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Calcul Symbolique Non Commutatif by Minh-V

Calcul Symbolique Non Commutatif

by Minh-V
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Book cover type: Paperback
  • ISBN13: 9783838171296
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 148
  • Original Price: GBP 43.0
  • Language: French
  • Edition: N/A
  • Item Weight: 227 grams
  • BISAC Subject(s): General

Il est bien établi que le calcul formel permet de vérifier des conjectures, des démonstrations, des formules longues et pénibles. L'innovation est qu'avec quelques opérations élémentaires sur des suites de symboles 0 et 1, on capte aussi, de façon exacte, de nouvelles formules, identités remarquables et conjectures insolites. Dans ce travail, nous illustrons cette dernière assertion en proposant des algorithmes via la combinatoire des mots de Lyndon. Nous montrons d'abord que l'algèbre des polylogarithmes est isomorphe à celle du mélange et nous en tirons des conséquences concernant le calcul effectif de la monodromie, du comportement asymptotique, des relations algébriques et des équations fonctionnelles. Nous examinons ensuite le rapport entre les séries génératrices commutatives des polylogarithmes et des fonctions hypergéométriques pour obtenir diverses sommations. La série génératrice non commutative des polylogarithmes nous mène au calcul de l'associateur de Drinfel'd mis sous forme factorisée. Nous appliquons finalement ces études aux équations intégro-différentielles et à l'obtention d'un système de réécriture des relations polynomiales entre les sommes d'Euler-Zagier.

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