# muList -- computes a list of mu-values associated to a given F-threshold or F-pure threshold

## Synopsis

• Usage:
muList(e,I,J)
muList(e,I)
muList(e,f,J)
muList(e,f)
Search => Symbol
UseColonIdeals => Boolean
• Inputs:
• Optional inputs:
• Search => , default value Binary, specifies the strategy in which to search for the largest integer n such that the n-th generalized Frobenius power of I is not contained in some specified Frobenius power of J.
• UseColonIdeals => , default value false, specifies whether to use colon ideals in a recursive manner when computing mu(e,I,J)
• Outputs:
• a list, a list of the e-th ν-values for e = 0,...,d

## Description

Given an ideal I in a polynomial ring k[x1,...,xn], this function computes mu(d, I, J) or mu(d,f,J) recursively for d = 0,...,e. In other words, calling muList is the same as calling nuList with the option ComparisonTest set to FrobeniusPower.

 `i1 : R = ZZ/3[x,y];` ```i2 : I = ideal(x^2, x+y); o2 : Ideal of R``` ```i3 : J = ideal(x, y^2); o3 : Ideal of R``` ```i4 : muList(2,I,J) o4 = {1, 5, 17} o4 : List``` ```i5 : muList(3,I) o5 = {0, 2, 8, 26} o5 : List``` ```i6 : muList(3,x^3+y^3,J) o6 = {0, 1, 5, 17} o6 : List```