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

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 type Las Vegas that computes a Riemann-Roch space in expected sub-quadr...

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Bibliographic Details
Published inApplicable algebra in engineering, communication and computing
Main Authors Abelard, Simon, Couvreur, Alain, Lecerf, Grégoire
Format Journal Article
LanguageEnglish
Published Springer Verlag 01.12.2022
Subjects
Algebraic Geometry
Computer Science
Mathematics
Symbolic Computation
Riemann-Roch spaces
Algebraic curves
Complexity
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Summary: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 type Las Vegas that computes a Riemann-Roch space in expected sub-quadratic time.
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-022-00588-x