CODEWITHSUNDEEP
clojure
Dev_109
Dev_109

Reputation: 53

Returning the terms of a polynomial in clojure

I simply need to write a function that will return a list of terms in a polynomial, so for ex: say we have 3x^4 + 2x^3 + x^2 + x +10 , it will return an output in the form : [coef variable exponent]

My function so far:

(defn terms-of-poly [poly]
    for [x (poly :coefficients)]
    for [y(poly :variables)]
    [x y])

Input:

(let [poly {:variable "y"
            :coefficients [3 2 1 10]}]
    (vec (terms-of-poly poly)))

Output: [[3 "x" 4] [2 "x" 3] [1 "x" 2] [10 "x" 0]]

Upvotes: 0

Views: 194

Answers (1)

leetwinski
leetwinski

Reputation: 17859

the solution could look something like this:

(let [poly {:variable "y"
            :coefficients [3 2 1 0 10]}]
  (mapv vector
        (rseq (:coefficients poly))
        (repeat (:variable poly))
        (range)))

;;=> [[10 "y" 0] [0 "y" 1] [1 "y" 2] [2 "y" 3] [3 "y" 4]]

it is inverted, but you can reverse it with rseq / reverse

(notice, i've changed the input, since there is one more member, namely 0x^1)

more or less the same with list comprehension approach:

(let [poly {:variable "y"
            :coefficients [3 2 1 0 10]}]
  (for [[pow coeff] (map-indexed vector (rseq (:coefficients poly)))]
    [coeff (:variable poly) pow]))

;;=> ([10 "y" 0] [0 "y" 1] [1 "y" 2] [2 "y" 3] [3 "y" 4])

you can also filter out coeffs with zero multipliers:

(let [poly {:variable "y"
            :coefficients [3 2 1 0 10]}]
  (for [[pow coeff] (map-indexed vector (rseq (:coefficients poly)))
        :when (pos? coeff)]
    [coeff (:variable poly) pow]))

;;=> ([10 "y" 0] [1 "y" 2] [2 "y" 3] [3 "y" 4])

update

if the order is important (though i guess reversed order should be ok, since every element is identified by it's power), you can do the following for example:

(defn terms-of-poly [{:keys [variable coefficients]}]
  (map vector
       coefficients
       (repeat variable)
       (range (dec (count coefficients)) -1 -1)))

(let [poly {:variable "y"
            :coefficients [3 2 1 0 10]}]
  (terms-of-poly poly))

;;=> ([3 "y" 4] [2 "y" 3] [1 "y" 2] [0 "y" 1] [10 "y" 0])

Upvotes: 2

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