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source: branches/f4grobner/symbolic-polynomial.lisp@ 3805

Last change on this file since 3805 was 3773, 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)
24 (:export "SYMBOLIC-POLY" "READ-INFIX-FORM" "STRING->POLY" "+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(defgeneric poly-eval (expr vars order)
65 (:documentation "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 (:method ((expr symbolic-poly) vars order) expr)
73 (:method (expr vars order)
74 (labels ((p-eval (p) (poly-eval p vars order))
75 (p-eval-scalar (p) (poly-eval p '() order))
76 (p-eval-list (plist) (mapcar #'p-eval plist)))
77 (cond
78 ((eq expr 0)
79 (make-instance 'symbolic-poly :dimension (length vars) :vars vars))
80 ((member expr vars :test #'equalp)
81 (let ((pos (position expr vars :test #'equalp)))
82 (make-poly-variable (length vars) pos)))
83 ((atom expr)
84 expr)
85 ((eq (car expr) +list-marker+)
86 (cons +list-marker+ (p-eval-list (cdr expr))))
87 (t
88 (case (car expr)
89 (+ (reduce #'add (p-eval-list (cdr expr))))
90 (- (apply #'subtract (p-eval-list (cdr expr))))
91 (*
92 (if (endp (cddr expr)) ;unary
93 (p-eval (cdr expr))
94 (reduce #'multiply (p-eval-list (cdr expr)))))
95 (/
96 ;; A polynomial can be divided by a scalar
97 (cond
98 ((endp (cddr expr))
99 ;; A special case (/ ?), the inverse
100 (divide (cadr expr)))
101 (t
102 (let ((num (p-eval (cadr expr)))
103 (denom-inverse (apply #'divide (mapcar #'p-eval-scalar (cddr expr)))))
104 (multiply denom-inverse num)))))
105 (expt
106 (cond
107 ((member (cadr expr) vars :test #'equalp)
108 ;;Special handling of (expt var pow)
109 (let ((pos (position (cadr expr) vars :test #'equalp)))
110 (make-poly-variable (length vars) pos (caddr expr))))
111 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
112 ;; Negative power means division in coefficient ring
113 ;; Non-integer power means non-polynomial coefficient
114 expr)
115 (t (universal-expt (p-eval (cadr expr)) (caddr expr)))))
116 (otherwise
117 expr)))))))
118
119#|
120(defun poly-eval-scalar (expr
121 &aux
122 (order #'lex>))
123 "Evaluate a scalar expression EXPR in ring RING."
124 (declare (type ring ring))
125 (poly-lc (poly-eval expr nil ring order)))
126|#
127
128
129(defun read-infix-form (&key (stream t))
130 "Parser of infix expressions with integer/rational coefficients
131The parser will recognize two kinds of polynomial expressions:
132
133- polynomials in fully expanded forms with coefficients
134 written in front of symbolic expressions; constants can be optionally
135 enclosed in (); for example, the infix form
136 X^2-Y^2+(-4/3)*U^2*W^3-5
137 parses to
138 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
139
140- lists of polynomials; for example
141 [X-Y, X^2+3*Z]
142 parses to
143 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
144 where the first symbol [ marks a list of polynomials.
145
146-other infix expressions, for example
147 [(X-Y)*(X+Y)/Z,(X+1)^2]
148parses to:
149 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
150Currently this function is implemented using M. Kantrowitz's INFIX package."
151 (read-from-string
152 (concatenate 'string
153 "#I("
154 (with-output-to-string (s)
155 (loop
156 (multiple-value-bind (line eof)
157 (read-line stream t)
158 (format s "~A" line)
159 (when eof (return)))))
160 ")")))
161
162(defun read-poly (vars &key
163 (stream t)
164 (order #'lex>))
165 "Reads an expression in prefix form from a stream STREAM.
166The expression read from the strem should represent a polynomial or a
167list of polynomials in variables VARS, over the ring RING. The
168polynomial or list of polynomials is returned, with terms in each
169polynomial ordered according to monomial order ORDER."
170 (poly-eval (read-infix-form :stream stream) vars order))
171
172(defun string->poly (str vars
173 &optional
174 (order #'lex>))
175 "Converts a string STR to a polynomial in variables VARS."
176 (with-input-from-string (s str)
177 (read-poly vars :stream s :order order)))
178
179(defun poly->alist (p)
180 "Convert a polynomial P to an association list. Thus, the format of the
181returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
182MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
183corresponding coefficient in the ring."
184 (cond
185 ((poly-p p)
186 (mapcar #'->list (poly-termlist p)))
187 ((and (consp p) (eq (car p) :[))
188 (cons :[ (mapcar #'poly->alist (cdr p))))))
189
190(defun string->alist (str vars
191 &optional
192 (order #'lex>))
193 "Convert a string STR representing a polynomial or polynomial list to
194an association list (... (MONOM . COEFF) ...)."
195 (poly->alist (string->poly str vars order)))
196
197(defun poly-equal-no-sugar-p (p q)
198 "Compare polynomials for equality, ignoring sugar."
199 (declare (type poly p q))
200 (equalp (poly-termlist p) (poly-termlist q)))
201
202(defun poly-set-equal-no-sugar-p (p q)
203 "Compare polynomial sets P and Q for equality, ignoring sugar."
204 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
205
206(defun poly-list-equal-no-sugar-p (p q)
207 "Compare polynomial lists P and Q for equality, ignoring sugar."
208 (every #'poly-equal-no-sugar-p p q))
209
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