CaTS is a software package whose main functions enumerate (1) all reduced Groebner bases of a lattice ideal, and (2) all monomial Agraded ideals that are flipconnected to a given one. Several variants of these enumeration algorithms are supported such as restricting the above enumerations to all initial ideals or monomial Agraded ideals with a fixed radical. CaTS supports several additional commands among which the highlights are:
CaTS began as a reimplementation of TiGERS, a software package to compute state polytopes of toric ideals, written by Birkett Huber based on algorithms in [Huber & Thomas]. The first version was developed for Jensen's Masters thesis at the University of Aarhus in Denmark. The program has been expanded since then. CaTS is faster than TiGERS (by a factor of 30 on some examples [Jensen]) and has several additional functionalities. To access the full range of commands, CaTS needs to be linked to the packages TOPCOM
[Rambau], 4ti2 [Hemmecke & Hemmecke], Normaliz
[Bruns & Koch], Macaulay 2 [Grayson & Stillman},
SoPlex [Wunderling] and cdd [Fukuda]. The last
two packages are used to solve linear programs and have
considerably increased the numerical stability of
CaTS. The basic installation only requires linking to the
LP solvers.

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PerformanceCaTS can compute the the 206444 reduced Groebner bases of the ideal associated to the matrix A9 in 529 seconds on a 1333MHz AMD Athlon processor. A9 is the matrix with a single row: (1,2,3,4,5,6,7,8,9).For more performance results view the table performance.html . Citations, research and examples@Misc{cats, author = {Jensen, Anders N.}, title = {CaTS, a software system for toric state polytopes}, howpublished = {Available at \href{http://www.soopadoopa.dk/anders/cats/cats.html}} }If you use CaTS for your research kindly send me a link to the work. If you compute interesting/large examples using CaTS I will be glad to list it on this page. References
