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source: branches/f4grobner/symbolic-polynomial.lisp@ 3241

Last change on this file since 3241 was 3240, 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 :initarg :vars :accessor symbolic-poly-vars))
33 (:default-initargs :termlist nil :vars nil))
34
35(defmethod print-object ((self poly) stream)
36 (print-unreadable-object (self stream :type t :identity t)
37 (with-accessors ((termlist poly-termlist)
38 (order poly-term-order)
39 (vars symbolic-poly-vars))
40 self
41 (format stream "TERMLIST=~A ORDER=~A VARS=~A"
42 termlist order vars))))
43
44
45#|
46
47(defun coerce-coeff (ring expr vars)
48 "Coerce an element of the coefficient ring to a constant polynomial."
49 (declare (type ring ring))
50 (make-poly-from-termlist (list (make-term :monom (make-monom :dimension (length vars))
51 :coeff (funcall (ring-parse ring) expr)))
52 0))
53
54(defun poly-eval (expr vars
55 &optional
56 (order #'lex>)
57 (list-marker :[))
58 "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
59variables VARS. Return the resulting polynomial or list of
60polynomials. Standard arithmetical operators in form EXPR are
61replaced with their analogues in the ring of polynomials, and the
62resulting expression is evaluated, resulting in a polynomial or a list
63of polynomials in internal form. A similar operation in another computer
64algebra system could be called 'expand' or so."
65 (declare (type ring ring))
66 (labels ((p-eval (arg) (poly-eval arg vars ring order))
67 (p-eval-scalar (arg) (poly-eval-scalar arg))
68 (p-eval-list (args) (mapcar #'p-eval args))
69 (p-add (x y) (poly-add ring-and-order x y)))
70 (cond
71 ((null expr) (error "Empty expression"))
72 ((eql expr 0) (make-poly-zero))
73 ((member expr vars :test #'equalp)
74 (let ((pos (position expr vars :test #'equalp)))
75 (make-poly-variable ring (length vars) pos)))
76 ((atom expr)
77 (coerce-coeff ring expr vars))
78 ((eq (car expr) list-marker)
79 (cons list-marker (p-eval-list (cdr expr))))
80 (t
81 (case (car expr)
82 (+ (reduce #'p-add (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(defun poly-eval-scalar (expr
120 &optional
121 (ring +ring-of-integers+)
122 &aux
123 (order #'lex>))
124 "Evaluate a scalar expression EXPR in ring RING."
125 (declare (type ring ring))
126 (poly-lc (poly-eval expr nil ring order)))
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 (ring +ring-of-integers+)
165 (order #'lex>))
166 "Reads an expression in prefix form from a stream STREAM.
167The expression read from the strem should represent a polynomial or a
168list of polynomials in variables VARS, over the ring RING. The
169polynomial or list of polynomials is returned, with terms in each
170polynomial ordered according to monomial order ORDER."
171 (poly-eval (read-infix-form :stream stream) vars ring order))
172
173(defun string->poly (str vars
174 &optional
175 (ring +ring-of-integers+)
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 :ring ring :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
213|#
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