ApCoCoA-1:Weyl.WDim

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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^3d^5d^5+x^5;
F2:=-3xd^5d^5+xd^3;
F3:=-2d^4d^5-xd^7+x^3d^5;
I:=Ideal(F1,F2,F3);
Weyl.WDim(I);
-- CoCoAServer: computing Cpu Time = 2.36
-------------------------------
2
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Example

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