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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Computation of the topological type of a real Riemann surface
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by C. Kalla and C. Klein PDF
Math. Comp. 83 (2014), 1823-1846 Request permission


We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$, namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the $\mathcal {A}$-cycles are invariant under the anti-holomorphic involution $\tau$.
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Additional Information
  • C. Kalla
  • Affiliation: Centre de recherches mathématiques Université de Montréal, Case postale 6128, Montréal H3C 3J7, Canada
  • Address at time of publication: MAPMO, Université d’Orléans, Rue de Chartres, B.P. 6759, 45007 Orléans Cedex 2, France
  • Email:
  • C. Klein
  • Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary, 21078 Dijon Cedex, France
  • Email:
  • Received by editor(s): April 22, 2012
  • Received by editor(s) in revised form: December 31, 2012
  • Published electronically: March 13, 2014
  • Additional Notes: The authors thank V. Shramchenko for useful discussions and hints. This work was supported in part by the project FroM-PDE funded by the European Research Council through the Advanced Investigator Grant Scheme, and the ANR via the program ANR-09-BLAN-0117-01.
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 1823-1846
  • MSC (2010): Primary 14Q05; Secondary 68W30
  • DOI:
  • MathSciNet review: 3194131