[−][src]Module maths_traits::algebra::ring_like
Traits
| Bezout | A trait for finding the Bezout coefficients of a pair of elements |
| BezoutDomain | A commutative ring where every pair of elements has a weighted sum to their GCD |
| CommutativeRing | A unital ring where multiplication is commutative |
| CommutativeSemiring | A unital semiring where multiplication is commutative |
| Distributive | A marker trait for stucts whose multiplication operation preserves addition,
ie |
| Divisibility | Common methods regarding multiplicative inverses in a ring or semiring |
| DivisionRing | A ring with a multiplicative inverse |
| DivisionSemiring | A semiring with a multiplicative inverse |
| Domain | A unital ring with no pairs of nonzero elements that multiply to zero |
| EuclideanDiv | A trait for performing division with with remainder |
| EuclideanDomain | A commutative ring with a division algorithm for dividing with a remainder |
| EuclideanSemidomain | A UF semidomain with a division algorithm for dividing with a remainder |
| Field | A set that is both an additive and multiplicative abelian group where multiplication distributes |
| GCD | A trait for finding the greatest common divisor and least common multiple of two elements |
| GCDDomain | A commutative ring where every pair of elements has a greatest common divisor |
| GCDSemidomain | An integral semidomain where every pair of elements has a greatest common divisor |
| IntegralDomain | A domain that is commutative |
| IntegralSemidomain | A semidomain that is commutative |
| NoZeroDivisors | A marker trait for semirings where there are no nonzero elements that multiply to zero |
| PID | An integral domain where every ideal is generated by one element |
| Primality | Methods for testing irreduciblity and primality |
| Ring | An additive abelian group with a distributive and associative multiplication operation |
| Semidomain | A unital semiring with no pairs of nonzero elements that multiply to zero |
| Semiring | A commutative and additive monoid with a distributive and associative multiplication operation |
| UFD | A commutative ring that is uniquely factorizable into irreducible (up to units) |
| UFSemidomain | A GCD semidomain where every pair of elements is uniquely factorizable into irreducible elements (up to units) |
| UniquelyFactorizable | A marker trait for semirings where each element's set of irreducible divisors is unique |
| UnitalRing | A ring with an identity element |
| UnitalSemiring | A semiring with an identity element |
Functions
| euclidean | Uses the Euclidean Algorithm to find the GCD of two ring elements using division with remainder |
| extended_euclidean | Uses the Extended Euclidean Algorithm to find the GCD of two ring elements and their bezout coefficients using division with remainder |
| miller_rabin | Determines if a given Natural number is prime using the Miller-Rabin primality test |