| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Plankton.Field
Description
Field classes
- class (MultiplicativeInvertible a, Ring a) => Semifield a
- class (AdditiveGroup a, MultiplicativeGroup a, Ring a) => Field a
- class Field a => ExpField a where
- class Field a => QuotientField a where
- class Field a => BoundedField a where
- infinity :: BoundedField a => a
- neginfinity :: BoundedField a => a
- class (Ord a, Field a) => TrigField a where
Documentation
class (MultiplicativeInvertible a, Ring a) => Semifield a Source #
A Semifield is a Field without Commutative Multiplication.
class (AdditiveGroup a, MultiplicativeGroup a, Ring a) => Field a Source #
A Field is a Ring plus additive invertible and multiplicative invertible operations.
A summary of the rules inherited from super-classes of Field
zero + a == a a + zero == a (a + b) + c == a + (b + c) a + b == b + a a - a = zero negate a = zero - a negate a + a = zero a + negate a = zero one * a == a a * one == a (a * b) * c == a * (b * c) a * (b + c) == a * b + a * c (a + b) * c == a * c + b * c a * zero == zero zero * a == zero a * b == b * a a / a = one recip a = one / a recip a * a = one a * recip a = one
class Field a => ExpField a where Source #
A hyperbolic field class
sqrt . (**2) == identity log . exp == identity for +ive b, a != 0,1: a ** logBase a b ≈ b
class Field a => QuotientField a where Source #
quotient fields explode constraints if they allow for polymorphic integral types
a - one < floor a <= a <= ceiling a < a + one round a == floor (a + one/(one+one))
Instances
class Field a => BoundedField a where Source #
A bounded field includes the concepts of infinity and NaN, thus moving away from error throwing.
one / zero + infinity == infinity infinity + a == infinity isNaN (infinity - infinity) isNaN (infinity / infinity) isNaN (nan + a) zero / zero != nan
Note the tricky law that, although nan is assigned to zero/zero, they are never-the-less not equal. A committee decided this.
Minimal complete definition
Instances
| BoundedField Double Source # | |
| BoundedField Float Source # | |
| BoundedField a => BoundedField (Complex a) Source # | todo: work out boundings for complex as it stands now, complex is different eg one / (zero :: Complex Float) == nan |
infinity :: BoundedField a => a Source #
prints as Infinity
neginfinity :: BoundedField a => a Source #
prints as `-Infinity`