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source: branches/f4grobner/symbolic-polynomial.lisp@ 3398

Last change on this file since 3398 was 3398, checked in by Marek Rychlik, 9 years ago

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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 :ring :monom :order :term :polynomial :infix)
24 (:export "SYMBOLIC-POLY" "READ-INFIX-FORM" "STRING->POLY" "+LIST-MARKER+")
25 (:documentation "Implements symbolic polynomials. A symbolic
26polynomial is and object which uses symbolic variables for reading and
27printing in standard human-readable (infix) form."))
28
29(in-package :symbolic-polynomial)
30
31(defparameter +list-marker+ :[
32 "A sexp with this head is considered a list of polynomials.")
33
34(defclass symbolic-poly (poly)
35 ((vars :initform nil
36 :initarg :vars
37 :accessor symbolic-poly-vars)
38 )
39 (:default-initargs :termlist nil :vars nil))
40
41(defmethod print-object ((self symbolic-poly) stream)
42 (print-unreadable-object (self stream :type t :identity t)
43 (with-accessors ((dimension poly-dimension)
44 (termlist poly-termlist)
45 (order poly-term-order)
46 (vars symbolic-poly-vars))
47 self
48 (format stream "DIMENSION=~A TERMLIST=~A ORDER=~A VARS=~A"
49 dimension termlist order vars))))
50
51
52(defmethod r-equalp ((self symbolic-poly) (other symbolic-poly))
53 (when (r-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
54 (call-next-method)))
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(defgeneric poly-eval (expr vars order)
62 (:documentation "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
63variables VARS. Return the resulting polynomial or list of
64polynomials. Standard arithmetical operators in form EXPR are
65replaced with their analogues in the ring of polynomials, and the
66resulting expression is evaluated, resulting in a polynomial or a list
67of polynomials in internal form. A similar operation in another computer
68algebra system could be called 'expand' or so.")
69 (:method ((expr symbolic-poly) vars order) expr)
70 (:method (expr vars order)
71 (labels ((p-eval (p) (poly-eval p vars order))
72 (p-eval-scalar (p) (poly-eval p '() order))
73 (p-eval-list (plist) (mapcar #'p-eval plist)))
74 (cond
75 ((eq expr 0)
76 (make-instance 'symbolic-poly :dimension (length vars) :vars vars))
77 ((member expr vars :test #'equalp)
78 (let ((pos (position expr vars :test #'equalp)))
79 (make-monom-variable (length vars) pos)))
80 ((atom expr)
81 expr)
82 ((eq (car expr) +list-marker+)
83 (cons +list-marker+ (p-eval-list (cdr expr))))
84 (t
85 (case (car expr)
86 (+ (reduce #'r+ (p-eval-list (cdr expr))))
87 (- (case (length expr)
88 (1 (make-poly-zero))
89 (2 (r- (p-eval (cadr expr))))
90 (3 (r- (p-eval (cadr expr)) (p-eval (caddr expr))))
91 (otherwise (r- (p-eval (cadr expr))
92 (reduce #'r+ (p-eval-list (cddr expr)))))))
93 (*
94 (if (endp (cddr expr)) ;unary
95 (p-eval (cdr expr))
96 (reduce #'r* (p-eval-list (cdr expr)))))
97 (/
98 ;; A polynomial can be divided by a scalar
99 (cond
100 ((endp (cddr expr))
101 ;; A special case (/ ?), the inverse
102 (r/ (cdr expr)))
103 (t
104 (let ((num (p-eval (cadr expr)))
105 (denom-inverse (r/ (mapcar #'p-eval-scalar (cddr expr)))))
106 (r* denom-inverse num)))))
107 (expt
108 (cond
109 ((member (cadr expr) vars :test #'equalp)
110 ;;Special handling of (expt var pow)
111 (let ((pos (position (cadr expr) vars :test #'equalp)))
112 (make-poly-variable ring (length vars) pos (caddr expr))))
113 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
114 ;; Negative power means division in coefficient ring
115 ;; Non-integer power means non-polynomial coefficient
116 (coerce-coeff ring expr vars))
117 (t (r-expt (p-eval (cadr expr)) (caddr expr)))))
118 (otherwise
119 (coerce-coeff ring expr vars))))))))
120
121#|
122(defun poly-eval-scalar (expr
123 &optional
124 (ring +ring-of-integers+)
125 &aux
126 (order #'lex>))
127 "Evaluate a scalar expression EXPR in ring RING."
128 (declare (type ring ring))
129 (poly-lc (poly-eval expr nil ring order)))
130|#
131
132
133(defun read-infix-form (&key (stream t))
134 "Parser of infix expressions with integer/rational coefficients
135The parser will recognize two kinds of polynomial expressions:
136
137- polynomials in fully expanded forms with coefficients
138 written in front of symbolic expressions; constants can be optionally
139 enclosed in (); for example, the infix form
140 X^2-Y^2+(-4/3)*U^2*W^3-5
141 parses to
142 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
143
144- lists of polynomials; for example
145 [X-Y, X^2+3*Z]
146 parses to
147 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
148 where the first symbol [ marks a list of polynomials.
149
150-other infix expressions, for example
151 [(X-Y)*(X+Y)/Z,(X+1)^2]
152parses to:
153 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
154Currently this function is implemented using M. Kantrowitz's INFIX package."
155 (read-from-string
156 (concatenate 'string
157 "#I("
158 (with-output-to-string (s)
159 (loop
160 (multiple-value-bind (line eof)
161 (read-line stream t)
162 (format s "~A" line)
163 (when eof (return)))))
164 ")")))
165
166(defun read-poly (vars &key
167 (stream t)
168 (order #'lex>))
169 "Reads an expression in prefix form from a stream STREAM.
170The expression read from the strem should represent a polynomial or a
171list of polynomials in variables VARS, over the ring RING. The
172polynomial or list of polynomials is returned, with terms in each
173polynomial ordered according to monomial order ORDER."
174 (poly-eval (read-infix-form :stream stream) vars order))
175
176(defun string->poly (str vars
177 &optional
178 (order #'lex>))
179 "Converts a string STR to a polynomial in variables VARS."
180 (with-input-from-string (s str)
181 (read-poly vars :stream s :order order)))
182
183(defun poly->alist (p)
184 "Convert a polynomial P to an association list. Thus, the format of the
185returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
186MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
187corresponding coefficient in the ring."
188 (cond
189 ((poly-p p)
190 (mapcar #'term->cons (poly-termlist p)))
191 ((and (consp p) (eq (car p) :[))
192 (cons :[ (mapcar #'poly->alist (cdr p))))))
193
194(defun string->alist (str vars
195 &optional
196 (ring +ring-of-integers+)
197 (order #'lex>))
198 "Convert a string STR representing a polynomial or polynomial list to
199an association list (... (MONOM . COEFF) ...)."
200 (poly->alist (string->poly str vars ring order)))
201
202(defun poly-equal-no-sugar-p (p q)
203 "Compare polynomials for equality, ignoring sugar."
204 (declare (type poly p q))
205 (equalp (poly-termlist p) (poly-termlist q)))
206
207(defun poly-set-equal-no-sugar-p (p q)
208 "Compare polynomial sets P and Q for equality, ignoring sugar."
209 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
210
211(defun poly-list-equal-no-sugar-p (p q)
212 "Compare polynomial lists P and Q for equality, ignoring sugar."
213 (every #'poly-equal-no-sugar-p p q))
214
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