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5.1.15 degree

Syntax:
degree ( ideal_expression )
degree ( module_expression )
Type:
int
Purpose:
If applied to an ideal_expression I, degree(I) computes the degree of the projective variety defined by the monomial ideal generated by the leading monomials of the input.
If applied to a module_expression M, degree(M) computes the degree of the sheaf over a projective variety defined by the graded 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 monomial ordering is a weighted degree ordering, the weighted degree of the variety, respectively sheaf is computed.
If the input is homogeneous and a standard basis then the result computed by degree is the degree of the projective variety, respectively sheaf, defined by the input ideal, respectively module.
If the projective variety is empty, 0 is returned. For computing with affine varieties, use mult.
Example:
 
ring r3=32003,(x,y,z,h),dp;
int a,b,c,t=11,10,3,1;
poly f=x^a+y^b+z^(3*c)+x^(c+2)*y^(c-1)+x^(c-1)*y^(c-1)*z3
  +x^(c-2)*y^c*(y2+t*x)^2;
ideal i=jacob(f);
i=homog(i,h);
ideal i0=std(i);
degree(i0);
i=std(maxideal(1));
degree(i);
mult(i);
See dim; hilb; ideal; mult; std; vdim.

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