Copyright	© 2014 Johan Kiviniemi
License	MIT
Maintainer	Johan Kiviniemi <devel@johan.kiviniemi.name>
Stability	provisional
Portability	ViewPatterns
Safe Haskell	None
Language	Haskell2010

Numeric.QuadraticIrrational

Description

An implementation of quadratic irrationals with support for conversion from and to periodic continued fractions.

Synopsis

Documentation

data QI Source

(a + b √c) / d

Instances

Eq QI
Read QI
Show QI

qi Source

Arguments

:: Integer	a
-> Integer	b
-> Integer	c
-> Integer	d
-> QI

Given a, b, c and d such that n = (a + b √c)/d, constuct a QI corresponding to n.

qi' Source

Arguments

:: Rational	a
-> Rational	b
-> Integer	c
-> QI

Given a, b and c such that n = a + b √c, constuct a QI corresponding to n.

qiModify :: QI -> (Integer -> Integer -> Integer -> (Integer, Integer, Integer)) -> QI Source

Given a QI corresponding to n = (a + b √c)/d, modify (a, b, d). Avoids having to simplify b √c.

runQI :: QI -> (Integer -> Integer -> Integer -> Integer -> a) -> a Source

Given n and f such that n = (a + b √c)/d, run f a b c d.

runQI' :: QI -> (Rational -> Rational -> Integer -> a) -> a Source

Given n and f such that n = a + b √c, run f a b c.

unQI :: QI -> (Integer, Integer, Integer, Integer) Source

Given n such that n = (a + b √c)/d, return (a, b, c, d).

unQI' :: QI -> (Rational, Rational, Integer) Source

Given n such that n = a + b √c, return (a, b, c).

qiZero :: QI Source

The constant zero. qi 0 0 0 1

qiOne :: QI Source

The constant one. qi 1 0 0 1

qiIsZero :: QI -> Bool Source

Check if the value is zero.

qiToFloat :: Floating a => QI -> a Source

Convert a QI number into a Floating one.

qiAddI :: QI -> Integer -> QI Source

Add an Integer to a QI.

qiSubI :: QI -> Integer -> QI Source

Subtract an Integer from a QI.

qiMulI :: QI -> Integer -> QI Source

Multiply a QI by an Integer.

qiDivI :: QI -> Integer -> QI Source

Divice a QI by an Integer.

qiAddR :: QI -> Rational -> QI Source

Add a Rational to a QI.

qiSubR :: QI -> Rational -> QI Source

Subtract a Rational from a QI.

qiMulR :: QI -> Rational -> QI Source

Multiply a QI by a Rational.

qiDivR :: QI -> Rational -> QI Source

Divice a QI by a Rational.

qiNegate :: QI -> QI Source

Negate a QI.

qiRecip :: QI -> Maybe QI Source

Compute the reciprocal of a QI.

qiAdd :: QI -> QI -> Maybe QI Source

Add two QIs if the square root terms are the same or zeros.

qiSub :: QI -> QI -> Maybe QI Source

Subtract two QIs if the square root terms are the same or zeros.

qiMul :: QI -> QI -> Maybe QI Source

Multiply two QIs if the square root terms are the same or zeros.

qiDiv :: QI -> QI -> Maybe QI Source

Divide two QIs if the square root terms are the same or zeros.

qiPow :: QI -> Integer -> QI Source

Exponentiate a QI to an Integer power.

qiFloor :: QI -> Integer Source

Compute the floor of a QI.

continuedFractionToQI :: (Integer, CycList Integer) -> QI Source

Convert a (possibly periodic) continued fraction to a QI.

qiToContinuedFraction :: QI -> (Integer, CycList Integer) Source

Convert a QI into a (possibly periodic) continued fraction.

module Numeric.QuadraticIrrational.CyclicList