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

Synopsis

Usage:

setAttemptsAtGenericReduction(R,n)
Inputs:
- R, a quotient ring, 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 a function closure.