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A Complete Example

MAXIMA already has a solve command for solving certain algebraic equations. But for our example we will forget that and build a quadratic equation solver for MAXIMA.

;;  File name:   quadsolve.lsp

;; maxima example 
;; defining a new facility called quadsolve

(in-package "MAXIMA")   ;; always use this line at the beginning

(defmfun $quadsolve(eqn var)   ;; top-level function
(prog(a b c)
    (cond (  (or (not (atom var))
	       (not (setq eqn (quadp eqn var)))
	     )
	     (merror "incorrect input to quadsolve %"))
    )
    (desetq (a b c) eqn)
    (return (quadformula a b c))
))

(defun quadp(eqn var)   ;; test for quad poly
(prog (a b c)
    (setq c (mcall '$substitute 0 var eqn))
    (setq eqn (mcall '$diff eqn var))
    (setq b  (mcall '$substitute 0 var eqn))
    (setq eqn (mcall '$diff eqn var))
    (setq a (div  (mcall '$substitute 0 var eqn) 2))
    (cond ( (and (not (mzerop a))
		(zerop (mcall '$diff eqn var))
	    )
	    (return (list a b c))
	  )
    )
))

(defun quadformula(a b c)  ;; apply quadratic formula
    (setq c (power
	       (addn (list (power b 2) (muln (list -4 a c) t)) t)
	       (div 1 2)
	    )
    )
    (list '(mlist)
       (div (addn (list (neg b) c) t) (muln (list 2 a) t))
       (div (sub (neg b) c) (muln (list 2 a) t))
    )
)

(defun mzerop(ex)
    (and (numberp ex) (zerop ex))
)