degree(ProjectiveVariety)

Synopsis

i1 : S = ZZ/32003[x,y,z];

i2 : I = ideal(x^4-4*x*y*z^2-z^4-y^4);

o2 : Ideal of S

i3 : R = S/I;

i4 : X = variety I

o4 = X

o4 : ProjectiveVariety

i5 : degree X

o5 = 4

The degree of a projective variety X = V(I) = Proj R is the degree of the homogeneous coordinate ring R = S/I of X.

i6 : degree X == degree I

o6 = true

i7 : degree X == degree R

o7 = true