This package can be used to make experiments, trying many ideals, perhaps over small fields. For example...what would you expect the regularities of "typical" monomial ideals with 10 generators of degree 3 in 6 variables to be? Try a bunch of examples -- it’s fast. Here we do only 500 -- this takes about a second on a fast machine -- but with a little patience, thousands can be done conveniently.
i1 : setRandomSeed(currentTime()) o1 = 1594135569 |
i2 : kk=ZZ/101; |
i3 : S=kk[vars(0..5)]; |
i4 : time tally for n from 1 to 500 list regularity randomMonomialIdeal(10:3,S) -- used 1.51951 seconds o4 = Tally{4 => 38 } 5 => 223 6 => 161 7 => 66 8 => 12 o4 : Tally |
How does this compare with the case of binomial ideals? or pure binomial ideals? We invite the reader to experiment, replacing "randomMonomialIdeal" above with "randomBinomialIdeal" or "randomPureBinomialIdeal", or taking larger numbers of examples. Click the link "Finding Extreme Examples" below to see some other, more elaborate ways to search.
This documentation describes version 2.0 of RandomIdeals.
The source code from which this documentation is derived is in the file RandomIdeals.m2.