# Project : galaad

## Section: Software

Keywords : linear algebra, bezoutian, C++, FFT, genericity, effective algebraic geometry, links symbolic-numeric, geometry, curves and surfaces, sparse matrices, structured matrices, iterative methods, polynomials, solving, resultant, stability, Eigenvalues.

### synaps, a module for symbolic and numeric computations

Participants : Guillaume Chèze, Ioannis Emiris, Grégory Gatellier, Bernard Mourrain [contact person], Jean-Pascal Pavone, Olivier Ruatta, Jean-Pierre Técourt, Philippe Trébuchet, Elias Tsigaridas.

See synaps web site: http://www-sop.inria.fr/galaad/logiciels/synaps/.

We consider problems handling algebraic data structures such as polynomials, ideals, ring quotients, ..., as well as numerical computations on vectors, matrices, iterative processes, ...etc. Until recently, these domains were separated: software for manipulating formulas is often not effective for numerical linear algebra; while the numerically stable and efficient tools in linear algebra are usually not adapted to the computations with polynomials.

We design the software synaps (SYmbolic Numeric APplicationS) for symbolic and numerical computations with polynomials. This powerful kernel contains univariate and multivariate solvers as well as several resultant-based methods for projection operations. Currently, we are developing a module that is related to factorization, which is relevant to the separation of irreducible components of a curve in .

In this library, a list of structures and functions makes it possible
to operate on vectors, matrices, and polynomials in one or more variables.
Specialized tools such as lapack, gmp, superlu, rs, gb, ... are also
connected and can be imported in a transparent way.
These developments are based on C++, and attention is paid to the generic
structures so that effectiveness would be maintained.
Thanks to the parameterization of the code (*template*)
and to the control of their instantiations (*traits,
template expression*), they offer generic programming without losing
effectiveness.