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5.1.100 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
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See
degree;
dim;
ideal;
std;
vdim.
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