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Algebra.Module | Portability | requires multi-parameter type classes | Stability | provisional | Maintainer | numericprelude@henning-thielemann.de |
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Description |
Abstraction of modules
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Synopsis |
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Documentation |
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A Module over a ring satisfies:
a *> (b + c) === a *> b + a *> c
(a * b) *> c === a *> (b *> c)
(a + b) *> c === a *> c + b *> c
| | Methods | | scale a vector by a scalar
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| | Instances | C Double Double | C Float Float | C Int Int | C Integer Integer | C a => C Integer (T a) | C a => C Integer (T a) | C a b => C a ([] b) | C a b => C a (T b) | C a b => C a (T b) | C a b => C a (T b) | (C a v, C v) => C a (T v) | C a b => C a (T b) | C a b => C a (T b) | C a b => C a (T b) | C a b => C a (c -> b) | (C a b0, C a b1) => C a ((,) b0 b1) | (Ord i, Eq a, Eq v, C a v) => C a (Map i v) | (C u, C a b) => C a (T u b) | (Ord i, C a v) => C a (T i v) | C a v => C a (T b v) | (C a b0, C a b1, C a b2) => C a ((,,) b0 b1 b2) | C a => C (T a) (T a) |
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Instances for atomic types
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Instances for composed types
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Related functions
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linearComb :: C a b => [a] -> [b] -> b | Source |
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Compute the linear combination of a list of vectors.
ToDo:
Should it use NumericPrelude.List.zipWithMatch ?
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integerMultiply :: (C a, C b) => a -> b -> b | Source |
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This function can be used to define any
C as a module over Integer.
Better move to Algebra.Additive?
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Properties
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propRightDistributive :: (Eq b, C a b) => a -> b -> b -> Bool | Source |
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propLeftDistributive :: (Eq b, C a b) => b -> a -> a -> Bool | Source |
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