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.

• Gnu Mpc

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

• Arb

  A C library for arbitrary-precision floating-point real and complex ball arithmetic.

• Cm

  A C program for the construction of ring class fields of imaginary quadratic number fields and of elliptic curves with complex multiplication via floating point approximations. It also contains an implementation of fastECPP for primality proving, including a parallel version for MPI.

• Calcium

  A C library for exact computation with real and complex numbers. It is capable of rigorously deciding the truth of any constant relation involving algebraic numbers and many relations involving transcendental numbers.

• Cmh

  A C program for the computation of Igusa class polynomials for abelian surfaces with complex multiplication via floating point approximations.

• 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.

• AVIsogenies

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

• KleinianGroups

  A Magma package that computes fundamental domains of arithmetic Kleinian groups.

• Cubic

  A C program (depending on the Pari library) generating equations for cubic fields of either signature and bounded discriminant.

• Euclid

  A C program to compute the Euclidean minimum of a number field. It uses the Pari library.

• Apip

  Another Pairing Implementation in Pari. A C library (relying on Pari) for computing cryptographic pairings on elliptic curves, notably the Weil and Tate pairings and loop-shortened pairings such as ate and optimal pairings as well as their twisted versions.