The package has routines for points in affine and projective spaces. The affine code, some of which uses the Buchberger-Moeller algorithm to more quickly compute the ideals of points in affine space, was written by Stillman, Smith and Stromme. The projective code was written separately by Eisenbud and Popescu.

The purpose of the projective code was to find as many counterexamples as possible to the minimal resolution conjecture; it was of use in the research for the paper "Exterior algebra methods for the minimal resolution conjecture", by David Eisenbud, Sorin Popescu, Frank-Olaf Schreyer and Charles Walter (Duke Mathematical Journal. 112 (2002), no.2, 379-395.) The first few of these counterexamples are: (6,11), (7,12), (8,13), (10,16), where the first integer denotes the ambient dimension and the second the number of points. Examples are known in every projective space of dimension >=6 except for P^{9}.

In version 3.0, F. Galetto and J.W. Skelton added code to compute ideals of fat points and projective points using the Buchberger-Moeller algorithm.

- Gregory G. Smith <ggsmith@mast.queensu.ca>
- Stein A. StrÃ¸mme <stromme@math.uib.no>
- David Eisenbud <de@msri.org>
- Joseph W. Skelton <jskelton@tulane.edu>

- Functions and commands
- affineFatPoints -- produces the ideal and initial ideal from the coordinates of a finite set of fat points
- affineFatPointsByIntersection -- computes ideal of fat points by intersecting powers of maximal ideals
- affineMakeRingMaps -- evaluation on points
- affinePoints -- produces the ideal and initial ideal from the coordinates of a finite set of points
- affinePointsByIntersection -- computes ideal of point set by intersecting maximal ideals
- affinePointsMat -- produces the matrix of values of the standard monomials on a set of points
- expectedBetti -- The betti table of r points in Pn according to the minimal resolution conjecture
- minMaxResolution -- Min and max conceivable Betti tables for generic points
- omegaPoints -- linear part of the presentation of canonical module of points
- points -- make the ideal of a set of points
- projectiveFatPoints -- produces the ideal and initial ideal from the coordinates of a finite set of fat points
- projectiveFatPointsByIntersection -- computes ideal of fat points by intersecting powers of point ideals
- projectivePoints -- produces the ideal and initial ideal from the coordinates of a finite set of projective points
- projectivePointsByIntersection -- computes ideal of projective points by intersecting point ideals
- randomPoints -- ideal of a random set of points
- randomPointsMat -- matrix of homogeneous coordinates of random points in projective space

- Symbols
- AllRandom -- Option to randomPointsMat.
- VerifyPoints -- Option to projectivePoints.