Python-FLINT

Python extension module wrapping FLINT (Fast Library for Number Theory) and Arb (arbitrary-precision ball arithmetic). Features:

• Integers, rationals, integers mod n

• Real and complex numbers with rigorous error tracking

• Polynomials and matrices over all the above types

• Lots of mathematical functions

Author: Fredrik Johansson <fredrik.johansson@gmail.com>

Repository: https://github.com/flintlib/python-flint/

Introduction

• Install
  • Install with pip or conda
  • Fully supported platforms
  • Platforms without binaries
  • Unsupported platforms
  • Testing your installation
• General concepts
  • Importing
  • Global context
  • Types and methods
  • Mutability
  • Crashing and burning
  • Inexact numbers and numerical evaluation
  • Power series
• Install/Build from source
  • Simple build instructions
  • Compatibility and supported versions
  • Installing python-flint from source
  • Installing older versions from source
  • Installing the dependencies
  • Installing from source on Windows
  • Using FLINT from a non-standard location
  • Installing in editable mode
• Development workflow
  • Outline of building python-flint for development
  • Building and installing dependencies locally
  • Meson and spin
  • Setting up the development environment
  • Common development tasks
  • Measuring code coverage
  • Building in release mode
  • Differences between meson and autotools

Reference

Scalar types

• fmpz – integers
• fmpq – rational numbers
• fmpz_mod – integers mod n
• nmod – integers mod wordsize n
• fq_default – finite fields
• arb – real numbers
• acb – complex numbers
• dirichlet_char – Dirichlet characters

Matrix types

• fmpz_mat – matrices over integers
• fmpq_mat – matrices over rational numbers
• nmod_mat – matrices over integers mod n
• fmpz_mod_mat – matrices over integers mod n for arbitrary n
• arb_mat – matrices over real numbers
• acb_mat – matrices over complex numbers
• acb_theta – Riemann theta functions

Polynomial types

• fmpz_poly – polynomials over integers
• fmpz_mpoly – multivariate polynomials over the integers
• fmpq_poly – polynomials over rational numbers
• fmpq_mpoly – multivariate polynomials over the rational numbers
• nmod_poly – polynomials over integers mod n
• nmod_mpoly – multivariate polynomials over the integers mod n (word-size n)
• fmpz_mod_poly – polynomials over integers mod n
• fmpz_mod_mpoly – multivariate polynomials over the integers mod n
• fq_default_poly – polynomials over finite fields
• arb_poly – polynomials over real numbers
• acb_poly – polynomials over complex numbers

Power series types

• fmpz_series – power series over integers
• fmpq_series – power series over rational numbers
• nmod_series – power series over integers mod n
• arb_series – power series over real numbers
• acb_series – power series over complex numbers

Experimental generic rings interface

• _gr – generic rings (unstable interface)
  • gr_ctx
  • gr_scalar_ctx
  • gr_poly_ctx
  • gr_mpoly_ctx
  • _gr_fmpz_ctx
  • _gr_fmpq_ctx
  • _gr_fmpzi_ctx
  • _gr_fexpr_ctx
  • gr_nmod_ctx
  • gr_fmpz_mod_ctx
  • gr_fq_ctx
  • gr_fq_nmod_ctx
  • gr_fq_zech_ctx
  • gr_nf_ctx
  • gr_nf_fmpz_poly_ctx
  • gr_real_qqbar_ctx
  • gr_complex_qqbar_ctx
  • gr_real_ca_ctx
  • gr_complex_ca_ctx
  • gr_real_algebraic_ca_ctx
  • gr_complex_algebraic_ca_ctx
  • gr_complex_extended_ca_ctx
  • gr_real_float_arf_ctx
  • gr_complex_float_acf_ctx
  • gr_real_arb_ctx
  • gr_complex_acb_ctx
  • gr_gr_poly_ctx
  • gr_gr_mpoly_ctx
  • gr_series_ctx
  • gr