ApCoCoA-1:Weyl.WStandardForm

Weyl.WNormalForm

Computes the Normal form of a Weyl polynomial.

Syntax

Weyl.WNormalForm(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 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.WNormalForm(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
-------------------------------