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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);
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See
dim;
hilb;
ideal;
mult;
std;
vdim.
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