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source: branches/f4grobner/symbolic-polynomial.lisp@ 3868

Last change on this file since 3868 was 3864, checked in by Marek Rychlik, 8 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 :monom :polynomial :infix :infix-printer)
24 (:export "SYMBOLIC-POLY" "READ-INFIX-FORM" "STRING->POLY" "POLY->STRING" "->INFIX" "+LIST-MARKER+")
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(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 universal-equalp ((self symbolic-poly) (other symbolic-poly))
53 (when (universal-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
54 (call-next-method)))
55
56(defmethod universal-equalp ((self symbol) (other symbol))
57 (eq self other))
58
59(defmethod update-instance-for-different-class :after ((old poly) (new symbolic-poly) &key)
60 "After adding variables to NEW, we need to make sure that the number
61of variables given by POLY-DIMENSION is consistent with VARS."
62 (assert (= (length (symbolic-poly-vars new)) (poly-dimension new))))
63
64(defun poly-eval (expr vars order)
65 "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
66variables VARS. Return the resulting polynomial or list of
67polynomials. Standard arithmetical operators in form EXPR are
68replaced with their analogues in the ring of polynomials, and the
69resulting expression is evaluated, resulting in a polynomial or a list
70of polynomials in internal form. A similar operation in another computer
71algebra system could be called 'expand' or so."
72 (labels ((p-eval (p) (poly-eval p vars order))
73 (p-eval-scalar (p) (poly-eval p '() order))
74 (p-eval-list (plist) (mapcar #'p-eval plist)))
75 (cond
76 ((eq expr 0)
77 (make-instance 'symbolic-poly :dimension (length vars) :vars vars))
78 ((member expr vars :test #'equalp)
79 (let ((pos (position expr vars :test #'equalp)))
80 (make-poly-variable (length vars) pos)))
81 ((atom expr)
82 expr)
83 ((eq (car expr) +list-marker+)
84 (cons +list-marker+ (p-eval-list (cdr expr))))
85 (t
86 (case (car expr)
87 (+ (reduce #'add (p-eval-list (cdr expr))))
88 (- (apply #'subtract (p-eval-list (cdr expr))))
89 (*
90 (if (endp (cddr expr)) ;unary
91 (p-eval (cdr expr))
92 (reduce #'multiply (p-eval-list (cdr expr)))))
93 (/
94 ;; A polynomial can be divided by a scalar
95 (cond
96 ((endp (cddr expr))
97 ;; A special case (/ ?), the inverse
98 (divide (cadr expr)))
99 (t
100 (let ((num (p-eval (cadr expr)))
101 (denom-inverse (apply #'divide (mapcar #'p-eval-scalar (cddr expr)))))
102 (multiply denom-inverse num)))))
103 (expt
104 (cond
105 ((member (cadr expr) vars :test #'equalp)
106 ;;Special handling of (expt var pow)
107 (let ((pos (position (cadr expr) vars :test #'equalp)))
108 (make-poly-variable (length vars) pos (caddr expr))))
109 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
110 ;; Negative power means division in coefficient ring
111 ;; Non-integer power means non-polynomial coefficient
112 expr)
113 (t (universal-expt (p-eval (cadr expr)) (caddr expr)))))
114 (otherwise
115 expr))))))
116
117#|
118(defun poly-eval-scalar (expr
119 &aux
120 (order #'lex>))
121 "Evaluate a scalar expression EXPR in ring RING."
122 (declare (type ring ring))
123 (poly-lc (poly-eval expr nil ring order)))
124|#
125
126
127(defun read-infix-form (&key (stream t))
128 "Parser of infix expressions with integer/rational coefficients
129The parser will recognize two kinds of polynomial expressions:
130
131- polynomials in fully expanded forms with coefficients
132 written in front of symbolic expressions; constants can be optionally
133 enclosed in (); for example, the infix form
134 X^2-Y^2+(-4/3)*U^2*W^3-5
135 parses to
136 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
137
138- lists of polynomials; for example
139 [X-Y, X^2+3*Z]
140 parses to
141 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
142 where the first symbol [ marks a list of polynomials.
143
144-other infix expressions, for example
145 [(X-Y)*(X+Y)/Z,(X+1)^2]
146parses to:
147 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
148Currently this function is implemented using M. Kantrowitz's INFIX package."
149 (read-from-string
150 (concatenate 'string
151 "#I("
152 (with-output-to-string (s)
153 (loop
154 (multiple-value-bind (line eof)
155 (read-line stream t)
156 (format s "~A" line)
157 (when eof (return)))))
158 ")")))
159
160(defun read-poly (vars &key
161 (stream t)
162 (order #'lex>))
163 "Reads an expression in prefix form from a stream STREAM.
164The expression read from the strem should represent a polynomial or a
165list of polynomials in variables VARS, over the ring RING. The
166polynomial or list of polynomials is returned, with terms in each
167polynomial ordered according to monomial order ORDER."
168 (poly-eval (read-infix-form :stream stream) vars order))
169
170(defun string->poly (str vars
171 &optional
172 (order #'lex>))
173 "Converts a string STR to a polynomial in variables VARS."
174 (with-input-from-string (s str)
175 (change-class (read-poly vars :stream s :order order) 'symbolic-poly :vars vars)))
176
177(defun poly->alist (p)
178 "Convert a polynomial P to an association list. Thus, the format of the
179returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
180MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
181corresponding coefficient in the ring."
182 (cond
183 ((poly-p p)
184 (mapcar #'->list (poly-termlist p)))
185 ((and (consp p) (eq (car p) :[))
186 (cons :[ (mapcar #'poly->alist (cdr p))))))
187
188(defun string->alist (str vars
189 &optional
190 (order #'lex>))
191 "Convert a string STR representing a polynomial or polynomial list to
192an association list (... (MONOM . COEFF) ...)."
193 (poly->alist (string->poly str vars order)))
194
195(defun poly-equal-no-sugar-p (p q)
196 "Compare polynomials for equality, ignoring sugar."
197 (declare (type poly p q))
198 (equalp (poly-termlist p) (poly-termlist q)))
199
200(defun poly-set-equal-no-sugar-p (p q)
201 "Compare polynomial sets P and Q for equality, ignoring sugar."
202 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
203
204(defun poly-list-equal-no-sugar-p (p q)
205 "Compare polynomial lists P and Q for equality, ignoring sugar."
206 (every #'poly-equal-no-sugar-p p q))
207
208(defmethod ->infix :around ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))
209 "Convert a symbolic polynomial SELF to infix form, using variables VARS. The default
210value of VARS is the corresponding slot value of SELF."
211 (call-next-method self vars))
212
213(defgeneric poly->string (self &optional vars)
214 (:documentation "Render polynomial SELF as a string, using symbolic variables VARS.")
215 (:method ((self poly) &optional (vars nil))
216 ;; Ensure that the number of variables matches the dimension
217 (assert (= (length vars) (poly-dimension self)))
218 (infix-print (->infix self vars)))
219 (:method ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))
220 (infix-print (->infix self vars))))
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