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galois

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mhostetter/galois

Getting Started
Basic Usage
Tutorials
Performance
Development
API Reference
Release Notes
Index

galois

mhostetter/galois

Getting Started
Getting Started
- Getting Started
Basic Usage
Basic Usage
Tutorials
Tutorials
- Intro to Prime Fields
- Intro to Extension Fields
Performance
Performance
Development
Development
API Reference
API Reference
- Arrays
  Arrays
  - C Array
    
    Array
    
    Constructors
    
    Constructors
    
    M Identity
    
    M Ones
    
    M Random
    
    M Range
    
    M Zeros
    
    Methods
    
    Methods
    
    M compile
    
    M repr
    
    Properties
    
    Properties
    
    P characteristic
    
    P default_ufunc_mode
    
    P degree
    
    P dtypes
    
    P element_repr
    
    P elements
    
    P irreducible_poly
    
    P name
    
    P order
    
    P primitive_element
    
    P ufunc_mode
    
    P ufunc_modes
    
    P units
  - V ArrayLike
  - V DTypeLike
  - V ElementLike
  - V IterableLike
  - V ShapeLike
- Galois fields
  Galois fields
  - C FieldArray
    
    FieldArray
    
    Constructors
    
    Constructors
    
    M __init__
    
    M Identity
    
    M Ones
    
    M Random
    
    M Range
    
    M Vandermonde
    
    M Zeros
    
    Conversions
    
    Conversions
    
    M Vector
    
    M vector
    
    Elements
    
    Elements
    
    P elements
    
    P non_squares
    
    P normal_element
    
    P normal_elements
    
    P primitive_element
    
    P primitive_elements
    
    M primitive_root_of_unity
    
    M primitive_roots_of_unity
    
    P squares
    
    P units
    
    String representation
    
    String representation
    
    M __repr__
    
    M __str__
    
    M arithmetic_table
    
    P properties
    
    M repr_table
    
    Element representation
    
    Element representation
    
    P element_repr
    
    M repr
    
    Arithmetic compilation
    
    Arithmetic compilation
    
    P default_ufunc_mode
    
    P dtypes
    
    P ufunc_mode
    
    P ufunc_modes
    
    M compile
    
    Methods
    
    Methods
    
    M additive_order
    
    M characteristic_poly
    
    M field_norm
    
    M field_trace
    
    M log
    
    M minimal_poly
    
    M multiplicative_order
    
    Linear algebra
    
    Linear algebra
    
    M column_space
    
    M left_null_space
    
    M lu_decompose
    
    M null_space
    
    M plu_decompose
    
    M row_reduce
    
    M row_space
    
    Properties
    
    Properties
    
    P characteristic
    
    P degree
    
    P irreducible_poly
    
    P name
    
    P order
    
    P prime_subfield
    
    Attributes
    
    Attributes
    
    P is_extension_field
    
    P is_prime_field
    
    P is_primitive_poly
    
    M is_square
  - C GF2
    
    GF2
    
    Elements
    
    Elements
    
    P elements
    
    P non_squares
    
    P normal_element
    
    P normal_elements
    
    P primitive_element
    
    P primitive_elements
    
    P squares
    
    P units
    
    String representation
    
    String representation
    
    P properties
    
    Element representation
    
    Element representation
    
    P element_repr
    
    Arithmetic compilation
    
    Arithmetic compilation
    
    P default_ufunc_mode
    
    P dtypes
    
    P ufunc_mode
    
    P ufunc_modes
    
    Properties
    
    Properties
    
    P characteristic
    
    P degree
    
    P irreducible_poly
    
    P name
    
    P order
    
    P prime_subfield
    
    Attributes
    
    Attributes
    
    P is_extension_field
    
    P is_prime_field
    
    P is_primitive_poly
  - F Field
  - F GF
  - Primitive elements
    
    Primitive elements
    
    F primitive_element
    
    F primitive_elements
    
    F is_primitive_element
  - Normal elements
    
    Normal elements
    
    F normal_element
    
    F normal_elements
    
    F is_normal_element
- Polynomials
  Polynomials
  - C Poly
    
    Poly
    
    Constructors
    
    Constructors
    
    M __init__
    
    M Degrees
    
    M Identity
    
    M Int
    
    M Like
    
    M One
    
    M Random
    
    M Roots
    
    M Str
    
    M Zero
    
    Special methods
    
    Special methods
    
    M __call__
    
    M __eq__
    
    M __int__
    
    M __len__
    
    String representation
    
    String representation
    
    M __repr__
    
    M __str__
    
    Methods
    
    Methods
    
    M derivative
    
    M reverse
    
    M roots
    
    Factorization methods
    
    Factorization methods
    
    M distinct_degree_factors
    
    M equal_degree_factors
    
    M factors
    
    M square_free_factors
    
    Coefficients
    
    Coefficients
    
    M coefficients
    
    P coeffs
    
    P degrees
    
    P nonzero_coeffs
    
    P nonzero_degrees
    
    Properties
    
    Properties
    
    P degree
    
    P field
    
    Attributes
    
    Attributes
    
    M is_conway
    
    M is_conway_consistent
    
    M is_irreducible
    
    P is_monic
    
    M is_primitive
    
    M is_square_free
  - V PolyLike
  - Irreducible polynomials
    
    Irreducible polynomials
    
    F irreducible_poly
    
    F irreducible_polys
  - Primitive polynomials
    
    Primitive polynomials
    
    F conway_poly
    
    F matlab_primitive_poly
    
    F primitive_poly
    
    F primitive_polys
  - Interpolating polynomials
    
    Interpolating polynomials
    
    F lagrange_poly
- Forward error correction
  Forward error correction
  - C BCH
    
    BCH
    
    Constructors
    
    Constructors
    
    M __init__
    
    String representation
    
    String representation
    
    M __repr__
    
    M __str__
    
    Methods
    
    Methods
    
    M decode
    
    M detect
    
    M encode
    
    Properties
    
    Properties
    
    P d
    
    P extension_field
    
    P field
    
    P k
    
    P n
    
    P t
    
    Attributes
    
    Attributes
    
    P is_narrow_sense
    
    P is_primitive
    
    P is_systematic
    
    Matrices
    
    Matrices
    
    P G
    
    P H
    
    Polynomials
    
    Polynomials
    
    P alpha
    
    P c
    
    P generator_poly
    
    P parity_check_poly
    
    P roots
  - C ReedSolomon
    
    ReedSolomon
    
    Constructors
    
    Constructors
    
    M __init__
    
    String representation
    
    String representation
    
    M __repr__
    
    M __str__
    
    Methods
    
    Methods
    
    M decode
    
    M detect
    
    M encode
    
    Properties
    
    Properties
    
    P c
    
    P d
    
    P field
    
    P k
    
    P n
    
    P t
    
    Attributes
    
    Attributes
    
    P is_narrow_sense
    
    P is_primitive
    
    P is_systematic
    
    Matrices
    
    Matrices
    
    P G
    
    P H
    
    Polynomials
    
    Polynomials
    
    P alpha
    
    P generator_poly
    
    P parity_check_poly
    
    P roots
- Linear sequences
  Linear sequences
  - C FLFSR
    
    FLFSR
    
    Constructors
    
    Constructors
    
    M __init__
    
    M Taps
    
    String representation
    
    String representation
    
    M __repr__
    
    M __str__
    
    Methods
    
    Methods
    
    M reset
    
    M step
    
    M to_galois_lfsr
    
    Properties
    
    Properties
    
    P field
    
    P order
    
    P taps
    
    Polynomials
    
    Polynomials
    
    P characteristic_poly
    
    P feedback_poly
    
    State
    
    State
    
    P initial_state
    
    P state
  - C GLFSR
    
    GLFSR
    
    Constructors
    
    Constructors
    
    M __init__
    
    M Taps
    
    String representation
    
    String representation
    
    M __repr__
    
    M __str__
    
    Methods
    
    Methods
    
    M reset
    
    M step
    
    M to_fibonacci_lfsr
    
    Properties
    
    Properties
    
    P field
    
    P order
    
    P taps
    
    Polynomials
    
    Polynomials
    
    P characteristic_poly
    
    P feedback_poly
    
    State
    
    State
    
    P initial_state
    
    P state
  - F berlekamp_massey
- Transforms
  Transforms
  - F intt
  - F ntt
- Number theory
  Number theory
  - Divisibility
    
    Divisibility
    
    F are_coprime
    
    F egcd
    
    F euler_phi
    
    F gcd
    
    F lcm
    
    F mobius
    
    F prod
    
    F totatives
  - Congruences
    
    Congruences
    
    F carmichael_lambda
    
    F crt
    
    F jacobi_symbol
    
    F kronecker_symbol
    
    F legendre_symbol
    
    F is_cyclic
  - Primitive roots
    
    Primitive roots
    
    F primitive_root
    
    F primitive_roots
    
    F is_primitive_root
  - Integer arithmetic
    
    Integer arithmetic
    
    F ilog
    
    F iroot
    
    F isqrt
- Factorization
  Factorization
  - Prime factorization
    
    Prime factorization
    
    F factors
  - Composite factorization
    
    Composite factorization
    
    F divisor_sigma
    
    F divisors
  - Specific factorization algorithms
    
    Specific factorization algorithms
    
    F perfect_power
    
    F pollard_p1
    
    F pollard_rho
    
    F trial_division
- Primes
  Primes
  - Prime number generation
    
    Prime number generation
    
    F kth_prime
    
    F mersenne_exponents
    
    F mersenne_primes
    
    F next_prime
    
    F prev_prime
    
    F primes
    
    F random_prime
  - Primality tests
    
    Primality tests
    
    F is_composite
    
    F is_perfect_power
    
    F is_powersmooth
    
    F is_prime
    
    F is_prime_power
    
    F is_smooth
    
    F is_square_free
  - Specific primality tests
    
    Specific primality tests
    
    F fermat_primality_test
    
    F miller_rabin_primality_test
- Configuration
  Configuration
Release Notes
Release Notes
- Versioning
- Unreleased Unreleased
  Table of contents
  - Changes currently on develop
- v0.4
- v0.3
- v0.2
- v0.1
- v0.0
Index
Index
- Index

Table of contents

Changes currently on develop

Unreleased¶

Changes currently on `develop`¶

Breaking changes¶

…

Features¶

…

Fixes¶

…

Documentation¶

…

Contributors¶

Matt Hostetter (@mhostetter)

Jan 02, 2026

© Copyright 2020-2025, Matt Hostetter.

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