Copyright	(c) Masahiro Sakai 2013
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

ToySolver.Data.AlgebraicNumber.Complex

Contents

Rectangular form
Properties
Operations

Description

Algebraic Numbers

Synopsis

data AComplex = !AReal :+ !AReal
realPart :: AComplex -> AReal
imagPart :: AComplex -> AReal
magnitude :: AComplex -> AReal
minimalPolynomial :: AComplex -> UPolynomial Rational
conjugate :: AComplex -> AComplex

Rectangular form

data AComplex Source #

Complex numbers are an algebraic type.

For a complex number z, abs z is a number with the magnitude of z, but oriented in the positive real direction, whereas signum z has the phase of z, but unit magnitude.

Constructors

!AReal :+ !AReal infix 6

Instances

Instances details

Num AComplex Source #
Instance details Defined in ToySolver.Data.AlgebraicNumber.Complex Methods (+) :: AComplex -> AComplex -> AComplex # (-) :: AComplex -> AComplex -> AComplex # (*) :: AComplex -> AComplex -> AComplex # negate :: AComplex -> AComplex # abs :: AComplex -> AComplex # signum :: AComplex -> AComplex # fromInteger :: Integer -> AComplex #
Fractional AComplex Source #
Instance details Defined in ToySolver.Data.AlgebraicNumber.Complex Methods (/) :: AComplex -> AComplex -> AComplex # recip :: AComplex -> AComplex # fromRational :: Rational -> AComplex #
Show AComplex Source #
Instance details Defined in ToySolver.Data.AlgebraicNumber.Complex Methods showsPrec :: Int -> AComplex -> ShowS # show :: AComplex -> String # showList :: [AComplex] -> ShowS #
Eq AComplex Source #
Instance details Defined in ToySolver.Data.AlgebraicNumber.Complex Methods (==) :: AComplex -> AComplex -> Bool # (/=) :: AComplex -> AComplex -> Bool #

Properties

realPart :: AComplex -> AReal Source #

Extracts the real part of a complex number.

imagPart :: AComplex -> AReal Source #

Extracts the imaginary part of a complex number.

magnitude :: AComplex -> AReal Source #

The nonnegative magnitude of a complex number.

minimalPolynomial :: AComplex -> UPolynomial Rational Source #

The polynomial of which the algebraic number is root.

Operations

conjugate :: AComplex -> AComplex Source #

The conjugate of a complex number.