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source: branches/f4grobner/symbolic-polynomial.lisp@ 4317

Last change on this file since 4317 was 4202, checked in by Marek Rychlik, 8 years ago

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File size: 6.9 KB
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1;;; -*- Mode: Lisp -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22(defpackage "SYMBOLIC-POLYNOMIAL"
23 (:use :cl :utils :monom :polynomial :infix :infix-printer)
24 (:export "SYMBOLIC-POLY" "READ-INFIX-FORM" "STRING->POLY" "POLY->STRING" "->INFIX")
25 (:documentation "Implements symbolic polynomials. A symbolic
26polynomial is polynomial which uses symbolic variables for reading and
27printing in standard human-readable (infix) form."))
28
29(in-package :symbolic-polynomial)
30
31(defclass symbolic-poly (poly)
32 ((vars :initform nil
33 :initarg :vars
34 :accessor symbolic-poly-vars)
35 )
36 (:default-initargs :termlist nil :vars nil))
37
38(defmethod print-object ((self symbolic-poly) stream)
39 (print-unreadable-object (self stream :type t :identity t)
40 (with-accessors ((dimension poly-dimension)
41 (termlist poly-termlist)
42 (order poly-term-order)
43 (vars symbolic-poly-vars))
44 self
45 (format stream "DIMENSION=~A TERMLIST=~A ORDER=~A VARS=~A"
46 dimension termlist order vars))))
47
48
49(defmethod universal-equalp ((self symbolic-poly) (other symbolic-poly))
50 (when (universal-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
51 (call-next-method)))
52
53(defmethod universal-equalp ((self symbol) (other symbol))
54 (eq self other))
55
56(defmethod update-instance-for-different-class :after ((old poly) (new symbolic-poly) &key)
57 "After adding variables to NEW, we need to make sure that the number
58of variables given by POLY-DIMENSION is consistent with VARS."
59 (assert (= (length (symbolic-poly-vars new)) (poly-dimension new))))
60
61
62#|
63(defun poly-eval-scalar (expr
64 &aux
65 (order #'lex>))
66 "Evaluate a scalar expression EXPR in ring RING."
67 (declare (type ring ring))
68 (poly-lc (poly-eval expr nil ring order)))
69|#
70
71
72(defun read-infix-form (&key (stream t))
73 "Parser of infix expressions with integer/rational coefficients
74The parser will recognize two kinds of polynomial expressions:
75
76- polynomials in fully expanded forms with coefficients
77 written in front of symbolic expressions; constants can be optionally
78 enclosed in (); for example, the infix form
79 X^2-Y^2+(-4/3)*U^2*W^3-5
80 parses to
81 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
82
83- lists of polynomials; for example
84 [X-Y, X^2+3*Z]
85 parses to
86 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
87 where the first symbol [ marks a list of polynomials.
88
89-other infix expressions, for example
90 [(X-Y)*(X+Y)/Z,(X+1)^2]
91parses to:
92 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
93Currently this function is implemented using M. Kantrowitz's INFIX package."
94 (read-from-string
95 (concatenate 'string
96 "#I("
97 (with-output-to-string (s)
98 (loop
99 (multiple-value-bind (line eof)
100 (read-line stream t)
101 (format s "~A" line)
102 (when eof (return)))))
103 ")")))
104
105(defun read-poly (vars &key
106 (stream t)
107 (order #'lex>))
108 "Reads an expression in prefix form from a stream STREAM.
109The expression read from the strem should represent a polynomial or a
110list of polynomials in variables VARS, over the ring RING. The
111polynomial or list of polynomials is returned, with terms in each
112polynomial ordered according to monomial order ORDER."
113 (poly-eval (read-infix-form :stream stream) vars order))
114
115(defun string->poly (str vars
116 &optional
117 (order #'lex>))
118 "Converts a string STR to a polynomial in variables VARS."
119 (with-input-from-string (s str)
120 (let ((p-or-plist (read-poly vars :stream s :order order)))
121 (etypecase p-or-plist
122 (poly (change-class p-or-plist 'symbolic-poly :vars vars))
123 (cons
124 (setf (cdr p-or-plist) (mapcar #'(lambda (p) (change-class p 'symbolic-poly :vars vars)) (cdr p-or-plist)))
125 p-or-plist)))))
126
127(defun poly->alist (p)
128 "Convert a polynomial P to an association list. Thus, the format of the
129returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
130MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
131corresponding coefficient in the ring."
132 (cond
133 ((poly-p p)
134 (mapcar #'->list (poly-termlist p)))
135 ((and (consp p) (eq (car p) :[))
136 (cons :[ (mapcar #'poly->alist (cdr p))))))
137
138(defun string->alist (str vars
139 &optional
140 (order #'lex>))
141 "Convert a string STR representing a polynomial or polynomial list to
142an association list (... (MONOM . COEFF) ...)."
143 (poly->alist (string->poly str vars order)))
144
145(defun poly-equal-no-sugar-p (p q)
146 "Compare polynomials for equality, ignoring sugar."
147 (declare (type poly p q))
148 (equalp (poly-termlist p) (poly-termlist q)))
149
150(defun poly-set-equal-no-sugar-p (p q)
151 "Compare polynomial sets P and Q for equality, ignoring sugar."
152 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
153
154(defun poly-list-equal-no-sugar-p (p q)
155 "Compare polynomial lists P and Q for equality, ignoring sugar."
156 (every #'poly-equal-no-sugar-p p q))
157
158(defmethod ->sexp :around ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))
159 "Convert a symbolic polynomial SELF to infix form, using variables VARS. The default
160value of VARS is the corresponding slot value of SELF."
161 (call-next-method self vars))
162
163(defgeneric poly->string (self &optional vars)
164 (:documentation "Render polynomial SELF as a string, using symbolic variables VARS.")
165 (:method ((self list) &optional (vars nil vars-p))
166 (assert (eql (car self) :[))
167 (cond (vars-p
168 (format nil "[~{~a~^, ~}]" (mapcar #'(lambda (p) (poly->string p vars)) (cdr self))))
169 (t
170 (format nil "[~{~a~^, ~}]" (mapcar #'(lambda (p) (poly->string p)) (cdr self))))))
171 (:method ((self poly) &optional (vars nil))
172 ;; Ensure that the number of variables matches the dimension
173 (assert (= (length vars) (poly-dimension self)))
174 (infix-print-to-string (->sexp self vars)))
175 (:method ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))
176 (infix-print-to-string (->sexp self vars))))
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