A framework for Symbolic and Numeric Computations

Bernard Mourrain 1 Hélène Prieto 1
1 SAGA - Algebraic Systems, Geometry and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The need to combine symbolic and numeric computations is ubiquitous is many problems such as the forward and inverse kinematics of robots, motion planning, the analysis of the geometric structure of molecules, computational geometry, geometric and solid modelling, graphics, computer-aided design, computer vision, signal processing ... Starting with an exact or approximate description of the equations, we will eventually have to compute a numerical approximation of the solutions. This leads to new, interesting and challenging questions either from a theoretical or practical point of view at the frontier between algebra and analysis. The objective of this report is to describe a framework for symbolic and numeric computations, called ALP, which can be used to validate these new developments and to build devoted applications or solvers. This environment allows us to define parameterised but efficient classes of basic algebraic objects such as vectors, matrices, monomials and polynomials, ... which can be used easily in the construction of more elaborated algorithms. We pay a special attention to genericity and to reusability of external libraries such as LAPACK, SUPERLU, GMP ... In this report, we describe the structure of the software and the main tools or classes which are available.
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Submitted on : Wednesday, May 24, 2006 - 10:26:44 AM
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Bernard Mourrain, Hélène Prieto. A framework for Symbolic and Numeric Computations. [Research Report] RR-4013, INRIA. 2000, pp.96. ⟨inria-00072629⟩

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