criticalExponentApproximation -- gives a list of approximates of a critical exponent

Synopsis

• Usage:
criticalExponentApproximation(e,I,J)
criticalExponentApproximation(e,f,J)
• Inputs:
• Outputs:

Description

This returns a list of μIJ(pd)/pd, or μfJ(pd)/pd, for d = 0,...,e.

As d approaches , the sequence of these terms converges to the critical exponent of I, or of f, with respect to J.

 `i1 : R = ZZ/5[x,y];` ```i2 : I = ideal(x^2,x*y,y^2); o2 : Ideal of R``` ```i3 : m = ideal(x,y); o3 : Ideal of R``` ```i4 : criticalExponentApproximation(2,I,m) 4 24 o4 = {0, -, --} 5 25 o4 : List``` `i5 : f = x^2 + y^3;` ```i6 : criticalExponentApproximation(2,f,m) 3 19 o6 = {0, -, --} 5 25 o6 : List```

• ftApproximation -- gives a list of terms in the sequence whose limit defines an F-threshold
• fptApproximation -- gives a list of terms in the sequence whose limit defines the F-pure threshold
• mu -- computes the largest Frobenius power of an ideal not contained in a specified Frobenius power
• muList -- computes a list of mu-values associated to a given F-threshold or F-pure threshold

Ways to use criticalExponentApproximation :

• criticalExponentApproximation(ZZ,Ideal,Ideal)
• criticalExponentApproximation(ZZ,RingElement,Ideal)