symbolicDefect -- computes the symbolic defect of an ideal

Synopsis

• Usage:
symbolicDefect(I,m)
• Inputs:
• 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

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

Ways to use symbolicDefect :

• "symbolicDefect(Ideal,ZZ)"

For the programmer

The object symbolicDefect is .