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 |