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| Synopsis |
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| (+) :: C a => a -> a -> a | | | (-) :: C a => a -> a -> a | | | negate :: C a => a -> a | | | zero :: C a => a | | | subtract :: C a => a -> a -> a | | | sum :: C a => [a] -> a | | | sum1 :: C a => [a] -> a | | | isZero :: C a => a -> Bool | | | (*) :: C a => a -> a -> a | | | one :: C a => a | | | fromInteger :: C a => Integer -> a | | | (^) :: C a => a -> Integer -> a | | | ringPower :: (C a, C b) => b -> a -> a | | | sqr :: C a => a -> a | | | product :: C a => [a] -> a | | | product1 :: C a => [a] -> a | | | div :: C a => a -> a -> a | | | mod :: C a => a -> a -> a | | | divMod :: C a => a -> a -> (a, a) | | | divides :: (C a, C a) => a -> a -> Bool | | | even :: (C a, C a) => a -> Bool | | | odd :: (C a, C a) => a -> Bool | | | (/) :: C a => a -> a -> a | | | recip :: C a => a -> a | | | fromRational' :: C a => Rational -> a | | | (^-) :: C a => a -> Integer -> a | | | fieldPower :: (C a, C b) => b -> a -> a | | | fromRational :: C a => Rational -> a | | | (^/) :: C a => a -> Rational -> a | | | sqrt :: C a => a -> a | | | pi :: C a => a | | | exp :: C a => a -> a | | | log :: C a => a -> a | | | logBase :: C a => a -> a -> a | | | (**) :: C a => a -> a -> a | | | sin :: C a => a -> a | | | cos :: C a => a -> a | | | tan :: C a => a -> a | | | asin :: C a => a -> a | | | acos :: C a => a -> a | | | atan :: C a => a -> a | | | sinh :: C a => a -> a | | | cosh :: C a => a -> a | | | tanh :: C a => a -> a | | | asinh :: C a => a -> a | | | acosh :: C a => a -> a | | | atanh :: C a => a -> a | | | abs :: C a => a -> a | | | signum :: C a => a -> a | | | quot :: C a => a -> a -> a | | | rem :: C a => a -> a -> a | | | quotRem :: C a => a -> a -> (a, a) | | | splitFraction :: (C a, C b) => a -> (b, a) | | | fraction :: C a => a -> a | | | truncate :: (C a, C b) => a -> b | | | round :: (C a, C b) => a -> b | | | ceiling :: (C a, C b) => a -> b | | | floor :: (C a, C b) => a -> b | | | approxRational :: (C a, C a) => a -> a -> Rational | | | atan2 :: C a => a -> a -> a | | | toRational :: C a => a -> Rational | | | toInteger :: C a => a -> Integer | | | fromIntegral :: (C a, C b) => a -> b | | | reduceRepeated :: (a -> a -> a) -> a -> a -> Integer -> a | | | isUnit :: C a => a -> Bool | | | stdAssociate :: C a => a -> a | | | stdUnit :: C a => a -> a | | | stdUnitInv :: C a => a -> a | | | extendedGCD :: C a => a -> a -> (a, (a, a)) | | | gcd :: C a => a -> a -> a | | | lcm :: C a => a -> a -> a | | | euclid :: (C a, C a) => (a -> a -> a) -> a -> a -> a | | | extendedEuclid :: (C a, C a) => (a -> a -> (a, a)) -> a -> a -> (a, (a, a)) | | | type Rational = T Integer | | | (%) :: C a => a -> a -> T a | | | numerator :: T a -> a | | | denominator :: T a -> a | | | data Integer | | | data Int | | | data Float | | | data Double | | | (*>) :: C a b => a -> b -> b |
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| Documentation |
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| add and subtract elements
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| inverse with respect to +
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| zero element of the vector space
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| subtract :: C a => a -> a -> a | Source |
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| subtract is (-) with swapped operand order.
This is the operand order which will be needed in most cases
of partial application.
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| Sum up all elements of a list.
An empty list yields zero.
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| Sum up all elements of a non-empty list.
This avoids including a zero which is useful for types
where no universal zero is available.
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The exponent has fixed type Integer in order
to avoid an arbitrarily limitted range of exponents,
but to reduce the need for the compiler to guess the type (default type).
In practice the exponent is most oftenly fixed, and is most oftenly 2.
Fixed exponents can be optimized away and
thus the expensive computation of Integers doesn't matter.
The previous solution used a Algebra.ToInteger.C constrained type
and the exponent was converted to Integer before computation.
So the current solution is not less efficient.
A variant of ^ with more flexibility is provided by Algebra.Core.ringPower.
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| ringPower :: (C a, C b) => b -> a -> a | Source |
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A prefix function of '(Algebra.Ring.^)'
with a parameter order that fits the needs of partial application
and function composition.
It has generalised exponent.
See: Argument order of expNat on
http://www.haskell.org/pipermail/haskell-cafe/2006-September/018022.html
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| divMod :: C a => a -> a -> (a, a) | Source |
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| fieldPower :: (C a, C b) => b -> a -> a | Source |
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| A prefix function of '(Algebra.Field.^-)'.
It has a generalised exponent.
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| Needed to work around shortcomings in GHC.
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| logBase :: C a => a -> a -> a | Source |
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| quotRem :: C a => a -> a -> (a, a) | Source |
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| splitFraction :: (C a, C b) => a -> (b, a) | Source |
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| TODO: Should be moved to a continued fraction module.
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| Lossless conversion from any representation of a rational to Rational
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| fromIntegral :: (C a, C b) => a -> b | Source |
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| stdAssociate :: C a => a -> a | Source |
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| extendedGCD :: C a => a -> a -> (a, (a, a)) | Source |
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Compute the greatest common divisor and
solve a respective Diophantine equation.
(g,(a,b)) = extendedGCD x y ==>
g==a*x+b*y && g == gcd x y
TODO: This method is not appropriate for the PID class,
because there are rings like the one of the multivariate polynomials,
where for all x and y greatest common divisors of x and y exist,
but they cannot be represented as a linear combination of x and y.
TODO: The definition of extendedGCD does not return the canonical associate.
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The Greatest Common Divisor is defined by:
gcd x y == gcd y x
divides z x && divides z y ==> divides z (gcd x y) (specification)
divides (gcd x y) x
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| Least common multiple
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| euclid :: (C a, C a) => (a -> a -> a) -> a -> a -> a | Source |
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| extendedEuclid :: (C a, C a) => (a -> a -> (a, a)) -> a -> a -> (a, (a, a)) | Source |
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| Arbitrary-precision integers.
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| A fixed-precision integer type with at least the range [-2^29 .. 2^29-1].
The exact range for a given implementation can be determined by using
Prelude.minBound and Prelude.maxBound from the Prelude.Bounded class.
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| Single-precision floating point numbers.
It is desirable that this type be at least equal in range and precision
to the IEEE single-precision type.
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| Double-precision floating point numbers.
It is desirable that this type be at least equal in range and precision
to the IEEE double-precision type.
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| scale a vector by a scalar
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| Produced by Haddock version 2.6.0 |
