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Explicit Coleman Integration for Hyperelliptic Curves

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6197)


Coleman’s theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage.


  • Hyperelliptic Curve
  • Weierstrass Point
  • Torsion Point
  • Multiple Zeta
  • Height Pairing

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Balakrishnan, J.S., Bradshaw, R.W., Kedlaya, K.S. (2010). Explicit Coleman Integration for Hyperelliptic Curves. In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14517-9

  • Online ISBN: 978-3-642-14518-6

  • eBook Packages: Computer ScienceComputer Science (R0)