eliminant(RingElement)

Synopsis

• Function: eliminant

• Usage:

  eliminant(f)

• Inputs:
  • f, a ring element
• Optional inputs:
  • Strategy (missing documentation) => ..., default value 0,
• Outputs:
  • a ring element, the eliminant offwith respect to the polynomial ring in one variableZ

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]