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5.1.81 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
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See
degree;
dim;
hilb;
ideal;
std;
vdim.
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