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extrasForTheKernel :: extrasForTheKernel

extrasForTheKernel -- constructions of prime fields and artinian reductions


Overview: A collection of a few functions that will be handy in many cases.

Perhaps the most interesting is the funcion randomKRationalPoint, which for a finite ground field K of moderate size, will find a K-rational points on a positive dimensional projective algebraic set X under the asumption that the degree of X is small compared to the char K.


This package requires Macaulay2 version 1.4 or newer.

Install this Package by doing



This documentation describes version 0.1.1 of extrasForTheKernel.

Source code

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


  • Functions and commands
    • artinianReduction -- compute an artinian quotient of an Cohen-Macaulay ideal
    • criticalKoszulDegrees -- compute all d with $\sum_{p+q=d} (-1)^q dim K_{p,q}(S/I)==0$ for an artinian ideal I
    • expectedSyzygies -- compute the expected Betti numbers of an artinian module
    • koszulMap -- compute the Koszul homology map whose kernel correspond the Koszulzycles for K_(p,q)(S/I)
    • koszulMaps -- compute all Koszul maps of total degree p for an artinian ideal I