**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.

**Setup:**

This package requires Macaulay2 version 1.4 or newer.

Install this Package by doing

installPackage("extrasForTheKernel")

- 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