, , p.90
,
93 7.2 Terse representations of vanilla Gröbner bases ,
100 7.4.1 Multiplications in the quotient algebra ,
, The results in this chapter were published in [HL18a]. A proof-of-concept Pour nir, on peut mentionner les résultats de ces dernières années sur le sujet
, HH19a] ont amélioré la complexité de la multiplication entière à O
, été établie également pour les polynômes sur les corps nis. Très récemment, Harvey et van der Hoeven ont prouvé que la multiplication avait une complexité de O(n log n), aussi bien pour les entiers
, Schönhage et Strassen avaient conjecturé qu'il n'est pas possible de descendre en dessous de n log n. Cette borne inférieure n'a pas encore été prouvée, mais elle est largement admise. Rappelons toutefois que l'algorithme naïf (quadratique) était initialement considéré optimal, à tort ; une preuve serait donc nécessaire pour apporter une réponse dénitive
The Truncated Fourier Transform for mixed radices, Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, ISSAC '17, p.261268, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01419442
The Frobenius FFT, Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, ISSAC '17, p.437444, 2017. ,
Implementing fast carryless multiplication, Proceedings of Mathematical Aspects of Computer and Information Sciences, p.121136, 2017. ,
Fast reduction of bivariate polynomials with respect to suciently regular Gröbner bases, Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, ISSAC '18, 2018. ,
Fast Gröbner basis computation and polynomial reduction for generic bivariate ideals. Applicable Algebra in Engineering, 2019. ,
Computing generic bivariate Gröbner bases with Mathemagix, 2019. ,
, Logiciels ? Routines pour la multiplication de polynômes dans F 2 [X] (voir [HLL17]), en collaboration avec Grégoire Lecerf et Joris van der Hoeven
, Une implémentation preuve-de-concept pour SageMath [Sag17] des algorithmes pour les bases de Gröbner bivariées génériques
, Une bibliothèque ecace pour le calcul des bases de Gröbner bivariées génériques dans le contexte de
, Une implémentation expérimentale pour le calcul avec des extensions de corps nis, en collaboration avec Luca De Feo. Disponible à l'adresse suivante
, La méthode et des résultats provisoires sont donnés en Annexe A. Bibliography
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