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source: branches/f4grobner/symbolic-polynomial.lisp@ 3371

Last change on this file since 3371 was 3371, 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")
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
33(defclass symbolic-poly (poly)
34 ((vars :initform nil
35 :initarg :vars
36 :accessor symbolic-poly-vars)
37 )
38 (:default-initargs :termlist nil :vars nil))
39
40(defmethod print-object ((self symbolic-poly) stream)
41 (print-unreadable-object (self stream :type t :identity t)
42 (with-accessors ((dimension poly-dimension)
43 (termlist poly-termlist)
44 (order poly-term-order)
45 (vars symbolic-poly-vars))
46 self
47 (format stream "DIMENSION=~A TERMLIST=~A ORDER=~A VARS=~A"
48 dimension termlist order vars))))
49
50
51(defmethod r-equalp ((self symbolic-poly) (other symbolic-poly))
52 (when (r-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
53 (call-next-method)))
54
55(defmethod update-instance-for-different-class :after ((old poly) (new symbolic-poly) &key)
56 "After adding variables to NEW, we need to make sure that the number
57of variables given by POLY-DIMENSION is consistent with VARS."
58 (assert (= (length (symbolic-poly-vars new)) (poly-dimension new))))
59
60(defgeneric poly-eval (expr vars order)
61 (:documentation "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
62variables VARS. Return the resulting polynomial or list of
63polynomials. Standard arithmetical operators in form EXPR are
64replaced with their analogues in the ring of polynomials, and the
65resulting expression is evaluated, resulting in a polynomial or a list
66of polynomials in internal form. A similar operation in another computer
67algebra system could be called 'expand' or so.")
68 (:method ((expr symbolic-poly) vars order) expr)
69 (:method (expr vars order)
70 (cond
71 ((eq expr 0)
72 (make-instance 'symbolic-poly :dimension (length vars) :vars vars))
73 ((member expr vars :test #'equalp)
74 (let ((pos (position expr vars :test #'equalp)))
75 (make-monom-variable (length vars) pos)))
76 ((atom expr)
77 expr)
78 ((eq (car expr) list-marker)
79 (cons list-marker (p-eval-list (cdr expr))))
80 (t
81 (case (car expr)
82 (+ (reduce #'add-to (p-eval-list (cdr expr))))
83 (- (case (length expr)
84 (1 (make-poly-zero))
85 (2 (poly-uminus ring (p-eval (cadr expr))))
86 (3 (poly-sub ring-and-order (p-eval (cadr expr)) (p-eval (caddr expr))))
87 (otherwise (poly-sub ring-and-order (p-eval (cadr expr))
88 (reduce #'p-add (p-eval-list (cddr expr)))))))
89 (*
90 (if (endp (cddr expr)) ;unary
91 (p-eval (cdr expr))
92 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (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 (coerce-coeff ring (apply (ring-div ring) (cdr expr)) vars))
99 (t
100 (let ((num (p-eval (cadr expr)))
101 (denom-inverse (apply (ring-div ring)
102 (cons (funcall (ring-unit ring))
103 (mapcar #'p-eval-scalar (cddr expr))))))
104 (scalar-times-poly ring 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 ring (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 (coerce-coeff ring expr vars))
115 (t (poly-expt ring-and-order (p-eval (cadr expr)) (caddr expr)))))
116 (otherwise
117 (coerce-coeff ring expr vars)))))))
118
119#|
120(defun poly-eval-scalar (expr
121 &optional
122 (ring +ring-of-integers+)
123 &aux
124 (order #'lex>))
125 "Evaluate a scalar expression EXPR in ring RING."
126 (declare (type ring ring))
127 (poly-lc (poly-eval expr nil ring order)))
128|#
129
130
131(defun read-infix-form (&key (stream t))
132 "Parser of infix expressions with integer/rational coefficients
133The parser will recognize two kinds of polynomial expressions:
134
135- polynomials in fully expanded forms with coefficients
136 written in front of symbolic expressions; constants can be optionally
137 enclosed in (); for example, the infix form
138 X^2-Y^2+(-4/3)*U^2*W^3-5
139 parses to
140 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
141
142- lists of polynomials; for example
143 [X-Y, X^2+3*Z]
144 parses to
145 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
146 where the first symbol [ marks a list of polynomials.
147
148-other infix expressions, for example
149 [(X-Y)*(X+Y)/Z,(X+1)^2]
150parses to:
151 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
152Currently this function is implemented using M. Kantrowitz's INFIX package."
153 (read-from-string
154 (concatenate 'string
155 "#I("
156 (with-output-to-string (s)
157 (loop
158 (multiple-value-bind (line eof)
159 (read-line stream t)
160 (format s "~A" line)
161 (when eof (return)))))
162 ")")))
163
164(defun read-poly (vars &key
165 (stream t)
166 (order #'lex>))
167 "Reads an expression in prefix form from a stream STREAM.
168The expression read from the strem should represent a polynomial or a
169list of polynomials in variables VARS, over the ring RING. The
170polynomial or list of polynomials is returned, with terms in each
171polynomial ordered according to monomial order ORDER."
172 (poly-eval (read-infix-form :stream stream) vars order))
173
174(defun string->poly (str vars
175 &optional
176 (order #'lex>))
177 "Converts a string STR to a polynomial in variables VARS."
178 (with-input-from-string (s str)
179 (read-poly vars :stream s :order order)))
180
181(defun poly->alist (p)
182 "Convert a polynomial P to an association list. Thus, the format of the
183returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
184MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
185corresponding coefficient in the ring."
186 (cond
187 ((poly-p p)
188 (mapcar #'term->cons (poly-termlist p)))
189 ((and (consp p) (eq (car p) :[))
190 (cons :[ (mapcar #'poly->alist (cdr p))))))
191
192(defun string->alist (str vars
193 &optional
194 (ring +ring-of-integers+)
195 (order #'lex>))
196 "Convert a string STR representing a polynomial or polynomial list to
197an association list (... (MONOM . COEFF) ...)."
198 (poly->alist (string->poly str vars ring order)))
199
200(defun poly-equal-no-sugar-p (p q)
201 "Compare polynomials for equality, ignoring sugar."
202 (declare (type poly p q))
203 (equalp (poly-termlist p) (poly-termlist q)))
204
205(defun poly-set-equal-no-sugar-p (p q)
206 "Compare polynomial sets P and Q for equality, ignoring sugar."
207 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
208
209(defun poly-list-equal-no-sugar-p (p q)
210 "Compare polynomial lists P and Q for equality, ignoring sugar."
211 (every #'poly-equal-no-sugar-p p q))
212
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