source: branches/f4grobner/symbolic-polynomial.lisp@ 3392

;;; -*-  Mode: Lisp -*- 
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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
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(defpackage "SYMBOLIC-POLYNOMIAL"
  (:use :cl :utils :ring :monom :order :term :polynomial :infix)
  (:export "SYMBOLIC-POLY" "READ-INFIX-FORM" "STRING->POLY" "+LIST-MARKER+")
  (:documentation "Implements symbolic polynomials. A symbolic
polynomial is and object which uses symbolic variables for reading and
printing in standard human-readable (infix) form."))

(in-package :symbolic-polynomial)

(defparameter +list-marker+ :[
  "A sexp with this head is considered a list of polynomials.")

(defclass symbolic-poly (poly)
  ((vars :initform nil 
         :initarg :vars 
         :accessor symbolic-poly-vars)
   )
  (:default-initargs :termlist nil :vars nil))

(defmethod print-object ((self symbolic-poly) stream)
  (print-unreadable-object (self stream :type t :identity t)
    (with-accessors ((dimension poly-dimension)
                     (termlist poly-termlist) 
                     (order poly-term-order)
                     (vars symbolic-poly-vars))
        self
      (format stream "DIMENSION=~A TERMLIST=~A ORDER=~A VARS=~A" 
              dimension termlist order vars))))


(defmethod r-equalp ((self symbolic-poly) (other symbolic-poly))
  (when (r-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
    (call-next-method)))

(defmethod update-instance-for-different-class :after ((old poly) (new  symbolic-poly) &key)
  "After adding variables to NEW, we need to make sure that the number
of variables given by POLY-DIMENSION is consistent with VARS."
  (assert (= (length (symbolic-poly-vars new)) (poly-dimension new))))

(defgeneric poly-eval (expr vars order) 
  (:documentation "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
variables VARS. Return the resulting polynomial or list of
polynomials.  Standard arithmetical operators in form EXPR are
replaced with their analogues in the ring of polynomials, and the
resulting expression is evaluated, resulting in a polynomial or a list
of polynomials in internal form. A similar operation in another computer
algebra system could be called 'expand' or so.")
  (:method ((expr symbolic-poly) vars order) expr)
  (:method (expr vars order) 
    (labels ((p-eval (p) (poly-eval p vars order))
             (p-eval-list (plist) (mapcar #'p-eval plist)))
      (cond 
        ((eq expr 0) 
         (make-instance 'symbolic-poly :dimension (length vars) :vars vars))
        ((member expr vars :test #'equalp)
         (let ((pos (position expr vars :test #'equalp)))
           (make-monom-variable (length vars) pos)))
        ((atom expr)
         expr)
        ((eq (car expr) +list-marker+)
         (cons +list-marker+ (p-eval-list (cdr expr))))
        (t
         (case (car expr)
           (+ (reduce #'r+ (p-eval-list (cdr expr))))
           (- (case (length expr)
                (1 (make-poly-zero))
                (2 (r- (p-eval (cadr expr))))
                (3 (r- (p-eval (cadr expr)) (p-eval (caddr expr))))
                (otherwise (r- (p-eval (cadr expr))
                               (reduce #'r+ (p-eval-list (cddr expr)))))))
           (*
            (if (endp (cddr expr))      ;unary
                (p-eval (cdr expr))
                (reduce #'(lambda (p q) (r* p q)) (p-eval-list (cdr expr)))))
           (/ 
            ;; A polynomial can be divided by a scalar
            (cond 
              ((endp (cddr expr))
               ;; A special case (/ ?), the inverse
               (coerce-coeff ring (apply (ring-div ring) (cdr expr)) vars))
              (t
               (let ((num (p-eval (cadr expr)))
                     (denom-inverse (apply (ring-div ring)
                                           (cons (funcall (ring-unit ring)) 
                                                 (mapcar #'p-eval-scalar (cddr expr))))))
                 (scalar-times-poly ring denom-inverse num)))))
           (expt
            (cond
              ((member (cadr expr) vars :test #'equalp)
               ;;Special handling of (expt var pow)
               (let ((pos (position (cadr expr) vars :test #'equalp)))
                 (make-poly-variable 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
               (coerce-coeff ring expr vars))
              (t (poly-expt ring-and-order (p-eval (cadr expr)) (caddr expr)))))
           (otherwise
            (coerce-coeff ring expr vars))))))))

#|
(defun poly-eval-scalar (expr 
                         &optional
                           (ring +ring-of-integers+)
                         &aux 
                           (order #'lex>))
  "Evaluate a scalar expression EXPR in ring RING."
  (declare (type ring ring))
  (poly-lc (poly-eval expr nil ring order)))
|#


(defun read-infix-form (&key (stream t))
  "Parser of infix expressions with integer/rational coefficients
The parser will recognize two kinds of polynomial expressions:

- polynomials in fully expanded forms with coefficients
  written in front of symbolic expressions; constants can be optionally
  enclosed in (); for example, the infix form
        X^2-Y^2+(-4/3)*U^2*W^3-5
  parses to
        (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))

- lists of polynomials; for example
        [X-Y, X^2+3*Z]          
  parses to
          (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
  where the first symbol [ marks a list of polynomials.

-other infix expressions, for example
        [(X-Y)*(X+Y)/Z,(X+1)^2]
parses to:
        (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
Currently this function is implemented using M. Kantrowitz's INFIX package."
  (read-from-string
   (concatenate 'string
                "#I(" 
                (with-output-to-string (s)
                  (loop
                     (multiple-value-bind (line eof)
                         (read-line stream t)
                       (format s "~A" line)
                       (when eof (return)))))
                ")")))

(defun read-poly (vars &key
                         (stream t) 
                         (order #'lex>))
  "Reads an expression in prefix form from a stream STREAM.
The expression read from the strem should represent a polynomial or a
list of polynomials in variables VARS, over the ring RING.  The
polynomial or list of polynomials is returned, with terms in each
polynomial ordered according to monomial order ORDER."
  (poly-eval (read-infix-form :stream stream) vars order))

(defun string->poly (str vars 
                     &optional
                       (order #'lex>))
  "Converts a string STR to a polynomial in variables VARS."
  (with-input-from-string (s str)
    (read-poly vars :stream s :order order)))

(defun poly->alist (p)
  "Convert a polynomial P to an association list. Thus, the format of the
returned value is  ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
corresponding coefficient in the ring."
  (cond
    ((poly-p p)
     (mapcar #'term->cons (poly-termlist p)))
    ((and (consp p) (eq (car p) :[))
     (cons :[ (mapcar #'poly->alist (cdr p))))))

(defun string->alist (str vars
                      &optional
                        (ring +ring-of-integers+) 
                        (order #'lex>))
  "Convert a string STR representing a polynomial or polynomial list to
an association list (... (MONOM . COEFF) ...)."
  (poly->alist (string->poly str vars ring order)))

(defun poly-equal-no-sugar-p (p q)
  "Compare polynomials for equality, ignoring sugar."
  (declare (type poly p q))
  (equalp (poly-termlist p) (poly-termlist q)))

(defun poly-set-equal-no-sugar-p (p q)
  "Compare polynomial sets P and Q for equality, ignoring sugar."
  (null (set-exclusive-or  p q :test #'poly-equal-no-sugar-p )))

(defun poly-list-equal-no-sugar-p (p q)
  "Compare polynomial lists P and Q for equality, ignoring sugar."
  (every #'poly-equal-no-sugar-p p q))