ApCoCoA-1:Weyl.IsHolonomic

Weyl.IsHolonomic

Checks whether an ideal in Weyl algebra A_n 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.

• @param I An ideal in the Weyl algebra A_n.

• @return TRUE if the given ideal is holonomic.

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.IsHolonomic(I);
-- CoCoAServer: computing Cpu Time = 2.36
-------------------------------
FALSE
-------------------------------

Example

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

See also

Introduction to CoCoAServer

Weyl.WDim