Nous formalisons des spécifications souhaitables pour un système algébro-élémentaire triangulaire dans le but de minimiser l'importance de la partie élémentaire. Une application algorithmique est donnée.
We formalize worthwhile specifications for triangular elementary-algebraic systems in order to minimize the importance of the elementary part. An algorithmic application is given.
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@article{CRMATH_2002__334_2_155_0, author = {Bellido, Anne-Mercedes and Jalby, Vincent}, title = {Sp\'ecifications des algorithmes de triangulation de~syst\`emes alg\'ebro-\'el\'ementaires}, journal = {Comptes Rendus. Math\'ematique}, pages = {155--159}, publisher = {Elsevier}, volume = {334}, number = {2}, year = {2002}, doi = {10.1016/S1631-073X(02)02219-7}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02219-7/} }
TY - JOUR AU - Bellido, Anne-Mercedes AU - Jalby, Vincent TI - Spécifications des algorithmes de triangulation de systèmes algébro-élémentaires JO - Comptes Rendus. Mathématique PY - 2002 SP - 155 EP - 159 VL - 334 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02219-7/ DO - 10.1016/S1631-073X(02)02219-7 LA - fr ID - CRMATH_2002__334_2_155_0 ER -
%0 Journal Article %A Bellido, Anne-Mercedes %A Jalby, Vincent %T Spécifications des algorithmes de triangulation de systèmes algébro-élémentaires %J Comptes Rendus. Mathématique %D 2002 %P 155-159 %V 334 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02219-7/ %R 10.1016/S1631-073X(02)02219-7 %G fr %F CRMATH_2002__334_2_155_0
Bellido, Anne-Mercedes; Jalby, Vincent. Spécifications des algorithmes de triangulation de systèmes algébro-élémentaires. Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 155-159. doi : 10.1016/S1631-073X(02)02219-7. http://www.numdam.org/articles/10.1016/S1631-073X(02)02219-7/
[1] On the theory of triangular sets, J. Symbolic Comput., Volume 28 (1999), pp. 105-124
[2] Triangular sets for solving polynomial systems; a comparative implementation of four methods, J. Symbolic Comput., Volume 28 (1999), pp. 125-154
[3] Sylvester's identity and multistep integer preserving Gaussian elimination, Math. Comp., Volume 22 (1968), pp. 565-578
[4] On the link between triangular set and dynamic constructible closure, J. Pure Appl. Algebra, Volume 163 (2001), pp. 49-68
[5] A lazy method for triangularizing polynomial systems, Publications du LACO, Volume 4 (1995)
[6] Complexity of stratifications of semi-Pfaffian sets, Discrete Comput. Geom., Volume 14 (1995), pp. 71-91
[7] Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa, Volume 18 (1964), pp. 449-474
[8] Weak Wu stratification in , J. Symbolic Comput., Volume 28 (1999), pp. 213-223
[9] Decomposing polynomial systems into simple systems, J. Symbolic Comput., Volume 16 (1998), pp. 83-114
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