ApCoCoA-1:Weyl.WDim

Weyl.WDim

Computes the dimension ideal I in Weyl algebra $A_{n}$.

Syntax

Weyl.WDim(I:IDEAL):INT

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use

it/them.

This function computes the dimension of an Ideal $I=(f_{1},f_{2},...,f_{r})$ which represents the module $A_{n}/I$ where every generator $f_{i}$ should be a Weyl polynomial in Normal form. This dimension of I is equal to the dimension of the associated graded module with respect to the Bernstein filtration

Example

W3::=ZZ/(7)[x[1..3],d[1..3]];
Use W3;
Cpu time = 0.00, User time = 0
-------------------------------
F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5;
F2:=-3x[2]d[2]^5d[3]^5+x[2]d[1]^3;
F3:=-2d[1]^4d[2]^5-x[1]d[2]^7+x[3]^3d[3]^5;
I:=Ideal(F1,F2,F3);
Weyl.WDim(I);
-- CoCoAServer: computing Cpu Time = 2.36
-------------------------------
2
-------------------------------

Example

A3::=QQ[x[1..2],d[1..2]];
Use A3;
-------------------------------
I:=Ideal(x[1]d[1] + 2x[2]d[2] - 5, d[1]^2 - d[2]);
-------------------------------
Weyl.WDim(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
2
-------------------------------
-- If the dimension is ZERO, -1 will be returned
Weyl.WDim(Ideal(x[1],d[1]));
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
-1
-------------------------------

See also

Weyl.WNormalForm

Weyl.WGB

Weyl.IsHolonomic