gin -- the generic initial ideal

Synopsis

• Usage:

  gin I

• Inputs:

  • I, an Ideal in a polynomialRing
• Outputs:

  • an Ideal, the generic initial ideal of I.
• Optional inputs:

  • AttemptCount => default value 7, sets the number of random coordinate changes the routine attempts before choosing the potentialgin .
  • Modular => default value false, if set to be true, computations are performed modulo a large random prime .
  • MonomialOrder => default value null, sets theMonomial Order used in the computation of gin .
  • Verbose => default value false, provides a summary of the random initial ideals generated and warns if the selected one is not strongly stable.

Description

i1 : R = QQ[a..d];

i2 : I = ideal(a^3+c^2*d, b^3-a*d^2);

o2 : Ideal of R

i3 : gin(I)

             3   2      3   5
o3 = ideal (a , a b, a*b , b )

o3 : Ideal of R

Caveat

See also

• lexgin -- the generic initial ideal with respect to lexicographical order