Singular Manual: mult

  | ### 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
See degree; dim; ideal; std; vdim.

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