5.1.80 mult

Syntax:

mult ( ideal_expression )
mult ( module_expression )

Type:

int

Purpose:

computes the degree of the monomial ideal, resp. module, generated by the leading monomials of the input.
If the input is a standard basis of a homogeneous ideal then it returns the degree of this ideal.
If the input is a standard basis of an ideal in a (local) ring with respect to a local degree ordering then it returns the multiplicity of the ideal (in the sense of Samuel, with respect to the maximal ideal).

Example:

ring r=32003,(x,y),ds; poly f=(x3+y5)^2+x2y7; ideal i=std(jacob(f)); mult(i); → 46 mult(std(f)); → 6

See degree; dim; ideal; std; vdim.