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degree(Ideal)

Synopsis

Description

The degree of an ideal I in a ring S is the degree of the module S/I. See degree(Module) for more details.
S = QQ[a..f];
I = ideal(a^195, b^195, c^195, d^195, e^195);
degree I
degree(S^1/I)
If the ideal is not homogeneous, then the degree returned is the degree of the ideal of initial monomials (which is homogeneous). If the monomial order is a degree order (the default), this is the same as the degree of the projective closure of the zero set of I.
I = intersect(ideal(a-1,b-1,c-1),ideal(a-2,b-1,c+1),ideal(a-4,b+7,c-3/4));
degree I

See also