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RandomIdeals :: RandomIdeals

RandomIdeals -- A package to construct various sorts of random ideals

Description

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 = 1532622225
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 0.637807 seconds

o4 = Tally{4 => 64 }
           5 => 199
           6 => 184
           7 => 43
           8 => 8
           9 => 2

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.

See also

Authors

Version

This documentation describes version 2.0 of RandomIdeals.

Source code

The source code from which this documentation is derived is in the file RandomIdeals.m2.

Exports