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PolyBoRi
The core of PolyBoRi is a C++ library, which provides high-level data types for Boolean polynomials and monomials, exponent vectors, as well as for the underlying polynomial rings and subsets of the powerset of the Boolean variables. As a unique approach, binary decision diagrams are used as internal storage type for polynomial structures. On top of this C++-library we provide a Python interface. This allows parsing of complex polynomial systems, as well as sophisticated and extendable strategies for Gröbner base computation. PolyBoRi features a powerful reference implementation for Gröbner basis computation.
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SAGE is a framework for number theory, algebra, and geometry computation. It is open source and freely available under the terms of the GNU General Public License (GPL). SAGE is a Python library with a customized interpreter. It is written in Python, C++, and C (via Pyrex). Python (http://www.python.org) is an open source object-oriented interpreted language, with a large number of libraries, e.g., for numerical analysis, which are available to users of SAGE. Python can also be accessed in library mode from C/C++ programs. SAGE provides an interface to several important open source libraries, including Cremona’s MWRANK library for computing with elliptic curves, the PARI library (pari.math.u-bordeaux.fr) for number theory, Shoup’s number theory library NTL (http://www.shoup.net/ntl/), SINGULAR (http://www.singular.uni-kl.de) for commutative algebra, GAP (http://www.gap-system.org) for group theory and combinatorics, and maxima (http://maxima.sourceforge.net) for symbolic computation and calculus.
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