Singular

7.5.4.0. isHolonomic

Usage:

isHolonomic(M); M an ideal/module/matrix

Return:

int, 1 if M is holonomic over the base ring, and 0 otherwise

Assume:

basering is a Weyl algebra in characteristic 0

Purpose:

check whether M is holonomic over the base ring

Note:

M is holonomic if 2*dim(M) = dim(R), where R is the
base ring; dim stands for Gelfand-Kirillov dimension

LIB "dmod.lib";
ring R = 0,(x,y),dp;
poly F = x*y*(x+y);
def A = annfsBM(F,0);
setring A;
LD;
==> LD[1]=x*Dx+y*Dy+3
==> LD[2]=x*y*Dy+y^2*Dy+x+2*y
==> LD[3]=y^2*Dx*Dy-y^2*Dy^2+2*y*Dx-4*y*Dy-2
isHolonomic(LD);
==> 1
ideal I = std(LD[1]);
I;
==> I[1]=x*Dx+y*Dy+3
isHolonomic(I);
==> 0