degree(Ideal)

Synopsis

• Function: degree
• Usage:
degree I
• Inputs:
• I, an ideal, in a polynomial ring or quotient of a polynomial ring
• Outputs:
• an integer, the degree of the zero set of I

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.
 i1 : S = QQ[a..f]; i2 : I = ideal(a^5, b^5, c^5, d^5, e^5); o2 : Ideal of S i3 : degree I o3 = 3125 i4 : degree(S^1/I) o4 = 3125
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.
 i5 : I = intersect(ideal(a-1,b-1,c-1),ideal(a-2,b-1,c+1),ideal(a-4,b+7,c-3/4)); o5 : Ideal of S i6 : degree I o6 = 3