Software

• AlgebraicSolving.jl: Open-source library, written in Julia, for solving multivariate polynomial systems through algebraic methods (mainly Groebner bases). It is based on the msolve library, providing its main functionalities (Groebner bases computations, real root isolation) as well as advanced ones for polynomial system solving (dimension and degree computation, equidimensional decomposition, etc.).


• msolve: Open-source library, written in plain C, for solving multivariate polynomial systems (Groebner bases computations, rational parametrization of solutions, real root isolation, etc.). It implements advanced algorithms for Groebner bases computations (F4 and signature based algorithms, modern change of order algorithms) leveraging vectorization and parallelism.
  The msolve library is now interfaced with leading computer algebra systems such as Oscar (see e.g. here), SageMath (see e.g. here) and Macaulay2 (see e.g. here or here).


• RAGlib : Open source library for solving polynomial systems of equations and inequalities over the real numbers.
  It implements fast algorithms based on the so-called critical point method for computing points in each connected component of real solutions sets to systems of polynomial constraints (or decide their emptiness).
  It is currently written using the Maple programming language and is based in the msolve library.


• PML : The Polynomial Matrix Library (PML) offers a wide range of tools for efficient computations with univariate polynomial matrices.


• MQsoft : MQsoft is an efficient library in C for implementing various multivariate schemes.

Former projects no more maintained (for the moment)

• GBLA: An open source C library for linear algebra specialized for eliminating matrices generated during Gröbner basis computations in algorithms like F4 or F5.


• Matrix database of large matrices coming from Groebner bases computations which are usable in GBLA.