Polynomial synthetic division: Difference between revisions
=={{header|Racket}}== created
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[1, -12, 0, -42] / [1, -3] = [1, -9, -27] remainder [-123]
</pre>
=={{header|Racket}}==
{{trans|Python}}
<lang racket>#lang racket/base
(require racket/list)
;; dividend and divisor are both polynomials, which are here simply lists of coefficients.
;; Eg: x^2 + 3x + 5 will be represented as (list 1 3 5)
(define (extended-synthetic-division dividend divisor)
(define out (list->vector dividend)) ; Copy the dividend
;; for general polynomial division (when polynomials are non-monic), we need to normalize by
;; dividing the coefficient with the divisor's first coefficient
(define normaliser (car divisor))
(define divisor-length (length divisor)) ; } we use these often enough
(define out-length (vector-length out)) ; }
(for ((i (in-range 0 (- out-length divisor-length -1))))
(vector-set! out i (quotient (vector-ref out i) normaliser))
(define coef (vector-ref out i))
(unless (zero? coef) ; useless to multiply if coef is 0
(for ((i+j (in-range (+ i 1) ; in synthetic division, we always skip the first
(+ i divisor-length))) ; coefficient of the divisior, because it's
(divisor_j (in-list (cdr divisor)))) ; only used to normalize the dividend coefficients
(vector-set! out i+j (+ (vector-ref out i+j) (* coef divisor_j -1))))))
;; The resulting out contains both the quotient and the remainder, the remainder being the size of
;; the divisor (the remainder has necessarily the same degree as the divisor since it's what we
;; couldn't divide from the dividend), so we compute the index where this separation is, and return
;; the quotient and remainder.
;; return quotient, remainder (conveniently like quotient/remainder)
(split-at (vector->list out) (- out-length (sub1 divisor-length))))
(module+ main
(displayln "POLYNOMIAL SYNTHETIC DIVISION")
(define N '(1 -12 0 -42))
(define D '(1 -3))
(define-values (Q R) (extended-synthetic-division N D))
(printf "~a / ~a = ~a remainder ~a~%" N D Q R))</lang>
{{out}}
<pre>POLYNOMIAL SYNTHETIC DIVISION
(1 -12 0 -42) / (1 -3) = (1 -9 -27) remainder (-123)</pre>
=={{header|zkl}}==
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