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5.1.82 mult

Syntax:
mult ( ideal_expression )
mult ( module_expression )
Type:
int
Purpose:
If applied to an ideal_expression I, mult(I) computes the degree of the graded ring defined by the monomial ideal generated by the leading monomials of the input.
If applied to a module_expression M, mult(M) computes the degree of the module coker(L(M)) where L(M) denotes the matrix with column entries the leading monomials of the given generators for M.
Note:
If the input is a standard basis for a homogeneous ideal then mult returns the degree of the projective cone over the projective variety defined by the input ideal.
If the input is a standard basis of an ideal with respect to a local degree ordering then mult 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; hilb; ideal; std; vdim.

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            User manual for Singular version 2-0-6, November 2004, generated by texi2html.