Functions for doing simple math problems

util.clj

(defn gcd [a b]
  (if (zero? b)
    a
    (recur b (mod a b))))

(defn factors [num]
  (loop [n num div 2 divs '()]
    (cond (<= n 1) divs
          (zero? (rem n div)) (recur (/ n div) div (cons div divs))
          :else (recur n (inc div) divs))))

(defn abs [x]
  (if (< x 0) (- x) x))

(defn pow [x n]
  (Math/pow x n))

; https://rosettacode.org/wiki/Nth_root#Clojure

(defn calc-delta [A x n]
  (/ (- (/ A (pow x (- n 1)))
          x)
       n))

(defn nth-root
  " nth root of algorithm: A = numer, n = root"
  ([A n] (nth-root A n 0.5 1.0))  ; Takes only two arguments A, n and calls version which takes A, n, guess-prev, guess-current
  ([A n guess-prev guess-current] ; version take takes in four arguments (A, n, guess-prev, guess-current)
   (if (< (abs (- guess-prev guess-current)) 1e-6)
     guess-current
     (recur A n guess-current (+ guess-current (calc-delta A guess-current n)))))) ; iterate answer using tail recursion
 

(defn sqrt [n]
  (nth-root n 2))

(defn cbrt [n]
  (nth-root n 3))