satSpecialFiber -- computes the saturated special fiber ring as a quotient ring

• Usage:

  satSpecialFiber(I)

  satSpecialFiber(I, nsteps)

• Inputs:
  • I, an ideal, a homogeneous ideal generated by elements of the same degree
  • nsteps, an integer, the number steps in the saturation of the powers of I. Optional.
• Outputs:
  • a ring, the saturated special fiber ring (as a quotient ring whose defining ideal is satSpecialFiberIdeal)

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : A = matrix{ {x, x^5 + y^5},
                 {-y, y^5 + z*x^2*y^2},
                 {0, x^5}
               };

             3      2
o2 : Matrix R  <-- R

i3 : I = minors(2, A) -- a birational map

             5       5    6    3 2    6    5
o3 = ideal (x y + x*y  + y  + x y z, x , -x y)

o3 : Ideal of R

i4 : satSpecialFiber I

o4 = QQ[Z ..Z ]
         1   3

o4 : PolynomialRing