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.

Given an ideal $I$ and integer $m$, this method returns the size of a minimal generating set for the $m$-th symbolic power of $I$ modulo $I^m$.

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