Sub-quadratic time for riemann-roch spaces | Zendy

Simon Abelard | Zendy; Alain Couvreur | Zendy; Grégoire Lecerf | Zendy

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Sub-quadratic time for riemann-roch spaces

Author(s) -

Simon Abelard,

Alain Couvreur,

Grégoire Lecerf

Publication year - 2020

Publication title -

hal (le centre pour la communication scientifique directe)

Language(s) - English

Resource type - Conference proceedings

ISBN - 978-1-4503-7100-1

DOI - 10.1145/3373207.3404053

Subject(s) - riemann hypothesis , noether's theorem , mathematics , quadratic equation , pure mathematics , plane (geometry) , algebra over a field , time complexity , discrete mathematics , algorithm , computer science , geometry , lagrangian

We revisit the seminal Brill-Noether algorithm in the rather generic situation of smooth divisors over a nodal plane projective curve. Our approach takes advantage of fast algorithms for polynomials and structured matrices. We reach sub-quadratic time for computing a basis of a Riemann-Roch space. This improves upon previously known complexity bounds.

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