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source: branches/f4grobner/symbolic-polynomial.lisp@ 3348

Last change on this file since 3348 was 3341, 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")
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(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 r-equalp ((self symbolic-poly) (other symbolic-poly))
50 (when (r-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
51 (call-next-method)))
52
53(defmethod update-instance-for-different-class :after ((old poly) (new symbolic-poly) &key)
54 "After adding variables to NEW, we need to make sure that the number
55of variables given by POLY-DIMENSION is consistent with VARS."
56 (assert (= (length (symbolic-poly-vars new)) (poly-dimension new))))
57
58
59#|
60(defun poly-eval (expr vars
61 &optional
62 (order #'lex>)
63 (list-marker :[))
64 "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
65variables VARS. Return the resulting polynomial or list of
66polynomials. Standard arithmetical operators in form EXPR are
67replaced with their analogues in the ring of polynomials, and the
68resulting expression is evaluated, resulting in a polynomial or a list
69of polynomials in internal form. A similar operation in another computer
70algebra system could be called 'expand' or so."
71 (declare (type ring ring))
72 (labels ((p-eval (arg) (poly-eval arg vars ring order))
73 (p-eval-scalar (arg) (poly-eval-scalar arg))
74 (p-eval-list (args) (mapcar #'p-eval args))
75 (p-add (x y) (poly-add ring-and-order x y)))
76 (cond
77 ((null expr) (error "Empty expression"))
78 ((eql expr 0) (make-poly-zero))
79 ((member expr vars :test #'equalp)
80 (let ((pos (position expr vars :test #'equalp)))
81 (make-poly-variable ring (length vars) pos)))
82 ((atom expr)
83 (coerce-coeff ring expr vars))
84 ((eq (car expr) list-marker)
85 (cons list-marker (p-eval-list (cdr expr))))
86 (t
87 (case (car expr)
88 (+ (reduce #'p-add (p-eval-list (cdr expr))))
89 (- (case (length expr)
90 (1 (make-poly-zero))
91 (2 (poly-uminus ring (p-eval (cadr expr))))
92 (3 (poly-sub ring-and-order (p-eval (cadr expr)) (p-eval (caddr expr))))
93 (otherwise (poly-sub ring-and-order (p-eval (cadr expr))
94 (reduce #'p-add (p-eval-list (cddr expr)))))))
95 (*
96 (if (endp (cddr expr)) ;unary
97 (p-eval (cdr expr))
98 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (p-eval-list (cdr expr)))))
99 (/
100 ;; A polynomial can be divided by a scalar
101 (cond
102 ((endp (cddr expr))
103 ;; A special case (/ ?), the inverse
104 (coerce-coeff ring (apply (ring-div ring) (cdr expr)) vars))
105 (t
106 (let ((num (p-eval (cadr expr)))
107 (denom-inverse (apply (ring-div ring)
108 (cons (funcall (ring-unit ring))
109 (mapcar #'p-eval-scalar (cddr expr))))))
110 (scalar-times-poly ring denom-inverse num)))))
111 (expt
112 (cond
113 ((member (cadr expr) vars :test #'equalp)
114 ;;Special handling of (expt var pow)
115 (let ((pos (position (cadr expr) vars :test #'equalp)))
116 (make-poly-variable ring (length vars) pos (caddr expr))))
117 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
118 ;; Negative power means division in coefficient ring
119 ;; Non-integer power means non-polynomial coefficient
120 (coerce-coeff ring expr vars))
121 (t (poly-expt ring-and-order (p-eval (cadr expr)) (caddr expr)))))
122 (otherwise
123 (coerce-coeff ring expr vars)))))))
124
125(defun poly-eval-scalar (expr
126 &optional
127 (ring +ring-of-integers+)
128 &aux
129 (order #'lex>))
130 "Evaluate a scalar expression EXPR in ring RING."
131 (declare (type ring ring))
132 (poly-lc (poly-eval expr nil ring order)))
133
134
135(defun read-infix-form (&key (stream t))
136 "Parser of infix expressions with integer/rational coefficients
137The parser will recognize two kinds of polynomial expressions:
138
139- polynomials in fully expanded forms with coefficients
140 written in front of symbolic expressions; constants can be optionally
141 enclosed in (); for example, the infix form
142 X^2-Y^2+(-4/3)*U^2*W^3-5
143 parses to
144 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
145
146- lists of polynomials; for example
147 [X-Y, X^2+3*Z]
148 parses to
149 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
150 where the first symbol [ marks a list of polynomials.
151
152-other infix expressions, for example
153 [(X-Y)*(X+Y)/Z,(X+1)^2]
154parses to:
155 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
156Currently this function is implemented using M. Kantrowitz's INFIX package."
157 (read-from-string
158 (concatenate 'string
159 "#I("
160 (with-output-to-string (s)
161 (loop
162 (multiple-value-bind (line eof)
163 (read-line stream t)
164 (format s "~A" line)
165 (when eof (return)))))
166 ")")))
167
168(defun read-poly (vars &key
169 (stream t)
170 (ring +ring-of-integers+)
171 (order #'lex>))
172 "Reads an expression in prefix form from a stream STREAM.
173The expression read from the strem should represent a polynomial or a
174list of polynomials in variables VARS, over the ring RING. The
175polynomial or list of polynomials is returned, with terms in each
176polynomial ordered according to monomial order ORDER."
177 (poly-eval (read-infix-form :stream stream) vars ring order))
178
179(defun string->poly (str vars
180 &optional
181 (ring +ring-of-integers+)
182 (order #'lex>))
183 "Converts a string STR to a polynomial in variables VARS."
184 (with-input-from-string (s str)
185 (read-poly vars :stream s :ring ring :order order)))
186
187(defun poly->alist (p)
188 "Convert a polynomial P to an association list. Thus, the format of the
189returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
190MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
191corresponding coefficient in the ring."
192 (cond
193 ((poly-p p)
194 (mapcar #'term->cons (poly-termlist p)))
195 ((and (consp p) (eq (car p) :[))
196 (cons :[ (mapcar #'poly->alist (cdr p))))))
197
198(defun string->alist (str vars
199 &optional
200 (ring +ring-of-integers+)
201 (order #'lex>))
202 "Convert a string STR representing a polynomial or polynomial list to
203an association list (... (MONOM . COEFF) ...)."
204 (poly->alist (string->poly str vars ring order)))
205
206(defun poly-equal-no-sugar-p (p q)
207 "Compare polynomials for equality, ignoring sugar."
208 (declare (type poly p q))
209 (equalp (poly-termlist p) (poly-termlist q)))
210
211(defun poly-set-equal-no-sugar-p (p q)
212 "Compare polynomial sets P and Q for equality, ignoring sugar."
213 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
214
215(defun poly-list-equal-no-sugar-p (p q)
216 "Compare polynomial lists P and Q for equality, ignoring sugar."
217 (every #'poly-equal-no-sugar-p p q))
218
219|#
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