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(
.-~! ) :: PseudoAffine x => x -> x -> Needle xmanifolds-core Math.Manifold.Core.PseudoAffine Unsafe version of .-~.. If the two points lie in disjoint regions, the behaviour is undefined. Whenever p and q lie in a connected region, the identity
p .+~^ (q.-~.p) ≡ q
should hold (up to possible floating point rounding etc.). Meanwhile, you will in general have(p.+~^v).-~^v ≠ p
(though in many instances this is at least for sufficiently small v approximately equal).(
.-~. ) :: PseudoAffine x => x -> x -> Maybe (Needle x)manifolds-core Math.Manifold.Core.PseudoAffine The path reaching from one point to another. Should only yield Nothing if the points are on disjoint segments of a non–path-connected space. For a connected manifold, you may define this method as
p.-~.q = pure (p.-~!q)
(
.-~^ ) :: Semimanifold x => x -> Needle x -> xmanifolds-core Math.Manifold.Core.PseudoAffine Shorthand for \p v -> p .+~^ negateV v, which should obey the asymptotic law
p .-~^ v .+~^ v ≅ p
Meaning: if v is scaled down with sufficiently small factors η, then the difference (p.-~^v.+~^v) .-~. p should eventually scale down even faster: as O (η²). For large vectors, it may however behave differently, except in flat spaces (where all this should be equivalent to the AffineSpace instance).(
.!. ) :: (Integral p, FiniteBits b, Bits p, Num b) => p -> Int -> bnetwork-house Net.Bits No documentation available.
(
.! ) :: (b -> c) -> (a -> b) -> a -> cpointless-fun Data.Function.Pointless Function composition which calls the right-hand function eagerly; i.e., making the left-hand function strict in its first argument.
(f .! g) x = f $! g x
This defines the composition for the sub-category of strict Haskell functions. If the Functor class were parameterized by the domain and codomain categories (e.g., a regular Functor f would be CFunctor (->) (->) f instead) then this would allow us to define functors CFunctor (->) (!->) f where fmap f . fmap g = fmap (f .! g).(
.: ) :: (c -> d) -> (a -> b -> c) -> a -> b -> dpointless-fun Data.Function.Pointless Binary composition: pass two args to the right argument before composing.
(f .: g) x y = f (g x y)
or,f .: g = curry (f . uncurry g)
This is the same as the common idiom (f .) . g but more easily extended to multiple uses, due to the fixity declaration.(
.^ ) :: (a -> c -> d) -> (b -> c) -> a -> b -> dpointless-fun Data.Function.Pointless Secondary composition: compose the right argument on the second arg of the left argument.
(f .^ g) x y = f x (g y)
(
.*. ) :: (OperatorContext c, Num a) => Record c a -> Record c a -> Record c arelational-record Database.Relational.Documentation Number operator corresponding SQL * .
(
.+. ) :: (OperatorContext c, Num a) => Record c a -> Record c a -> Record c arelational-record Database.Relational.Documentation Number operator corresponding SQL + .
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.-. ) :: (OperatorContext c, Num a) => Record c a -> Record c a -> Record c arelational-record Database.Relational.Documentation Number operator corresponding SQL - .