MathObj.PowerSum

For a multi-set of numbers, we describe a sequence of the sums of powers of the numbers in the set. These can be easily converted to polynomials and back. Thus they provide an easy way for computations on the roots of a polynomial.

Documentation

newtype T a

Constructors

Cons

Fields

• sums :: [a]

Instances

(C a v, C v) => C a (T v)

Defined in MathObj.PowerSum

Methods

(*>) :: a -> T v -> T v

(C a v, C v) => C a (T v)

Defined in MathObj.PowerSum

Show a => Show (T a)

Defined in MathObj.PowerSum

Methods

showsPrec :: Int -> T a -> ShowS

show :: T a -> String

showList :: [T a] -> ShowS

C a => C (T a)

Defined in MathObj.PowerSum

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

C a => C (T a)

Defined in MathObj.PowerSum

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

(C a, C a) => C (T a)

Defined in MathObj.PowerSum

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational' :: Rational -> T a

(^-) :: T a -> Integer -> T a

(C a, C a) => C (T a)

Defined in MathObj.PowerSum

Methods

sqrt :: T a -> T a

root :: Integer -> T a -> T a

(^/) :: T a -> Rational -> T a

Conversions

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

fromElemSym :: (Eq a, C a) => [a] -> [a]

divOneFlip :: (Eq a, C a) => [a] -> [a] -> [a]

fromElemSymDenormalized :: (C a, C a) => [a] -> [a]

toElemSym :: (C a, C a) => [a] -> [a]

toElemSymInt :: (C a, C a) => [a] -> [a]

fromPolynomial :: (C a, C a) => T a -> [a]

elemSymFromPolynomial :: C a => T a -> [a]

binomials :: C a => [[a]]

Show

appPrec :: Int

Additive

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

Ring

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

pow :: Integer -> [a] -> [a]

Module

Field.C

Algebra

root :: C a => Integer -> [a] -> [a]

approxSeries :: C a b => [b] -> [a] -> [b]

propOp :: (Eq a, C a, C a) => ([a] -> [a] -> [a]) -> (a -> a -> a) -> [a] -> [a] -> [Bool]