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MathObj.RootSet | Portability | requires multi-parameter type classes | Stability | provisional | Maintainer | numericprelude@henning-thielemann.de |
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Description |
Computations on the set of roots of a polynomial.
These are represented as the list of their elementar symmetric terms.
The difference between a polynomial and the list of elementar symmetric terms
is the reversed order and the alternated signs.
Cf. MathObj.PowerSum .
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Synopsis |
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newtype T a = Cons {} | | lift0 :: [a] -> T a | | lift1 :: ([a] -> [a]) -> T a -> T a | | lift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a | | const :: C a => a -> T a | | toPolynomial :: T a -> T a | | fromPolynomial :: T a -> T a | | toPowerSums :: (C a, C a) => [a] -> [a] | | fromPowerSums :: (C a, C a) => [a] -> [a] | | addRoot :: C a => a -> [a] -> [a] | | fromRoots :: C a => [a] -> [a] | | liftPowerSum1Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a]) -> [a] -> [a] | | liftPowerSum2Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] | | liftPowerSum1 :: (C a, C a) => ([a] -> [a]) -> [a] -> [a] | | liftPowerSum2 :: (C a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] | | liftPowerSumInt1 :: (C a, Eq a, C a) => ([a] -> [a]) -> [a] -> [a] | | liftPowerSumInt2 :: (C a, Eq a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] | | appPrec :: Int | | add :: (C a, C a) => [a] -> [a] -> [a] | | addInt :: (C a, Eq a, C a) => [a] -> [a] -> [a] | | mul :: (C a, C a) => [a] -> [a] -> [a] | | mulInt :: (C a, Eq a, C a) => [a] -> [a] -> [a] | | pow :: (C a, C a) => Integer -> [a] -> [a] | | powInt :: (C a, Eq a, C a) => Integer -> [a] -> [a] |
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Documentation |
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Constructors | | Instances | |
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Conversions
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lift1 :: ([a] -> [a]) -> T a -> T a | Source |
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lift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a | Source |
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toPowerSums :: (C a, C a) => [a] -> [a] | Source |
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fromPowerSums :: (C a, C a) => [a] -> [a] | Source |
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addRoot :: C a => a -> [a] -> [a] | Source |
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cf. MathObj.Polynomial.mulLinearFactor
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fromRoots :: C a => [a] -> [a] | Source |
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liftPowerSum1Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a]) -> [a] -> [a] | Source |
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liftPowerSum2Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] | Source |
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liftPowerSum1 :: (C a, C a) => ([a] -> [a]) -> [a] -> [a] | Source |
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liftPowerSum2 :: (C a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] | Source |
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liftPowerSumInt1 :: (C a, Eq a, C a) => ([a] -> [a]) -> [a] -> [a] | Source |
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liftPowerSumInt2 :: (C a, Eq a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] | Source |
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Show
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Additive
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add :: (C a, C a) => [a] -> [a] -> [a] | Source |
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addInt :: (C a, Eq a, C a) => [a] -> [a] -> [a] | Source |
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Ring
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mul :: (C a, C a) => [a] -> [a] -> [a] | Source |
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mulInt :: (C a, Eq a, C a) => [a] -> [a] -> [a] | Source |
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Field.C
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Algebra
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Produced by Haddock version 2.6.0 |