Computing with Constructible Sets in Maple

Constructible sets are the geometrical objects naturally attached to triangular decompositions, as polynomial ideals are the algebraic concept underlying the computation of Gröbner bases. This relation becomes even more complex and essential in the case of polynomial systems with infinitely many solutions. In this paper, we introduce ConstructibleSetTools a new module of the RegularChains library in Maple. To our knowledge, this is the first computer algebra package providing constructible set as a type and exporting a rich collection of operations for manipulating constructible sets. Besides, this module provides routines in support of solving parametric polynomial systems. Simplifying set-theoretical expressions on constructible sets is at the core of fundamental and challenging operations, like the removal of redundant components when decomposing a polynomial system. We present practically efficient approaches for this purpose together with an application to solver verification.