A fast randomized geometric algorithm for computing Riemann-Roch spaces

DOI10.1090/mcom/3517zbMath1454.14140arXiv1811.08237OpenAlexW2901954812MaRDI QIDQ5113675

Aude le Gluher, Pierre-Jean Spaenlehauer

Publication date: 15 June 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08237

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computational aspects of algebraic curves (14Q05)

Related Items (5)

Asymptotically-good arithmetic secret sharing over \(\mathbb{Z}/p^{\ell }\mathbb{Z}\) with strong multiplication and its applications to efficient MPC ⋮ Computing Riemann-Roch spaces via Puiseux expansions ⋮ Quasi-equivalence of heights in algebraic function fields of one variable ⋮ Unnamed Item ⋮ Projective toric codes

Uses Software

• Magma

Cites Work

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• Le formalisme du résultant. (The formalism of resultant)
• On fast multiplication of polynomials over arbitrary algebras
• The Magma algebra system. I: The user language
• An elementary approach to subresultants theory.
• Computing Riemann-Roch spaces in algebraic function fields and related topics.
• Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve
• Fast computation of generic bivariate resultants
• Modern Computer Algebra
• Geometry of Algebraic Curves
• Powers of tensors and fast matrix multiplication
• Asymptotically fast group operations on Jacobians of general curves
• Triangular Factorization and Inversion by Fast Matrix Multiplication
• Effective construction of algebraic geometry codes
• Fast Computation of the Roots of Polynomials Over the Ring of Power Series
• On Computing the Resultant of Generic Bivariate Polynomials
• Algorithme de Brill-Noether et codes de Goppa
• A Gröbner free alternative for polynomial system solving

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