This directory will provide the polynomial systems used in the ISSAC 2008 paper

When does (T) equal sat(T)?

by authors Francois Lemaire, Marc Moreno Maza, Wei Pan and Yuzhen Xie.

We also make the following remarks.

Each file contains two parts: variables and sys. The former is a list of variables in decreasing order and the latter is a list of defining polynomials. These systems have been uesd in the experimentation section of the paper. We ran examples in the RegularChains library (a beta version based on the one in Maple 11) under Kalkbrener's mode, that is,

dec := Triangularize(sys, R);

where R is a polynomial ring defined as

R := PolynomialRing(variables);

In general triangular decompositions are not canonical and may contain redundant regular chains. Heuristic inclusion test algorithm used in the library may affect the output. Hence output in Maple 10 may differ from the one in Maple 11 or in higher version, though it rarely happens.

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