ntheory.h File Reference
#include <symengine/integer.h>
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Namespaces | |
| SymEngine | |
| Main namespace for SymEngine package. | |
Functions | |
| int | SymEngine::probab_prime_p (const Integer &a, unsigned reps=25) |
| Probabilistic Prime. | |
| RCP< const Integer > | SymEngine::nextprime (const Integer &a) |
| RCP< const Integer > | SymEngine::gcd (const Integer &a, const Integer &b) |
| Greatest Common Divisor. | |
| RCP< const Integer > | SymEngine::lcm (const Integer &a, const Integer &b) |
| Least Common Multiple. | |
| void | SymEngine::gcd_ext (const Ptr< RCP< const Integer >> &g, const Ptr< RCP< const Integer >> &s, const Ptr< RCP< const Integer >> &t, const Integer &a, const Integer &b) |
| Extended GCD. | |
| RCP< const Integer > | SymEngine::mod (const Integer &n, const Integer &d) |
| modulo round toward zero | |
| RCP< const Integer > | SymEngine::quotient (const Integer &n, const Integer &d) |
| void | SymEngine::quotient_mod (const Ptr< RCP< const Integer >> &q, const Ptr< RCP< const Integer >> &r, const Integer &n, const Integer &d) |
| RCP< const Integer > | SymEngine::mod_f (const Integer &n, const Integer &d) |
| modulo round toward -inf | |
| RCP< const Integer > | SymEngine::quotient_f (const Integer &n, const Integer &d) |
| void | SymEngine::quotient_mod_f (const Ptr< RCP< const Integer >> &q, const Ptr< RCP< const Integer >> &r, const Integer &n, const Integer &d) |
| int | SymEngine::mod_inverse (const Ptr< RCP< const Integer >> &b, const Integer &a, const Integer &m) |
| inverse modulo | |
| bool | SymEngine::crt (const Ptr< RCP< const Integer >> &R, const std::vector< RCP< const Integer >> &rem, const std::vector< RCP< const Integer >> &mod) |
| Chinese remainder function. Return true when a solution exists. | |
| RCP< const Integer > | SymEngine::fibonacci (unsigned long n) |
| Fibonacci number. | |
| void | SymEngine::fibonacci2 (const Ptr< RCP< const Integer >> &g, const Ptr< RCP< const Integer >> &s, unsigned long n) |
| Fibonacci n and n-1. | |
| RCP< const Integer > | SymEngine::lucas (unsigned long n) |
| Lucas number. | |
| void | SymEngine::lucas2 (const Ptr< RCP< const Integer >> &g, const Ptr< RCP< const Integer >> &s, unsigned long n) |
| Lucas number n and n-1. | |
| RCP< const Integer > | SymEngine::binomial (const Integer &n, unsigned long k) |
| Binomial Coefficient. | |
| RCP< const Integer > | SymEngine::factorial (unsigned long n) |
| Factorial. | |
| bool | SymEngine::divides (const Integer &a, const Integer &b) |
| int | SymEngine::factor (const Ptr< RCP< const Integer >> &f, const Integer &n, double B1) |
| int | SymEngine::factor_trial_division (const Ptr< RCP< const Integer >> &f, const Integer &n) |
| int | SymEngine::factor_lehman_method (const Ptr< RCP< const Integer >> &f, const Integer &n) |
| Factor using lehman's methods. | |
| int | SymEngine::factor_pollard_pm1_method (const Ptr< RCP< const Integer >> &f, const Integer &n, unsigned B=10, unsigned retries=5) |
| Factor using Pollard's p-1 method. | |
| int | SymEngine::factor_pollard_rho_method (const Ptr< RCP< const Integer >> &f, const Integer &n, unsigned retries=5) |
| Factor using Pollard's rho methods. | |
| void | SymEngine::prime_factors (std::vector< RCP< const Integer >> &primes, const Integer &n) |
Find prime factors of n | |
| void | SymEngine::prime_factor_multiplicities (map_integer_uint &primes, const Integer &n) |
Find multiplicities of prime factors of n | |
| RCP< const Number > | SymEngine::bernoulli (unsigned long n) |
| RCP< const Number > | SymEngine::harmonic (unsigned long n, long m=1) |
| Computes the sum of the inverses of the first perfect mth powers. | |
| bool | SymEngine::primitive_root (const Ptr< RCP< const Integer >> &g, const Integer &n) |
| Computes a primitive root. Returns false if no primitive root exists. | |
| void | SymEngine::primitive_root_list (std::vector< RCP< const Integer >> &roots, const Integer &n) |
| RCP< const Integer > | SymEngine::totient (const RCP< const Integer > &n) |
| Euler's totient function. | |
| RCP< const Integer > | SymEngine::carmichael (const RCP< const Integer > &n) |
| Carmichael function. | |
| bool | SymEngine::multiplicative_order (const Ptr< RCP< const Integer >> &o, const RCP< const Integer > &a, const RCP< const Integer > &n) |
| Multiplicative order. Return false if order does not exist. | |
| int | SymEngine::legendre (const Integer &a, const Integer &n) |
| Legendre Function. | |
| int | SymEngine::jacobi (const Integer &a, const Integer &n) |
| Jacobi Function. | |
| int | SymEngine::kronecker (const Integer &a, const Integer &n) |
| Kronecker Function. | |
| void | SymEngine::nthroot_mod_list (std::vector< RCP< const Integer >> &roots, const RCP< const Integer > &a, const RCP< const Integer > &n, const RCP< const Integer > &m) |
| All Solutions to x**n == a mod m. Return false if none exists. | |
| bool | SymEngine::nthroot_mod (const Ptr< RCP< const Integer >> &root, const RCP< const Integer > &a, const RCP< const Integer > &n, const RCP< const Integer > &m) |
| A solution to x**n == a mod m. Return false if none exists. | |
| bool | SymEngine::powermod (const Ptr< RCP< const Integer >> &powm, const RCP< const Integer > &a, const RCP< const Number > &b, const RCP< const Integer > &m) |
| void | SymEngine::powermod_list (std::vector< RCP< const Integer >> &pows, const RCP< const Integer > &a, const RCP< const Number > &b, const RCP< const Integer > &m) |
| vec_integer_class | SymEngine::quadratic_residues (const Integer &a) |
| Finds all Quadratic Residues of a Positive Integer. | |
| bool | SymEngine::is_quad_residue (const Integer &a, const Integer &p) |
| Returns true if 'a' is a quadratic residue of 'p'. | |
| bool | SymEngine::is_nth_residue (const Integer &a, const Integer &n, const Integer &mod) |
| Returns true if 'a' is a nth power residue of 'mod'. | |
| int | SymEngine::mobius (const Integer &a) |
| Mobius Function. | |
| long | SymEngine::mertens (const unsigned long a) |
| integer_class | SymEngine::mp_polygonal_number (const integer_class &s, const integer_class &n) |
| Numeric calculation of the n:th s-gonal number. More... | |
| integer_class | SymEngine::mp_principal_polygonal_root (const integer_class &s, const integer_class &x) |
| Numeric calculation of the principal s-gonal root of x. More... | |
| std::pair< integer_class, integer_class > | SymEngine::mp_perfect_power_decomposition (const integer_class &n, bool lowest_exponent=false) |
| Decompose a positive integer into perfect powers. More... | |
Detailed Description
Basic number theory functions
Definition in file ntheory.h.