# Singular

##### 7.7.21.0. holonomicRank
Procedure from library `dmodloc.lib` (see dmodloc_lib).

Usage:
holonomicRank(I[,e]); I ideal, e optional int

Assume:
The basering is the n-th Weyl algebra over a field of characteristic 0 and for all 1<=i<=n the identity
var(i+n)*var(i)=var(i)*var(i+1)+1 holds, i.e. the sequence of variables is given by x(1),...,x(n),D(1),...,D(n), where D(i) is the differential operator belonging to x(i).

Return:
int, the holonomic rank of I

Remarks:
The holonomic rank of I is defined to be the K(x(1..n))-dimension of the module W/WI, where W is the rational Weyl algebra K(x(1..n))<D(1..n)>.
If this dimension is infinite, -1 is returned.

Note:
If e<>0, `std` is used for Groebner basis computations, otherwise (and by default) `slimgb` is used.
If printlevel=1, progress debug messages will be printed, if printlevel>=2, all the debug messages will be printed.

Example:
 ```LIB "dmodloc.lib"; // (OTW), Example 8 ring r3 = 0,(x,y,z,Dx,Dy,Dz),dp; def D3 = Weyl(); setring D3; poly f = x^3-y^2*z^2; ideal I = f^2*Dx+3*x^2, f^2*Dy-2*y*z^2, f^2*Dz-2*y^2*z; // I annihilates exp(1/f) holonomicRank(I); ==> 1 ```