Skip to content
You're not viewing the latest version. Click here to go to latest.
logo
galois
galois.kronecker_symbol
Initializing search
    mhostetter/galois
    • Getting Started
    • Basic Usage
    • Tutorials
    • Performance
    • Development
    • API Reference
    • Release Notes
    mhostetter/galois
      • Getting Started
      • Galois Field Classes
      • Compilation Modes
      • Field Element Representation
      • Array Creation
      • Array Arithmetic
      • Linear Algebra
      • Polynomial Creation
      • Polynomial Arithmetic
      • Intro to Prime Fields
      • Intro to Extension Fields
      • Prime Fields
      • Binary Extension Fields
      • Benchmarks
      • Installation
      • Linter
      • Unit Tests
      • Documentation
      • API Reference
        • Class factory functions
          • galois.Field
          • galois.GF
        • Classes
          • galois.BCH
          • galois.FLFSR
          • galois.FieldArray
          • galois.FieldClass
          • galois.GF2
          • galois.GLFSR
          • galois.Poly
          • galois.ReedSolomon
        • Functions
          • galois.are_coprime
          • galois.bch_valid_codes
          • galois.berlekamp_massey
          • galois.carmichael_lambda
          • galois.conway_poly
          • galois.crt
          • galois.distinct_degree_factorization
          • galois.divisor_sigma
          • galois.divisors
          • galois.egcd
          • galois.equal_degree_factorization
          • galois.euler_phi
          • galois.factors
          • galois.fermat_primality_test
          • galois.gcd
          • galois.generator_to_parity_check_matrix
          • galois.ilog
          • galois.intt
          • galois.iroot
          • galois.irreducible_poly
          • galois.irreducible_polys
          • galois.is_composite
          • galois.is_cyclic
          • galois.is_irreducible
          • galois.is_monic
          • galois.is_perfect_power
          • galois.is_powersmooth
          • galois.is_prime
          • galois.is_prime_power
          • galois.is_primitive
          • galois.is_primitive_element
          • galois.is_primitive_root
          • galois.is_smooth
          • galois.is_square_free
          • galois.isqrt
          • galois.jacobi_symbol
          • galois.kronecker_symbol
            • Fgalois.kronecker_symbol
              • Parameters
                • pa
                • pn
              • Returns
              • Return type
          • galois.kth_prime
          • galois.lagrange_poly
          • galois.lcm
          • galois.legendre_symbol
          • galois.matlab_primitive_poly
          • galois.mersenne_exponents
          • galois.mersenne_primes
          • galois.miller_rabin_primality_test
          • galois.next_prime
          • galois.ntt
          • galois.parity_check_to_generator_matrix
          • galois.perfect_power
          • galois.pollard_p1
          • galois.pollard_rho
          • galois.poly_to_generator_matrix
          • galois.prev_prime
          • galois.primes
          • galois.primitive_element
          • galois.primitive_elements
          • galois.primitive_poly
          • galois.primitive_polys
          • galois.primitive_root
          • galois.primitive_roots
          • galois.prod
          • galois.random_prime
          • galois.roots_to_parity_check_matrix
          • galois.square_free_factorization
          • galois.totatives
          • galois.trial_division
      • Galois Fields
        • Galois field classes
          • Class factory functions
            • galois.GF
            • galois.Field
          • Abstract base classes
            • galois.FieldArray
            • galois.FieldClass
          • Pre-made Galois field array classes
            • galois.GF2
        • Prime field functions
          • Primitive roots
            • galois.primitive_root
            • galois.primitive_roots
            • galois.is_primitive_root
        • Extension field functions
          • Irreducible polynomials
            • galois.irreducible_poly
            • galois.irreducible_polys
            • galois.is_irreducible
          • Primitive polynomials
            • galois.primitive_poly
            • galois.primitive_polys
            • galois.conway_poly
            • galois.matlab_primitive_poly
            • galois.is_primitive
          • Primitive elements
            • galois.primitive_element
            • galois.primitive_elements
            • galois.is_primitive_element
      • Polynomials
        • Polynomial classes
          • galois.Poly
        • Special polynomials
          • Irreducible polynomials
            • galois.irreducible_poly
            • galois.irreducible_polys
          • Primitive polynomials
            • galois.primitive_poly
            • galois.primitive_polys
            • galois.conway_poly
            • galois.matlab_primitive_poly
          • Interpolating polynomials
            • galois.lagrange_poly
        • Polynomial functions
          • Divisibility
            • galois.gcd
            • galois.egcd
            • galois.lcm
            • galois.prod
            • galois.are_coprime
          • Congruences
            • galois.crt
          • Factorization
            • galois.factors
            • galois.square_free_factorization
            • galois.distinct_degree_factorization
            • galois.equal_degree_factorization
          • Tests
            • galois.is_monic
            • galois.is_irreducible
            • galois.is_primitive
            • galois.is_square_free
      • Forward Error Correction
        • FEC classes
          • galois.BCH
          • galois.ReedSolomon
        • Linear block code functions
          • galois.generator_to_parity_check_matrix
          • galois.parity_check_to_generator_matrix
        • Cyclic code functions
          • galois.bch_valid_codes
          • galois.poly_to_generator_matrix
          • galois.roots_to_parity_check_matrix
      • Transforms
        • Number-theoretic transform
          • galois.ntt
          • galois.intt
      • Linear Sequences
        • Linear-feedback shift registers
          • galois.FLFSR
          • galois.GLFSR
        • Sequence analysis functions
          • galois.berlekamp_massey
      • Number Theory
        • Divisibility
          • galois.gcd
          • galois.egcd
          • galois.lcm
          • galois.prod
          • galois.euler_phi
          • galois.totatives
          • galois.are_coprime
        • Congruences
          • galois.crt
          • galois.primitive_root
          • galois.primitive_roots
          • galois.carmichael_lambda
          • galois.legendre_symbol
          • galois.jacobi_symbol
          • galois.kronecker_symbol
            • Fgalois.kronecker_symbol
              • Parameters
                • pa
                • pn
              • Returns
              • Return type
          • galois.kronecker_symbol
            • Fgalois.kronecker_symbol
              • Parameters
                • pa
                • pn
              • Returns
              • Return type
          • galois.is_primitive_root
          • galois.is_cyclic
        • Integer arithmetic
          • galois.isqrt
          • galois.iroot
          • galois.ilog
      • Integer Factorization
        • Prime factorization
          • galois.factors
        • Composite factorization
          • galois.divisors
          • galois.divisor_sigma
        • Specific factorization algorithms
          • galois.perfect_power
          • galois.trial_division
          • galois.pollard_p1
          • galois.pollard_rho
        • 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
        • 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
          • 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
          • galois.fermat_primality_test
          • galois.miller_rabin_primality_test
      • Versioning
      • 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
    • Fgalois.kronecker_symbol
      • Parameters
        • pa
        • pn
      • Returns
      • Return type

    galois.kronecker_symbol¶

    galois.kronecker_symbol(a, n)¶

    Computes the Kronecker symbol \((\frac{a}{n})\).

    The Kronecker symbol extends the Jacobi symbol for all \(n\).

    Parameters¶
    a : int¶

    An integer.

    n : int¶

    An integer.

    Returns¶

    The Kronecker symbol \((\frac{a}{n})\) with value in \(\{0, -1, 1\}\).

    Return type¶

    int

    See also

    legendre_symbol, jacobi_symbol

    References

    • Algorithm 2.149 from https://cacr.uwaterloo.ca/hac/about/chap2.pdf


    Last update: Feb 09, 2022
    Back to top
    Previous galois.jacobi_symbol
    Next galois.kth_prime
    © Copyright 2020-2022, Matt Hostetter.
    Created using Sphinx 5.3.0. and Sphinx-Immaterial