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RealRoots :: numTrace(QuotientRing)

numTrace(QuotientRing)

Synopsis

Description

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

See also