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galois

galois.Field

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mhostetter/galois

Getting Started
Basic Usage
Tutorials
Performance
Development
API Reference
Release Notes

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
- API Reference
  API Reference
- Galois Fields
  Galois Fields
  - Galois field classes
    
    Galois field classes
    
    Class factory functions
    
    Class factory functions
    
    galois.GF
    
    galois.Field
    
    galois.Field
    
    Fgalois.Field
    
    galois.Field galois.Field
    Table of contents
    
    Fgalois.Field
    
    Abstract base classes
    
    Abstract base classes
    
    galois.FieldArray
    
    Pre-made FieldArray subclasses
    
    Pre-made FieldArray subclasses
    
    galois.GF2
  - Prime field functions
    
    Prime field functions
    
    Primitive roots
    
    Primitive roots
    
    galois.primitive_root
    
    galois.primitive_roots
    
    galois.is_primitive_root
  - Extension field functions
    
    Extension field functions
    
    Irreducible polynomials
    
    Irreducible polynomials
    
    galois.irreducible_poly
    
    galois.irreducible_polys
    
    galois.is_irreducible
    
    Primitive polynomials
    
    Primitive polynomials
    
    galois.primitive_poly
    
    galois.primitive_polys
    
    galois.conway_poly
    
    galois.matlab_primitive_poly
    
    galois.is_primitive
    
    Primitive elements
    
    Primitive elements
    
    galois.primitive_element
    
    galois.primitive_elements
    
    galois.is_primitive_element
- Polynomials
  Polynomials
  - Polynomial classes
    
    Polynomial classes
    
    galois.Poly
  - Special polynomials
    
    Special polynomials
    
    Irreducible polynomials
    
    Irreducible polynomials
    
    galois.irreducible_poly
    
    galois.irreducible_polys
    
    Primitive polynomials
    
    Primitive polynomials
    
    galois.primitive_poly
    
    galois.primitive_polys
    
    galois.conway_poly
    
    galois.matlab_primitive_poly
    
    Interpolating polynomials
    
    Interpolating polynomials
    
    galois.lagrange_poly
  - Polynomial functions
    
    Polynomial functions
    
    Divisibility
    
    Divisibility
    
    galois.gcd
    
    galois.egcd
    
    galois.lcm
    
    galois.prod
    
    galois.are_coprime
    
    Congruences
    
    Congruences
    
    galois.crt
    
    Factorization
    
    Factorization
    
    galois.factors
    
    galois.square_free_factorization
    
    galois.distinct_degree_factorization
    
    galois.equal_degree_factorization
    
    Tests
    
    Tests
    
    galois.is_monic
    
    galois.is_irreducible
    
    galois.is_primitive
    
    galois.is_square_free
- Forward Error Correction
  Forward Error Correction
  - FEC classes
    
    FEC classes
    
    galois.BCH
    
    galois.ReedSolomon
  - Linear block code functions
    
    Linear block code functions
    
    galois.generator_to_parity_check_matrix
    
    galois.parity_check_to_generator_matrix
  - Cyclic code functions
    
    Cyclic code functions
    
    galois.bch_valid_codes
    
    galois.poly_to_generator_matrix
    
    galois.roots_to_parity_check_matrix
- Transforms
  Transforms
  - Number-theoretic transform
    
    Number-theoretic transform
    
    galois.ntt
    
    galois.intt
- Linear Sequences
  Linear Sequences
  - Linear-feedback shift registers
    
    Linear-feedback shift registers
    
    galois.FLFSR
    
    galois.GLFSR
  - Sequence analysis functions
    
    Sequence analysis functions
    
    galois.berlekamp_massey
- Number Theory
  Number Theory
  - Divisibility
    
    Divisibility
    
    galois.gcd
    
    galois.egcd
    
    galois.lcm
    
    galois.prod
    
    galois.euler_phi
    
    galois.totatives
    
    galois.are_coprime
  - Congruences
    
    Congruences
    
    galois.crt
    
    galois.primitive_root
    
    galois.primitive_roots
    
    galois.carmichael_lambda
    
    galois.legendre_symbol
    
    galois.jacobi_symbol
    
    galois.kronecker_symbol
    
    galois.is_primitive_root
    
    galois.is_cyclic
  - Integer arithmetic
    
    Integer arithmetic
    
    galois.isqrt
    
    galois.iroot
    
    galois.ilog
- Integer Factorization
  Integer Factorization
  - Prime factorization
    
    Prime factorization
    
    galois.factors
  - Composite factorization
    
    Composite factorization
    
    galois.divisors
    
    galois.divisor_sigma
  - Specific factorization algorithms
    
    Specific factorization algorithms
    
    galois.perfect_power
    
    galois.trial_division
    
    galois.pollard_p1
    
    galois.pollard_rho
  - Tests
    
    Tests
    
    galois.is_prime
    
    galois.is_prime_power
    
    galois.is_composite
    
    galois.is_perfect_power
    
    galois.is_square_free
    
    galois.is_smooth
    
    galois.is_powersmooth
- Primes
  Primes
  - Prime number generation
    
    Prime number generation
    
    galois.primes
    
    galois.kth_prime
    
    galois.prev_prime
    
    galois.next_prime
    
    galois.random_prime
    
    galois.mersenne_exponents
    
    galois.mersenne_primes
  - Primality tests
    
    Primality tests
    
    galois.is_prime
    
    galois.is_prime_power
    
    galois.is_perfect_power
    
    galois.is_composite
    
    galois.is_square_free
    
    galois.is_smooth
    
    galois.is_powersmooth
  - Specific primality tests
    
    Specific primality tests
    
    galois.fermat_primality_test
    
    galois.miller_rabin_primality_test
- Typing
  Typing
  - Array-related
    
    Array-related
    
    galois.typing.ElementLike
    
    galois.typing.IterableLike
    
    galois.typing.ArrayLike
    
    galois.typing.ShapeLike
    
    galois.typing.DTypeLike
  - Polynomial-related
    
    Polynomial-related
    
    galois.typing.PolyLike
Release Notes
Release Notes
- Versioning
- v0.0.27
- v0.0.26
- v0.0.25
- v0.0.24
- v0.0.23
- v0.0.22
- v0.0.21
- v0.0.20
- v0.0.19
- v0.0.18
- v0.0.17
- v0.0.16
- v0.0.15
- v0.0.14

Table of contents

Fgalois.Field

galois.Field¶

galois.Field()¶: Alias of GF().

Last update: Apr 18, 2022

Previous galois.typing

© Copyright 2020-2022, Matt Hostetter.

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