Software

A number of programs written or maintained by the team and distributed under free licenses have their own pages.

• PARI/GP

  A C library and a computer algebra system designed for fast computations in number theory.
  • PariDroid, a port of Pari/GP to Android.
  • PariTwine, bindings of GNUMP (GMP), GNU MPFR, GNU MPC and Arb into the Pari/GP system.

• FLINT

  The FLINT C library has been rewritten to incorporate Arb, a library for arbitrary-precision floating-point real and complex ball arithmetic, and Calcium, a library for exact computation with real and complex numbers. The latter is capable of rigorously deciding the truth of any constant relation involving algebraic numbers and many relations involving transcendental numbers.

• GNU MPC

  A C library for the arithmetic of complex numbers with arbitrarily high precision and correct rounding of the result.

• CM and CMH

  These are C programs for computing ring class fields of imaginary-quadratic number fields or Shimura class fields of quartic CM fields; or, equivalently, elliptic curves or Jacobians of genus 2 curves with complex multiplication. Both use multiprecision floating point approximations. The CM code also contains an implementation of fastECPP for primality proving, including a parallel version for MPI.

• AVIsogenies

  A Magma package for working with abelian varieties, with a particular emphasis on explicit isogeny computation.

• ThetaIsogenies/2-isogenies

  Software implementing efficiently 2ⁿ-isogenies in dimension 2 via theta functions; a high level Sage implementation and low level constant time Rust implementation are provided.

• FromLatticesToModularForms

  Software for enumerating the isogeny class of a power of an elliptic curve via a Hermitian module representation and for computing it effectively using AVIsogenies.

• MPFRCX

  A C library for the arithmetic of univariate polynomials over arbitrary precision real or complex numbers.

• abelianbnf

  A GP script that computes the class group of certain Galois number fields by exploiting the existence of norm relations.

• quartic

  A C program (depending on the Pari library) to compute tables of primitive quartic number fields with absolute discriminant bounded by some given constant.

More software has been developed in the LFANT team, the CANARI predecessor.