source: branches/f4grobner/mx-parsing.lisp@ 74

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;; Maxima expression parsing
;;
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(defun equal-test-p (expr1 expr2)
  (alike1 expr1 expr2))

(defun coerce-maxima-list (expr)
  "convert a maxima list to lisp list."
  (cond
   ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
   (t expr)))

(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))

(defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
  "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
  (labels ((parse (arg) (parse-poly arg vars))
           (parse-list (args) (mapcar #'parse args)))
    (cond
     ((eql expr 0) (make-poly-zero))
     ((member expr vars :test #'equal-test-p)
      (let ((pos (position expr vars :test #'equal-test-p)))
        (make-variable *maxima-ring* (length vars) pos)))
     ((free-of-vars expr vars)
      ;;This means that variable-free CRE and Poisson forms will be converted
      ;;to coefficients intact
      (coerce-coeff *maxima-ring* expr vars))
     (t
      (case (caar expr)
        (mplus (reduce #'(lambda (x y) (poly-add *maxima-ring* x y)) (parse-list (cdr expr))))
        (mminus (poly-uminus *maxima-ring* (parse (cadr expr))))
        (mtimes
         (if (endp (cddr expr))         ;unary
             (parse (cdr expr))
           (reduce #'(lambda (p q) (poly-mul *maxima-ring* p q)) (parse-list (cdr expr)))))
        (mexpt
         (cond
          ((member (cadr expr) vars :test #'equal-test-p)
           ;;Special handling of (expt var pow)
           (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
             (make-variable *maxima-ring* (length vars) pos (caddr expr))))
          ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
           ;; Negative power means division in coefficient ring
           ;; Non-integer power means non-polynomial coefficient
           (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
                  expr)
           (coerce-coeff *maxima-ring* expr vars))
          (t (poly-expt *maxima-ring* (parse (cadr expr)) (caddr expr)))))
        (mrat (parse ($ratdisrep expr)))
        (mpois (parse ($outofpois expr)))
        (otherwise
         (coerce-coeff *maxima-ring* expr vars)))))))

(defun parse-poly-list (expr vars)
  (case (caar expr)
    (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
    (t (merror "Expression ~M is not a list of polynomials in variables ~M."
               expr vars))))
(defun parse-poly-list-list (poly-list-list vars)
  (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))