inria-00099520
https://inria.hal.science/inria-00099520
[CNRS] CNRS - Centre national de la recherche scientifique
[INRIA] INRIA - Institut National de Recherche en Informatique et en Automatique
[INPL] Institut National Polytechnique de Lorraine
[INRIA-LORRAINE] INRIA Nancy - Grand Est
[LORIA2] Publications du LORIA
[INRIA-NANCY-GRAND-EST] INRIA Nancy - Grand Est
[TESTALAIN1] TESTALAIN1
[UNIV-LORRAINE] Université de Lorraine
[INRIA2] INRIA 2
[LORIA] Laboratoire Lorrain de Recherche en Informatique et ses Applications
Elimination Practice: Software Tools and Applications
Wang, Dongming
[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH]
OUV
software
computer algebra
logiciel
calcul formel
raisonnement géométrique
geometric reasoning
élimination polynomiale
polynomial elimination
The first half of the book presents the library Epsilon that has been built up for symbolic polynomial elimination and decomposition with (geometric) applications. It has 8 modules and contains more than 70 functions, which allow one to triangularize systems of multivariate (differential) polynomials, decompose polynomial systems into triangular systems of various kinds (regular, normal, simple, irreducible, or with projection property), decompose algebraic varieties into unmixed or irreducible subvarieties, decompose polynomial ideals into primary components, factorize polynomials over algebraic extension fields, solve systems of polynomial equations and inequations, and handle and prove geometric theorems automatically. The usefulness of the software tools are demonstrated in the second half of the book by a number of selected applications, ranging from qualitative analysis of differential equations in pure mathematics to geometry theorem discovering in automated reasoning and to surface blending and offsetting in computer-aided geometric design. These applications are illuminated with many examples and illustrations. The compact disk distributed with this book contains the entire Epsilon library with documentation, examples, and Maple worksheets.
2003
en
Imperial College Press, London,