FieldOfFractionsGCD
Field defined as a field of fractions with a default implementation of GCD/LCM such that
- gcd(a/b, c/d) = gcd(a, c) / lcm(b, d)
- lcm(a/b, c/d) = lcm(a, c) / gcd(b, d)
which corresponds to the convention of the GCD domains of SageMath; on rational numbers, it "yields the unique extension of gcd from integers to rationals presuming the natural extension of the divisibility relation from integers to rationals", see http://math.stackexchange.com/a/151431
Value members
Concrete methods
Inherited methods
- Definition Classes
- AdditiveCommutativeGroup -> AdditiveCommutativeMonoid -> AdditiveCommutativeSemigroup -> AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
- Inherited from
- AdditiveCommutativeGroup
Convert the given BigInt to an instance of A.
Convert the given BigInt to an instance of A.
This is equivalent to n repeated summations of this ring's one, or
-n summations of -one if n is negative.
Most type class instances should consider overriding this method for performance reasons.
- Inherited from
- Ring
This is implemented in terms of basic Field ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method be overriden.
This is implemented in terms of basic Field ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method be overriden.
This is possible because a Double is a rational number.
- Inherited from
- Field
Convert the given integer to an instance of A.
Convert the given integer to an instance of A.
Defined to be equivalent to sumN(one, n).
That is, n repeated summations of this ring's one, or -n
summations of -one if n is negative.
Most type class instances should consider overriding this method for performance reasons.
- Inherited from
- Ring
- Definition Classes
- MultiplicativeCommutativeGroup -> MultiplicativeCommutativeMonoid -> MultiplicativeCommutativeSemigroup -> MultiplicativeGroup -> MultiplicativeMonoid -> MultiplicativeSemigroup
- Inherited from
- MultiplicativeCommutativeGroup
- Definition Classes
- MultiplicativeGroup -> MultiplicativeMonoid -> MultiplicativeSemigroup
- Inherited from
- MultiplicativeGroup
Given a sequence of as, compute the product.
Given a sequence of as, compute the product.
- Inherited from
- MultiplicativeMonoid
Given a sequence of as, compute the sum.
Given a sequence of as, compute the sum.
- Inherited from
- AdditiveMonoid
- Definition Classes
- AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
- Inherited from
- AdditiveGroup
- Definition Classes
- MultiplicativeMonoid -> MultiplicativeSemigroup
- Inherited from
- MultiplicativeMonoid