C#代写：CS112 Rational Number

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关于Rational Number的编程练习。

Rational Number

Preamble

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.

Requirements

Implement the following operations on Rational Numbers:

  • addition, subtraction, multiplication, and division of two rational numbers,
  • absolute value of a given rational number,
  • 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, and
  • display as n/d, where n is the numerator and d is the denominator.

Your implementation should meet the following conditions:

  • All rational numbers should be immutable; that is, there should be no external mechanism to change the components of the number after it has been created; most of your methods will simply return a new rational number.
  • The denominator may not be zero.
  • The denominator should never be negative.
    (You may provide a negative number for the denominator via the constructor when you create the rational, but a negative rational should be represented internally with a negative numerator and a positive denominator.)
  • Zero should be represented as 0/1.
  • 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.
    For example, the gcd(12, 8) = 4, therefore r = 12/8 can be reduced to (12/4)/(8/4) = 3/2.
  • Use (at least) one additional [extension method][extension].
  • Utilise [operator overloading methods][overload] for the +, -, *, and / operators.

Assume that the programming language you are using does not have an implementation of rational numbers.

The code

  • You are provided with some skeletal code for both for the Rational entity and its tests.
  • You are required to complete the code.
  • You should not assume the provided code is correct — check it thoroughly.
  • In particular you should remember to add initial tests as the provided tests are “minimal”.
  • Your goal in writing the tests for the Rational class is too test for every possible condition, including that the correct exceptions are thrown (where appropriate).

Testing

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 to pass remove the Skip property from the next test, and continue to work on getting that test to pass (and the previous test(s)) - repeat until all the tests pass.

Resources

Percentage Criteria
40% For functionality, including testing, using the facilities of the language if possible, and that your program works according to the specification!
40% For coding in the idiomatic style of the programming language (i.e., C#).
20% For adequate comments, proper formatting, indentation, choosing proper names, following naming conventions, and for correct submission.

Important Information

  • Need to write in C#
  • Need to write clean code
  • Premature Optimisation, as described by one of the current programming Gurus — Martin Fowler (“Yet Another Optimisation Article“), is frowned upon.
  • Code needs to be well structured
  • Need to write comments each line to explain what it does
  • Need to have proper formatting, indentation, choosing proper names, and following naming conventions.
  • Need to have clear identifier names and abbreviations
  • Code don’t contain inappropriate hard-coded values
  • Code need to be easily maintainable
  • Need to write testing, using the facilities of C# language