FLINT: Fast Library for Number Theory

Welcome to FLINT’s documentation! FLINT is a C library for doing number theory, maintained by William Hart.

• Source code on GitHub: https://github.com/wbhart/flint2
• Issue tracker: https://github.com/wbhart/flint2/issues
• Mailing list: https://groups.google.com/group/flint-devel

FLINT is free software distributed under the GNU Lesser General Public License (LGPL), version 2.1 or later.

General utilities

• flint.h – global definitions
• profiler.h – performance profiling
• threadpool.h – thread pool
• perm.h – permutations
• mpoly.h – support functions for multivariate polynomials

Integers

• ulong_extras.h – arithmetic and number-theoretic functions for single-word integers
• fmpz.h – integers
• fmpz_vec.h – vectors of integers
• fmpz_factor.h – integer factorisation
• fmpz_mat.h – matrices over the integers
• fmpz_lll.h – LLL reduction
• fmpz_poly.h – univariate polynomials over the integers
• fmpz_poly_mat.h – matrices of polynomials over the integers
• fmpz_poly_factor.h – factorisation of polynomials over the integers
• fmpz_mpoly.h – multivariate polynomials over the integers
• long_extras.h – support functions for signed word arithmetic
• longlong.h – support functions for multi-word arithmetic
• mpn_extras.h – support functions for limb arrays
• aprcl.h – APRCL primality testing
• arith.h – arithmetic and special functions
• fft.h – Schoenhage-Strassen FFT
• qsieve.h – Quadratic sieve

Rational numbers

• fmpq.h – rational numbers
• fmpq_vec.h – vectors over rational numbers
• fmpq_mat.h – matrices over the rational numbers
• fmpq_poly.h – univariate polynomials over the rational numbers
• fmpq_mpoly.h – multivariate polynomials over the rational numbers
• fmpz_poly_q.h – rational functions over the rational numbers

Integers mod n

• nmod_vec.h – vectors over integers mod n (word-size n)
• nmod_mat.h – matrices over integers mod n (word-size n)
• nmod_poly.h – univariate polynomials over integers mod n (word-size n)
• nmod_poly_mat.h – matrices of univariate polynomials over integers mod n (word-size n)
• nmod_poly_factor.h – factorisation of univariate polynomials over integers mod n (word-size n)
• nmod_mpoly.h – multivariate polynomials over integers mod n (word-size n)
• fmpz_mod_poly.h – polynomials over integers mod n
• fmpz_mod_poly_factor.h – factorisation of polynomials over integers mod n

Finite fields

• fq.h – finite fields
• fq_vec.h – vectors over finite fields
• fq_mat.h – matrices over finite fields
• fq_poly.h – univariate polynomials over finite fields
• fq_poly_factor.h – factorisation of univariate polynomials over finite fields

• fq_nmod.h – finite fields (word-size characteristic)
• fq_nmod_vec.h – vectors over finite fields (word-size characteristic)
• fq_nmod_mat.h – matrices over finite fields (word-size characteristic)
• fq_nmod_poly.h – univariate polynomials over finite fields (word-size characteristic)
• fq_nmod_poly_factor.h – factorisation of univariate polynomials over finite fields (word-size characteristic)

• fq_zech.h – finite fields (Zech logarithm representation)
• fq_zech_vec.h – vectors over finite fields (Zech logarithm representation)
• fq_zech_mat.h – matrices over finite fields (Zech logarithm representation)
• fq_zech_poly.h – univariate polynomials over finite fields (Zech logarithm representation)
• fq_zech_poly_factor.h – factorisation of univariate polynomials over finite fields (Zech logarithm representation)

p-adic numbers

• padic.h – p-adic numbers
• padic_poly.h – polynomials over p-adic numbers
• padic_mat.h – matrices over p-adic numbers
• qadic.h – unramified extensions over p-adic numbers

Floating-point support code

• double_extras.h – support functions for double arithmetic
• d_vec.h – double precision vectors
• d_mat.h – double precision matrices
• mpf_vec.h – vectors of MPF floating-point numbers
• mpf_mat.h – matrices of MPF floating-point numbers
• mpfr_vec.h – vectors of MPFR floating-point numbers
• mpfr_mat.h – matrices of MPFR floating-point numbers