Function name is changed to WNormalForm(L)) |
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| Line 7: | Line 7: | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | Input is a list of lists where each list represents a monomial of a Weyl polynomial. The result is a Weyl polynomial in Normal form. | + | 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. |
<example> | <example> | ||
| Line 17: | Line 17: | ||
------------------------------- | ------------------------------- | ||
-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.WNormalForm(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> | ||
Revision as of 11:05, 20 April 2009
Weyl.WeylNormalForm
Computes the Normal form of a Weyl polynomial.
Syntax
Weyl.WeylNormalForm(L:List):POLY
Description
Input L is a list of lists where each list represents a monomial of a Weyl polynomial. The result is a Weyl polynomial in Normal 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.WeylNormalForm(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.WNormalForm(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 -------------------------------
