Simple Clojure Exercises

Create a Clojure source file called simple.clj. At the begining of the file add this code:

(require '[clojure.test :refer [deftest is run-tests]])

and at the end add:

(run-tests)

All the code you write should go between these two instructions.

1. Write a function called f2c that takes a temperature \(f\) in degrees Fahrenheit and converts it to degrees Celsius. Unit tests:

   (deftest test-f2c
     (is (= 100.0 (f2c 212.0)))
     (is (= 0.0 (f2c 32.0)))
     (is (= -40.0 (f2c -40.0))))

   TIP: If \(F\) is a temperature in degrees Fahrenheit, to convert it to \(C\) degrees Celsius we must use the following formula:

   $$ C = \frac{5 (F - 32)}{9} $$

2. Write a function called sign that takes an integer value n. It returns -1 if n is negative, 1 if n is positive greater than zero, or 0 if n is zero. Unit tests:

   (deftest test-sign
     (is (= -1 (sign -5)))
     (is (= 1 (sign 10)))
     (is (= 0 (sign 0))))
   

3. Write a function called roots that returns a vector containing the two possible roots that solve a quadratic equation given its three coefficients (a, b, c) using the following formula:

   $$ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} $$

   Unit tests:

   (deftest test-roots
     (is (= [-1 -1] (roots 2 4 2)))
     (is (= [0 0] (roots 1 0 0)))
     (is (= [-1/4 -1] (roots 4 5 1))))
   

   Tip: To obtain the square root of a number, use the sqrt function defined in the clojure.math.numeric-tower namespace, like this:

   (require '[clojure.math.numeric-tower :refer [sqrt]])
   
   (sqrt 25)
   => 5
   

4. The BMI (body mass index) is used to determine if a person's weight and height proportion is adequate. The BMI may be calculated using the following formula:

   $$ \textit{BMI} = \frac{\textit{weight}}{\textit{height}^2} $$

   Where \( \textit{weight} \) should be given in kilograms and \( \textit{height} \) in meters. The following table shows how different BMI ranges are classified:

   BMI range	Description
   BMI < 20	underweight
   20 ≤ BMI < 25	normal
   25 ≤ BMI < 30	obese1
   30 ≤ BMI < 40	obese2
   40 ≤ BMI	obese3

   Write a function called bmi that takes two arguments: weight and height. It should return a symbol that represents the corresponding BMI description computed from its input.

   Unit tests:

   (deftest test-bmi
     (is (= 'underweight (bmi 45 1.7)))
     (is (= 'normal (bmi 55 1.5)))
     (is (= 'obese1 (bmi 76 1.7)))
     (is (= 'obese2 (bmi 81 1.6)))
     (is (= 'obese3 (bmi 120 1.6))))