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Section: New Software and Platforms
Mathemagix
Scientific Description
The project aims at building a bridge between symbolic computation and numerical analysis. It is structured by collaborative software developments of different groups in the domain of algebraic and symbolic-numeric computation.
In this framework, we are working more specifically on the following components:
realroot: a set of solvers using subdivision methods to isolate the roots of polynomial equations in one or several variables, continued fraction expansion of roots of univariate polynomials, Bernstein basis representation of univariate and multivariate polynomials and related algorithms, exact computation with real algebraic numbers, sign evaluation, comparison, certified numerical approximation.
shape: tools to manipulate curves and surfaces of different types including parameterized, implicit with different type of coefficients, algorithms to compute their topology, intersection points or curves, self-intersection locus, singularities, ...
These packages are integrated from the former library Synaps (SYmbolic Numeric APplicationS) dedicated to symbolic and numerical computations. There are also used in the algebraic-geometric modeler axel .
Functional Description
Mathemagix is a free computer algebra system which consists of a general purpose interpreter, which can be used for non-mathematical tasks as well, and efficient modules on algebraic objects. It includes the development of standard libraries for basic arithmetic on dense and sparse objects (numbers, univariate and multivariate polynomials, power series, matrices, etc., based on FFT and other fast algorithms). These developments, based on C++, offer generic programming without losing effectiveness, via the parameterization of the code (template) and the control of their instantiations.