symbolicDefect -- computes the symbolic defect of an ideal

Synopsis

• Usage:

  symbolicDefect(I,m)

• Inputs:
  • I, an ideal,
  • m, an integer,
• Optional inputs:
  • CIPrimes => ..., default value false, compute the symbolic power by taking the intersection of the powers of the primary components
  • UseMinimalPrimes => ..., default value false, an option to only use minimal primes to calculate symbolic powers
• Outputs:
  • an integer, the size of a minimal generating set of the m-th symbolic power of I modulo I^m.

Description

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

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x*y,x*z,y*z);

o2 : Ideal of R

i3 : symbolicDefect(I,2)

o3 = 1