This computes the number of real points of SpecR where R is an Artinian ring with characteristic zero
i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing |
i2 : F = {y^2-x^2-1,x-y^2+4*y-2}
2 2 2
o2 = {- x + y - 1, - y + x + 4y - 2}
o2 : List
|
i3 : I = ideal F
2 2 2
o3 = ideal (- x + y - 1, - y + x + 4y - 2)
o3 : Ideal of R
|
i4 : S = R/I o4 = S o4 : QuotientRing |
i5 : numTrace(S) o5 = 2 |
i6 : R = QQ[x,y] o6 = R o6 : PolynomialRing |
i7 : I = ideal(1 - x^2*y + 2*x*y^2, y - 2*x - x*y + x^2)
2 2 2
o7 = ideal (- x y + 2x*y + 1, x - x*y - 2x + y)
o7 : Ideal of R
|
i8 : numTrace(I) o8 = 3 |