haskell的分数运算

孩子要上3年级了，里面涉及分数的部分，先准备一下。

haskell中涉及分数的模块是Ratio。

Ratio

Synopsis

Documentation

data Ratio a

Rational numbers, with numerator and denominator of some Integral type.

Instances

Typeable1 Ratio
Integral a => Enum (Ratio a)
Eq a => Eq (Ratio a)
Integral a => Fractional (Ratio a)
Integral a => Num (Ratio a)
Integral a => Ord (Ratio a)
(Integral a, Read a) => Read (Ratio a)
Integral a => Real (Ratio a)
Integral a => RealFrac (Ratio a)
(Integral a, Show a) => Show (Ratio a)

type Rational = Ratio Integer

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

(%) :: Integral a => a -> a -> Ratio a

Forms the ratio of two integral numbers.

numerator :: Integral a => Ratio a -> a

Extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

denominator :: Integral a => Ratio a -> a

Extract the denominator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

approxRational :: RealFrac a => a -> a -> Rational

approxRational, applied to two real fractional numbers x and epsilon, returns the simplest rational number within epsilon of x. A rational number y is said to be simpler than another y' if

• abs (numerator y) <= abs (numerator y'), and
• denominator y <= denominator y'.

Any real interval contains a unique simplest rational; in particular, note that 0/1 is the simplest rational of all.

比如：

Prelude Ratio> (2%3) * (3%4)
1 % 2
Prelude Ratio> (2%3) + (3%4)
17 % 12
Prelude Ratio> (2%3) / (3%4)
8 % 9
Prelude Ratio> (2%3) - (3%4)
(-1) % 12

Prelude Ratio> 3 % 2                                         --分数二分之三
3 % 2
Prelude Ratio> numerator (3 % 2)                     --分子
3
Prelude Ratio> denominator (3 % 2)                 --分母
2
Prelude Ratio> approxRational 1.5123 0.2      --在(1.5123 - 0.2, 1.5123 + 0.2)之间的最简单的分数
3 % 2

numerator：分子
denominator：分母
approxRational ：approximate rational 近似分数