source: branches/f4grobner/symbolic-polynomial.lisp@ 3882

;;; -*-  Mode: Lisp -*- 

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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          

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;;;  This program is free software; you can redistribute it and/or modify        

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(defpackage "SYMBOLIC-POLYNOMIAL"

  (:use :cl :utils :monom :polynomial :infix :infix-printer)

  (:export "SYMBOLIC-POLY" "READ-INFIX-FORM" "STRING->POLY" "POLY->STRING" "->INFIX" "+LIST-MARKER+")

  (:documentation "Implements symbolic polynomials. A symbolic

polynomial is polynomial 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 universal-equalp ((self symbolic-poly) (other symbolic-poly))

  (when (universal-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))

    (call-next-method)))



(defmethod universal-equalp ((self symbol) (other symbol))

  (eq self other))



(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))))



(defun poly-eval (expr vars order) 

  "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."

  (labels ((p-eval (p) (poly-eval p vars order))

           (p-eval-scalar (p) (poly-eval p '() 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-poly-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 #'add (p-eval-list (cdr expr))))

         (- (apply #'subtract (p-eval-list (cdr expr))))

         (*

          (if (endp (cddr expr))        ;unary

              (p-eval (cdr expr))

              (reduce #'multiply (p-eval-list (cdr expr)))))

         (/ 

          ;; A polynomial can be divided by a scalar

          (cond 

            ((endp (cddr expr))

             ;; A special case (/ ?), the inverse

             (divide (cadr expr)))

            (t

             (let ((num (p-eval (cadr expr)))

                   (denom-inverse (apply #'divide (mapcar #'p-eval-scalar (cddr expr)))))

               (multiply 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 (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

             expr)

            (t (universal-expt (p-eval (cadr expr)) (caddr expr)))))

         (otherwise

          expr))))))



#|

(defun poly-eval-scalar (expr 

                         &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)

    (change-class (read-poly vars :stream s :order order) 'symbolic-poly :vars vars)))



(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 #'->list (poly-termlist p)))

    ((and (consp p) (eq (car p) :[))

     (cons :[ (mapcar #'poly->alist (cdr p))))))



(defun string->alist (str vars

                      &optional

                        (order #'lex>))

  "Convert a string STR representing a polynomial or polynomial list to

an association list (... (MONOM . COEFF) ...)."

  (poly->alist (string->poly str vars 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))



(defmethod ->infix :around ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))

  "Convert a symbolic polynomial SELF to infix form, using variables VARS. The default

value of VARS is the corresponding slot value of SELF."

  (call-next-method self vars))



(defgeneric poly->string (self &optional vars)

  (:documentation "Render polynomial SELF as a string, using symbolic variables VARS.")

  (:method ((self poly) &optional (vars nil))

    ;; Ensure that the number of variables matches the dimension

    (assert (= (length vars) (poly-dimension self)))

    (infix-print (->infix self vars)))

  (:method ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))

    (infix-print (->infix self vars))))