rationalUnivariateRepresentation -- the rational univariate representation of a zero-dimensional ideal in a polynomial ring

• Usage:

  rationalUnivariateRepresentation(I)

  rationalUnivariateRepresentation(S)

• Inputs:
  • I, an ideal, a zero-dimensional ideal in a polynomial ring
  • S, a quotient ring, an Artinian ring as a quotient of a polynomial ring
• Outputs:
  • a list, the rational univariate representation of I or the rational univariate representation of S

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x*y - 1,2*x - y + 3)

o2 = ideal (x*y - 1, 2x - y + 3)

o2 : Ideal of R

i3 : rationalUnivariateRepresentation(I)

              2   3        - 3Z + 15  6Z + 21
o3 = (x + y, Z  - -Z - 9, {---------, -------})
                  2          4Z - 3    4Z - 3

o3 : Sequence

i4 : rationalUnivariateRepresentation(R/I)

              2   3        - 3Z + 15  6Z + 21
o4 = (x + y, Z  - -Z - 9, {---------, -------})
                  2          4Z - 3    4Z - 3

o4 : Sequence