;;; -*- 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>		 
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;;;  This program is free software; you can redistribute it and/or modify	 
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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.
;;
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(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)))))
     ")")))

;; 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))