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 * b1 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 qth 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.
This exercise requires you to write an extension method. For more information, see this page.
This exercise also requires you to write operator overloading methods for +, -, * and / operators. For more information, see this page.
To run the tests, run the command dotnet test from within the exercise directory.
Initially, only the first test will be enabled. This is to encourage you to solve the exercise one step at a time.
Once you get the first test passing, remove the Skip property from the next test and work on getting that test passing.
Once none of the tests are skipped and they are all passing, you can submit your solution
using exercism submit RationalNumbers.cs
For more detailed information about the C# track, including how to get help if you're having trouble, please visit the exercism.io C# language page.