C: rational-numbers

c/rational-numbers/README.md

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+# Rational Numbers
+
+A rational number is defined as the quotient of two integers `a` and `b`, called the numerator and denominator, respectively, where `b != 0`.
+
+The absolute value `|r|` of the rational number `r = a/b` is equal to `|a|/|b|`.
+
+The sum of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ + r₂ = a₁/b₁ + a₂/b₂ = (a₁ * b₂ + a₂ * b₁) / (b₁ * b₂)`.
+
+The difference of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ - r₂ = a₁/b₁ - a₂/b₂ = (a₁ * b₂ - a₂ * b₁) / (b₁ * b₂)`.
+
+The product (multiplication) of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ * r₂ = (a₁ * a₂) / (b₁ * b₂)`.
+
+Dividing a rational number `r₁ = a₁/b₁` by another `r₂ = a₂/b₂` is `r₁ / r₂ = (a₁ * b₂) / (a₂ * b₁)` if `a₂` is not zero.
+
+Exponentiation of a rational number `r = a/b` to a non-negative integer power `n` is `r^n = (a^n)/(b^n)`.
+
+Exponentiation of a rational number `r = a/b` to a negative integer power `n` is `r^n = (b^m)/(a^m)`, where `m = |n|`.
+
+Exponentiation of a rational number `r = a/b` to a real (floating-point) number `x` is the quotient `(a^x)/(b^x)`, which is a real number.
+
+Exponentiation of a real number `x` to a rational number `r = a/b` is `x^(a/b) = root(x^a, b)`, where `root(p, q)` is the `q`th root of `p`.
+
+Implement the following operations:
+ - addition, subtraction, multiplication and division of two rational numbers,
+ - absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.
+
+Your implementation of rational numbers should always be reduced to lowest terms. For example, `4/4` should reduce to `1/1`, `30/60` should reduce to `1/2`, `12/8` should reduce to `3/2`, etc. To reduce a rational number `r = a/b`, divide `a` and `b` by the greatest common divisor (gcd) of `a` and `b`. So, for example, `gcd(12, 8) = 4`, so `r = 12/8` can be reduced to `(12/4)/(8/4) = 3/2`.
+
+Assume that the programming language you are using does not have an implementation of rational numbers.
+
+## Getting Started
+
+Make sure you have read the "Guides" section of the
+[C track][c-track] on the Exercism site. This covers
+the basic information on setting up the development environment expected
+by the exercises.
+
+## Passing the Tests
+
+Get the first test compiling, linking and passing by following the [three
+rules of test-driven development][3-tdd-rules].
+
+The included makefile can be used to create and run the tests using the `test`
+task.
+
+    make test
+
+Create just the functions you need to satisfy any compiler errors and get the
+test to fail. Then write just enough code to get the test to pass. Once you've
+done that, move onto the next test.
+
+As you progress through the tests, take the time to refactor your
+implementation for readability and expressiveness and then go on to the next
+test.
+
+Try to use standard C99 facilities in preference to writing your own
+low-level algorithms or facilities by hand.
+
+## Source
+
+Wikipedia [https://en.wikipedia.org/wiki/Rational_number](https://en.wikipedia.org/wiki/Rational_number)
+
+## Submitting Incomplete Solutions
+It's possible to submit an incomplete solution so you can see how others have completed the exercise.
+
+[c-track]: https://exercism.io/my/tracks/c
+[3-tdd-rules]: http://butunclebob.com/ArticleS.UncleBob.TheThreeRulesOfTdd