Structure of polyzetas and explicit representation on transcendence bases of shuffle and stuffle algebras. (November 2017)

• Record Type: Journal Article
• Authors: Bui, V.C.; Duchamp, G.H.E.; Hoang Ngoc Minh, V.
• Is Part Of: Journal of symbolic computation. Volume 83(2017)
• Page Start: 93
• Page End: 111
• Publication Date: 2017-11
• Subjects: Poincaré–Birkhoff–Witt basis -- Transcendence basis -- Schützenberger's factorization -- Noncommutative generating series -- Shuffle algebra -- Polyzetas; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.11.007
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Polyzetas, indexed by words, satisfy shuffle and quasi-shuffle identities. In this respect, one can explore the multiplicative and algorithmic (locally finite) properties of their generating series. In this paper, we construct pairs of bases in duality on which polyzetas are established in order to compute local coordinates in the infinite dimensional Lie groups where their non-commutative generating series live. We also propose new algorithms leading to the ideal of polynomial relations, homogeneous in weight, among polyzetas (the graded kernel) and their explicit representation (as data structures) in terms of irreducible elements.