Safe Haskell	None
Language	Haskell98

MathObj.Polynomial.Core

Description

This module implements polynomial functions on plain lists. We use such functions in order to implement methods of other datatypes.

The module organization differs from that of ResidueClass: Here the Polynomial module exports the type that fits to the NumericPrelude type classes, whereas in ResidueClass the sub-modules export various flavors of them.

Synopsis

horner :: C a => a -> [a] -> a
hornerCoeffVector :: C a v => a -> [v] -> v
hornerArgVector :: (C a v, C v) => v -> [a] -> v
normalize :: C a => [a] -> [a]
shift :: C a => [a] -> [a]
unShift :: [a] -> [a]
equal :: (Eq a, C a) => [a] -> [a] -> Bool
add :: C a => [a] -> [a] -> [a]
sub :: C a => [a] -> [a] -> [a]
negate :: C a => [a] -> [a]
scale :: C a => a -> [a] -> [a]
collinear :: (Eq a, C a) => [a] -> [a] -> Bool
tensorProduct :: C a => [a] -> [a] -> [[a]]
tensorProductAlt :: C a => [a] -> [a] -> [[a]]
mul :: C a => [a] -> [a] -> [a]
mulShear :: C a => [a] -> [a] -> [a]
mulShearTranspose :: C a => [a] -> [a] -> [a]
divMod :: (C a, C a) => [a] -> [a] -> ([a], [a])
divModRev :: (C a, C a) => [a] -> [a] -> ([a], [a])
stdUnit :: (C a, C a) => [a] -> a
progression :: C a => [a]
differentiate :: C a => [a] -> [a]
integrate :: C a => a -> [a] -> [a]
integrateInt :: (C a, C a) => a -> [a] -> [a]
mulLinearFactor :: C a => a -> [a] -> [a]
alternate :: C a => [a] -> [a]
dilate :: C a => a -> [a] -> [a]
shrink :: C a => a -> [a] -> [a]

Documentation

horner :: C a => a -> [a] -> a Source #

Horner's scheme for evaluating a polynomial in a ring.

hornerCoeffVector :: C a v => a -> [v] -> v Source #

Horner's scheme for evaluating a polynomial in a module.

hornerArgVector :: (C a v, C v) => v -> [a] -> v Source #

normalize :: C a => [a] -> [a] Source #

It's also helpful to put a polynomial in canonical form. normalize strips leading coefficients that are zero.

shift :: C a => [a] -> [a] Source #

Multiply by the variable, used internally.

unShift :: [a] -> [a] Source #

equal :: (Eq a, C a) => [a] -> [a] -> Bool Source #

add :: C a => [a] -> [a] -> [a] Source #

sub :: C a => [a] -> [a] -> [a] Source #

negate :: C a => [a] -> [a] Source #

scale :: C a => a -> [a] -> [a] Source #

collinear :: (Eq a, C a) => [a] -> [a] -> Bool Source #

tensorProduct :: C a => [a] -> [a] -> [[a]] Source #

tensorProductAlt :: C a => [a] -> [a] -> [[a]] Source #

mul :: C a => [a] -> [a] -> [a] Source #

mul is fast if the second argument is a short polynomial, ** relies on that fact.

mulShear :: C a => [a] -> [a] -> [a] Source #

mulShearTranspose :: C a => [a] -> [a] -> [a] Source #

divMod :: (C a, C a) => [a] -> [a] -> ([a], [a]) Source #

divModRev :: (C a, C a) => [a] -> [a] -> ([a], [a]) Source #

The modulus will always have one element less than the divisor. This means that the modulus will be denormalized in some cases, e.g. mod [2,1,1] [1,1,1] == [1,0] instead of [1].

stdUnit :: (C a, C a) => [a] -> a Source #

progression :: C a => [a] Source #

differentiate :: C a => [a] -> [a] Source #

integrate :: C a => a -> [a] -> [a] Source #

integrateInt :: (C a, C a) => a -> [a] -> [a] Source #

Integrates if it is possible to represent the integrated polynomial in the given ring. Otherwise undefined coefficients occur.

mulLinearFactor :: C a => a -> [a] -> [a] Source #

alternate :: C a => [a] -> [a] Source #

dilate :: C a => a -> [a] -> [a] Source #

shrink :: C a => a -> [a] -> [a] Source #