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RealRoots :: eliminant(RingElement)

eliminant(RingElement)

Synopsis

Description

This computes the eliminant of an element f of an Artinian ring R and returns a polynomial in Z

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 : eliminant(x)

      4     3     2
o5 = Z  - 2Z  - 9Z  - 6Z - 7

o5 : QQ[Z]
i6 : eliminant(y)	      

      4     3      2
o6 = Z  - 8Z  + 19Z  - 16Z + 5

o6 : QQ[Z]