Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities

Simon Abelard; Alain Couvreur; Grégoire Lecerf

doi:10.1007/s00200-022-00588-x

Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities

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Résumé

We revisit the seminal Brill–Noether algorithm for plane curves with ordinary singularities. Our new approach takes advantage of fast algorithms for polynomials and structured matrices. We design a new probabilistic algorithm of Las Vegas type that computes a Riemann–Roch space in expected sub-quadratic time.

langue originale	Anglais
Pages (de - à)	739-804
Nombre de pages	66
journal	Applicable Algebra in Engineering, Communication and Computing
Volume	35
Numéro de publication	6
Les DOIs	https://doi.org/10.1007/s00200-022-00588-x
état	Publié - 1 nov. 2024

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10.1007/s00200-022-00588-x

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title = "Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities",

abstract = "We revisit the seminal Brill–Noether algorithm for plane curves with ordinary singularities. Our new approach takes advantage of fast algorithms for polynomials and structured matrices. We design a new probabilistic algorithm of Las Vegas type that computes a Riemann–Roch space in expected sub-quadratic time.",

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author = "Simon Abelard and Alain Couvreur and Gr{\'e}goire Lecerf",

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AU - Couvreur, Alain

AU - Lecerf, Grégoire

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AB - We revisit the seminal Brill–Noether algorithm for plane curves with ordinary singularities. Our new approach takes advantage of fast algorithms for polynomials and structured matrices. We design a new probabilistic algorithm of Las Vegas type that computes a Riemann–Roch space in expected sub-quadratic time.

KW - Algebraic curves

KW - Complexity

KW - Riemann–Roch spaces

U2 - 10.1007/s00200-022-00588-x

DO - 10.1007/s00200-022-00588-x

M3 - Article

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JO - Applicable Algebra in Engineering, Communication and Computing

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Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities

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