# setAttemptsAtGenericReduction -- control the number of attempts to compute Bass numbers via a generic reduction

## Synopsis

• Usage:
setAttemptsAtGenericReduction(R,n)
• Inputs:
• R, , of a polynomial algebra by an ideal contained in the irrelevant maximal ideal
• n, an integer, must be non-negative
• Outputs:
• an integer, the number of attempts that will be made to perform a generic reduction to compute the Bass numbers of the local ring obtained by localizing R at the irrelevant maximal ideal

## Description

Changes the number of attempts made to reduce R modulo a generic regular sequence of generators of the irrelevant maximal ideal in order to compute the Bass numbers of the local ring obtained by localizing R at the irrelevant maximal ideal. The function has the effect of setting R.attemptsAtGenericReduction = n, and the number of attempts made is at most n^2. The default value is 25, so if R.attemptsAtGenericReduction is not set, then at most 625 attempts are made.

 i1 : Q = ZZ/2[u,v,w,x,y,z]; i2 : R = Q/ideal(x*y,y*z,x^3,x^2*z,x*z^2-y^3,z^3); i3 : R.?attemptsAtGenericReduction o3 = false i4 : setAttemptsAtGenericReduction(R,100) o4 = 10000 attempt(s) will be made to compute the Bass numbers via a generic reduction i5 : R.attemptsAtGenericReduction o5 = 100

If the value of R.attemptsAtGenericReduction is too small, then the computation of Bass numbers may fail resulting in an error message. Notice, though, that if the local ring obtained by localizing R at the irrelevant maximal ideal has embedding dimension at most 3, then the Bass numbers are computed without any attempt to reduce the ring, and R.attemptsAtGenericReduction has no significance.

 i6 : Q = ZZ/2[x,y,z]; i7 : R = Q/ideal(x*y,y*z,x^3,x^2*z,x*z^2-y^3,z^3); i8 : setAttemptsAtGenericReduction(R,0) o8 = 0 attempt(s) will be made to compute the Bass numbers via a generic reduction i9 : torAlgClass R o9 = G(3)

## For the programmer

The object setAttemptsAtGenericReduction is .