source: branches/f4grobner/parse.lisp@ 1056

;;; -*- Mode: Lisp; Syntax: Common-Lisp; Package: Grobner; Base: 10 -*-

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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
;;;                                                                              
;;;  This program is free software; you can redistribute it and/or modify        
;;;  it under the terms of the GNU General Public License as published by        
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;;;  GNU General Public License for more details.                                
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;;
;; Parser of infix notation. This package enables input
;; of polynomials in human-readable notation outside of Maxima,
;; which is very useful for debugging.
;;
;; NOTE: This package is adapted from CGBLisp.
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defpackage "PARSE"
  (:use :cl :order :ring-and-order :monomial :term :polynomial :ring)
  (:export "PARSE PARSE-TO-ALIST" "PARSE-STRING-TO-ALIST" 
           "PARSE-TO-SORTED-ALIST" "PARSE-STRING-TO-SORTED-ALIST" "^" "["
           "POLY-EVAL"
           ))

(in-package "PARSE")

(proclaim '(optimize (speed 0) (space 0) (safety 3) (debug 3)))

;; The function PARSE yields the representations as above.  The two functions
;; PARSE-TO-ALIST and PARSE-STRING-TO-ALIST parse polynomials to the alist
;; representations. For example
;;
;; >(parse)x^2-y^2+(-4/3)*u^2*w^3-5 --->
;; (+ (* 1 (^ X 2)) (* -1 (^ Y 2)) (* -4/3 (^ U 2) (^ W 3)) (* -5))
;;
;; >(parse-to-alist '(x y u w))x^2-y^2+(-4/3)*u^2*w^3-5 --->
;; (((0 0 2 3) . -4/3) ((0 2 0 0) . -1) ((2 0 0 0) . 1) ((0 0 0 0) . -5))
;;
;; >(parse-string-to-alist "x^2-y^2+(-4/3)*u^2*w^3-5" '(x y u w)) --->
;; (((0 0 2 3) . -4/3) ((0 2 0 0) . -1) ((2 0 0 0) . 1) ((0 0 0 0) . -5))
;;
;; >(parse-string-to-alist "[x^2-y^2+(-4/3)*u^2*w^3-5,y]" '(x y u w))
;; ([ (((0 0 2 3) . -4/3) ((0 2 0 0) . -1) ((2 0 0 0) . 1)
;;     ((0 0 0 0) . -5))
;;    (((0 1 0 0) . 1)))
;; The functions PARSE-TO-SORTED-ALIST and PARSE-STRING-TO-SORTED-ALIST
;; in addition sort terms by the predicate defined in the ORDER package
;; For instance:
;; >(parse-to-sorted-alist '(x y u w))x^2-y^2+(-4/3)*u^2*w^3-5
;; (((2 0 0 0) . 1) ((0 2 0 0) . -1) ((0 0 2 3) . -4/3) ((0 0 0 0) . -5))
;; >(parse-to-sorted-alist '(x y u w) t #'grlex>)x^2-y^2+(-4/3)*u^2*w^3-5
;; (((0 0 2 3) . -4/3) ((2 0 0 0) . 1) ((0 2 0 0) . -1) ((0 0 0 0) . -5))

;;(eval-when (compile)
;;  (proclaim '(optimize safety)))


(defun parse (&optional stream)
  "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)))))
     ")")))

;; Translate output from parse to a pure list form
;; assuming variables are VARS

(defun alist-form (plist vars)
  "Translates an expression PLIST, which should be a list of polynomials
in variables VARS, to an alist representation of a polynomial.
It returns the alist. See also PARSE-TO-ALIST."
  (cond
   ((endp plist) nil)
   ((eql (first plist) '[)
    (cons '[ (mapcar #'(lambda (x) (alist-form x vars)) (rest plist))))
   (t
    (assert (eql (car plist) '+))
    (alist-form-1 (rest plist) vars))))

(defun alist-form-1 (p vars
                         &aux (ht (make-hash-table
                                   :test #'equal :size 16))
                         stack)
  (dolist (term p)
    (assert (eql (car term) '*))
    (incf  (gethash (powers (cddr term) vars) ht 0) (second term)))
  (maphash #'(lambda (key value) (unless (zerop value)
                                   (push (cons key value) stack))) ht)
  stack)
    
(defun powers (monom vars
                     &aux (tab (pairlis vars (make-list (length vars)
                                                        :initial-element 0))))
  (dolist (e monom (mapcar #'(lambda (v) (cdr (assoc v tab))) vars))
    (assert (equal (first e) '^))
    (assert (integerp (third e)))
    (assert (= (length e) 3))
    (let ((x (assoc (second e) tab)))
      (if (null x) (error "Variable ~a not in the list of variables." 
                         (second e))
        (incf (cdr x) (third e))))))
  

;; New implementation based on the INFIX package of Mark Kantorowitz
(defun parse-to-alist (vars &optional stream)
  "Parse an expression already in prefix form to an association list form
according to the internal CGBlisp polynomial syntax: a polynomial is an
alist of pairs (MONOM . COEFFICIENT). For example:
  (WITH-INPUT-FROM-STRING (S \"X^2-Y^2+(-4/3)*U^2*W^3-5\")
        (PARSE-TO-ALIST '(X Y U W) S))
evaluates to
(((0 0 2 3) . -4/3) ((0 2 0 0) . -1) ((2 0 0 0) . 1) ((0 0 0 0) . -5))"
  (poly-eval (parse stream) vars))


(defun parse-string-to-alist (str vars)
  "Parse string STR and return a polynomial as a sorted association
list of pairs (MONOM . COEFFICIENT). For example:
(parse-string-to-alist \"[x^2-y^2+(-4/3)*u^2*w^3-5,y]\" '(x y u w))
 ([ (((0 0 2 3) . -4/3) ((0 2 0 0) . -1) ((2 0 0 0) . 1)
     ((0 0 0 0) . -5))
    (((0 1 0 0) . 1)))
The functions PARSE-TO-SORTED-ALIST and PARSE-STRING-TO-SORTED-ALIST
sort terms by the predicate defined in the ORDER package."
  (with-input-from-string (stream str)
    (parse-to-alist vars stream)))


(defun parse-to-sorted-alist (vars &optional (order #'lex>) (stream t))
  "Parses streasm STREAM and returns a polynomial represented as 
a sorted alist. For example:
(WITH-INPUT-FROM-STRING (S \"X^2-Y^2+(-4/3)*U^2*W^3-5\")
  (PARSE-TO-SORTED-ALIST '(X Y U W) S))
returns
(((2 0 0 0) . 1) ((0 2 0 0) . -1) ((0 0 2 3) . -4/3) ((0 0 0 0) . -5))
and
(WITH-INPUT-FROM-STRING (S \"X^2-Y^2+(-4/3)*U^2*W^3-5\")
  (PARSE-TO-SORTED-ALIST '(X Y U W) T #'GRLEX>) S)
returns
(((0 0 2 3) . -4/3) ((2 0 0 0) . 1) ((0 2 0 0) . -1) ((0 0 0 0) . -5))"
  (sort-poly (parse-to-alist vars stream) order))

(defun parse-string-to-sorted-alist (str vars &optional (order #'lex>))
  "Parse a string to a sorted alist form, the internal representation
of polynomials used by our system."
  (with-input-from-string (stream str)
    (parse-to-sorted-alist vars order stream)))

(defun sort-poly-1 (p order)
  "Sort the terms of a single polynomial P using an admissible monomial order ORDER.
Returns the sorted polynomial. Destructively modifies P."
  (sort p order :key #'first))

;; Sort a polynomial or polynomial list
(defun sort-poly (poly-or-poly-list &optional (order #'lex>))
  "Sort POLY-OR-POLY-LIST, which could be either a single polynomial
or a list of polynomials in internal alist representation, using
admissible monomial order ORDER. Each polynomial is sorted using
SORT-POLY-1."
  (cond
   ((eql poly-or-poly-list :syntax-error) nil)
   ((null poly-or-poly-list) nil)
   ((eql (car poly-or-poly-list) '[)
    (cons '[ (mapcar #'(lambda (p) (sort-poly-1 p order)) 
                     (rest poly-or-poly-list))))
   (t (sort-poly-1 poly-or-poly-list order))))