ApCoCoA-1:Weyl.IsHolonomic

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Weyl.IsHolonomic

Checks whether an ideal in Weyl algebra An is Holonomic or not.

Syntax

Weyl.IsHolonomic(I:IDEAL):BOOL

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.

An ideal I is holonomic if it has dimension n, the number of variables in the Weyl algebra $A_{n}=C[x_{1},...,x_{n},y_{1},...,y_{n}]$ This function determines whether an ideal I is holonomic by checking its dimension.

Example

W3::=ZZ/(7)[x[1..3],d[1..3]];
Use W3;
Cpu time = 0.00, User time = 0
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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.IsHolonomic(I);
-- CoCoAServer: computing Cpu Time = 2.36
-------------------------------
FALSE
-------------------------------

Example

A2::=QQ[x[1..2],d[1..2]];
Use A2;
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I:=Ideal(xd + 2xd - 5, d^2 - d);
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Weyl.IsHolonomic(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
TRUE
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