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source: branches/f4grobner/symbolic-polynomial.lisp@ 3394

Last change on this file since 3394 was 3394, 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" "+LIST-MARKER+")
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 "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 r-equalp ((self symbolic-poly) (other symbolic-poly))
53 (when (r-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
54 (call-next-method)))
55
56(defmethod update-instance-for-different-class :after ((old poly) (new symbolic-poly) &key)
57 "After adding variables to NEW, we need to make sure that the number
58of variables given by POLY-DIMENSION is consistent with VARS."
59 (assert (= (length (symbolic-poly-vars new)) (poly-dimension new))))
60
61(defgeneric poly-eval (expr vars order)
62 (:documentation "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
63variables VARS. Return the resulting polynomial or list of
64polynomials. Standard arithmetical operators in form EXPR are
65replaced with their analogues in the ring of polynomials, and the
66resulting expression is evaluated, resulting in a polynomial or a list
67of polynomials in internal form. A similar operation in another computer
68algebra system could be called 'expand' or so.")
69 (:method ((expr symbolic-poly) vars order) expr)
70 (:method (expr vars order)
71 (labels ((p-eval (p) (poly-eval p vars order))
72 (p-eval-list (plist) (mapcar #'p-eval plist)))
73 (cond
74 ((eq expr 0)
75 (make-instance 'symbolic-poly :dimension (length vars) :vars vars))
76 ((member expr vars :test #'equalp)
77 (let ((pos (position expr vars :test #'equalp)))
78 (make-monom-variable (length vars) pos)))
79 ((atom expr)
80 expr)
81 ((eq (car expr) +list-marker+)
82 (cons +list-marker+ (p-eval-list (cdr expr))))
83 (t
84 (case (car expr)
85 (+ (reduce #'r+ (p-eval-list (cdr expr))))
86 (- (case (length expr)
87 (1 (make-poly-zero))
88 (2 (r- (p-eval (cadr expr))))
89 (3 (r- (p-eval (cadr expr)) (p-eval (caddr expr))))
90 (otherwise (r- (p-eval (cadr expr))
91 (reduce #'r+ (p-eval-list (cddr expr)))))))
92 (*
93 (if (endp (cddr expr)) ;unary
94 (p-eval (cdr expr))
95 (reduce #'r* (p-eval-list (cdr expr)))))
96 (/
97 ;; A polynomial can be divided by a scalar
98 (cond
99 ((endp (cddr expr))
100 ;; A special case (/ ?), the inverse
101 (coerce-coeff ring (apply (ring-div ring) (cdr expr)) vars))
102 (t
103 (let ((num (p-eval (cadr expr)))
104 (denom-inverse (apply (ring-div ring)
105 (cons (funcall (ring-unit ring))
106 (mapcar #'p-eval-scalar (cddr expr))))))
107 (scalar-times-poly ring denom-inverse num)))))
108 (expt
109 (cond
110 ((member (cadr expr) vars :test #'equalp)
111 ;;Special handling of (expt var pow)
112 (let ((pos (position (cadr expr) vars :test #'equalp)))
113 (make-poly-variable ring (length vars) pos (caddr expr))))
114 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
115 ;; Negative power means division in coefficient ring
116 ;; Non-integer power means non-polynomial coefficient
117 (coerce-coeff ring expr vars))
118 (t (r-expt (p-eval (cadr expr)) (caddr expr)))))
119 (otherwise
120 (coerce-coeff ring expr vars))))))))
121
122#|
123(defun poly-eval-scalar (expr
124 &optional
125 (ring +ring-of-integers+)
126 &aux
127 (order #'lex>))
128 "Evaluate a scalar expression EXPR in ring RING."
129 (declare (type ring ring))
130 (poly-lc (poly-eval expr nil ring order)))
131|#
132
133
134(defun read-infix-form (&key (stream t))
135 "Parser of infix expressions with integer/rational coefficients
136The parser will recognize two kinds of polynomial expressions:
137
138- polynomials in fully expanded forms with coefficients
139 written in front of symbolic expressions; constants can be optionally
140 enclosed in (); for example, the infix form
141 X^2-Y^2+(-4/3)*U^2*W^3-5
142 parses to
143 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
144
145- lists of polynomials; for example
146 [X-Y, X^2+3*Z]
147 parses to
148 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
149 where the first symbol [ marks a list of polynomials.
150
151-other infix expressions, for example
152 [(X-Y)*(X+Y)/Z,(X+1)^2]
153parses to:
154 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
155Currently this function is implemented using M. Kantrowitz's INFIX package."
156 (read-from-string
157 (concatenate 'string
158 "#I("
159 (with-output-to-string (s)
160 (loop
161 (multiple-value-bind (line eof)
162 (read-line stream t)
163 (format s "~A" line)
164 (when eof (return)))))
165 ")")))
166
167(defun read-poly (vars &key
168 (stream t)
169 (order #'lex>))
170 "Reads an expression in prefix form from a stream STREAM.
171The expression read from the strem should represent a polynomial or a
172list of polynomials in variables VARS, over the ring RING. The
173polynomial or list of polynomials is returned, with terms in each
174polynomial ordered according to monomial order ORDER."
175 (poly-eval (read-infix-form :stream stream) vars order))
176
177(defun string->poly (str vars
178 &optional
179 (order #'lex>))
180 "Converts a string STR to a polynomial in variables VARS."
181 (with-input-from-string (s str)
182 (read-poly vars :stream s :order order)))
183
184(defun poly->alist (p)
185 "Convert a polynomial P to an association list. Thus, the format of the
186returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
187MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
188corresponding coefficient in the ring."
189 (cond
190 ((poly-p p)
191 (mapcar #'term->cons (poly-termlist p)))
192 ((and (consp p) (eq (car p) :[))
193 (cons :[ (mapcar #'poly->alist (cdr p))))))
194
195(defun string->alist (str vars
196 &optional
197 (ring +ring-of-integers+)
198 (order #'lex>))
199 "Convert a string STR representing a polynomial or polynomial list to
200an association list (... (MONOM . COEFF) ...)."
201 (poly->alist (string->poly str vars ring order)))
202
203(defun poly-equal-no-sugar-p (p q)
204 "Compare polynomials for equality, ignoring sugar."
205 (declare (type poly p q))
206 (equalp (poly-termlist p) (poly-termlist q)))
207
208(defun poly-set-equal-no-sugar-p (p q)
209 "Compare polynomial sets P and Q for equality, ignoring sugar."
210 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
211
212(defun poly-list-equal-no-sugar-p (p q)
213 "Compare polynomial lists P and Q for equality, ignoring sugar."
214 (every #'poly-equal-no-sugar-p p q))
215
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