quadratic-equation.egi

(define $quadratic-formula q-f)

(define $q-f
  (lambda [$f $x]
    (match (coefficients f x) (list math-expr)
      {[<cons $a_0 <cons $a_1 <cons $a_2 <nil>>>>
        (q-f' a_2 a_1 a_0)]})))

(define $q-f'
  (lambda [$a $b $c]
    (match [a b c] [math-expr math-expr math-expr]
      {[[,1 ,0 _]
        [(sqrt (* -1 c)) (* -1 (sqrt (* -1 c)))]]
       [[,1 _ _]
        (2#[(+ (* -1 (/ b 2)) %1) (+ (* -1 (/ b 2)) %2)]
           (with-symbols {x y}
             (q-f (substitute {[x (- y (/ b 2))]} (+ x^2 (* b x) c)) y)))]
       [[_ _ _] (q-f' 1 (/ b a) (/ c a))]})))


(q-f (+ x^2 x 1) x)
;=>
;[(/ (+ -1 (* i (sqrt 3))) 2)
; (/ (+ -1 (* -1 i (sqrt 3))) 2)]

(q-f (+ (* a x^2) (* b x) c) x)
;=>
;[(/ (+ (* -1 b) (sqrt (+ b^2 (* -4 c a))))
;    (* 2 a))
; (/ (+ (* -1 b) (* -1 (sqrt (+ b^2 (* -4 c a)))))
;    (* 2 a))]

(q-f (+ (* a x^2) (* 2 b x) c) x)
;=>
;[(/ (+ (* -1 b) (sqrt (+ b^2 (* -1 c a)))) a)
; (/ (+ (* -1 b) (* -1 (sqrt (+ b^2 (* -1 c a))))) a)]