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source: branches/f4grobner/symbolic-polynomial.lisp@ 4437

Last change on this file since 4437 was 4435, 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 :ring)
24 (:export "SYMBOLIC-POLY" "READ-INFIX-FORM" "STRING->POLY" "POLY->STRING" "->INFIX")
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(defclass symbolic-poly (poly)
32 ((vars :initform nil
33 :initarg :vars
34 :accessor symbolic-poly-vars)
35 )
36 (:default-initargs :termlist nil :vars nil))
37
38(defmethod print-object ((self symbolic-poly) stream)
39 (print-unreadable-object (self stream :type t :identity t)
40 (with-accessors ((dimension poly-dimension)
41 (termlist poly-termlist)
42 (order poly-term-order)
43 (vars symbolic-poly-vars))
44 self
45 (format stream "DIMENSION=~A TERMLIST=~A ORDER=~A VARS=~A"
46 dimension termlist order vars))))
47
48
49(defmethod universal-equalp ((self symbolic-poly) (other symbolic-poly))
50 (when (universal-equalp (symbolic-poly-vars self) (symbolic-poly-vars other))
51 (call-next-method)))
52
53(defmethod universal-equalp ((self symbolic-poly) (other poly))
54 "Compare SELF, which is an instance of SYMBOLIC-POLY, to OTHER, which
55is an instance of POLY. We simply ignore variables of SELF, and compare
56SELF and OTHER as POLY."
57 (call-next-method))
58
59(defmethod universal-equalp ((self symbol) (other symbol))
60 (eq self other))
61
62(defmethod update-instance-for-different-class :after ((old poly) (new symbolic-poly) &key)
63 "After adding variables to NEW, we need to make sure that the number
64of variables given by POLY-DIMENSION is consistent with VARS."
65 (assert (= (length (symbolic-poly-vars new)) (poly-dimension new))))
66
67
68#|
69(defun poly-eval-scalar (expr
70 &aux
71 (order #'lex>))
72 "Evaluate a scalar expression EXPR in ring RING."
73 (declare (type ring ring))
74 (poly-lc (poly-eval expr nil ring order)))
75|#
76
77
78(defun read-infix-form (&key (stream t))
79 "Parser of infix expressions with integer/rational coefficients
80The parser will recognize two kinds of polynomial expressions:
81
82- polynomials in fully expanded forms with coefficients
83 written in front of symbolic expressions; constants can be optionally
84 enclosed in (); for example, the infix form
85 X^2-Y^2+(-4/3)*U^2*W^3-5
86 parses to
87 (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
88
89- lists of polynomials; for example
90 [X-Y, X^2+3*Z]
91 parses to
92 (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
93 where the first symbol [ marks a list of polynomials.
94
95-other infix expressions, for example
96 [(X-Y)*(X+Y)/Z,(X+1)^2]
97parses to:
98 (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
99Currently this function is implemented using M. Kantrowitz's INFIX package."
100 (read-from-string
101 (concatenate 'string
102 "#I("
103 (with-output-to-string (s)
104 (loop
105 (multiple-value-bind (line eof)
106 (read-line stream t)
107 (format s "~A" line)
108 (when eof (return)))))
109 ")")))
110
111(defun read-poly (vars &key
112 (stream t)
113 (order #'lex>)
114 (coefficient-class *coefficient-class*))
115 "Reads an expression in prefix form from a stream STREAM.
116The expression read from the strem should represent a polynomial or a
117list of polynomials in variables VARS, over the ring RING. The
118polynomial or list of polynomials is returned, with terms in each
119polynomial ordered according to monomial order ORDER."
120 (poly-eval (read-infix-form :stream stream) vars order coefficient-class))
121
122(defun string->poly (str vars
123 &optional
124 (order #'lex>)
125 (coefficient-class *coefficient-class*))
126 "Converts a string STR to a polynomial in variables VARS."
127 (with-input-from-string (s str)
128 (let ((p-or-plist (read-poly vars :stream s :order order :coefficient-class coefficient-class)))
129 (etypecase p-or-plist
130 (poly (change-class p-or-plist 'symbolic-poly :vars vars))
131 (cons
132 (setf (cdr p-or-plist) (mapcar #'(lambda (p) (change-class p 'symbolic-poly :vars vars)) (cdr p-or-plist)))
133 p-or-plist)))))
134
135(defun poly->alist (p)
136 "Convert a polynomial P to an association list. Thus, the format of the
137returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
138MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
139corresponding coefficient in the ring."
140 (cond
141 ((poly-p p)
142 (mapcar #'->list (poly-termlist p)))
143 ((and (consp p) (eq (car p) :[))
144 (cons :[ (mapcar #'poly->alist (cdr p))))))
145
146(defun string->alist (str vars
147 &optional
148 (order #'lex>)
149 (coefficient-class *coefficient-class*))
150 "Convert a string STR representing a polynomial or polynomial list to
151an association list (... (MONOM . COEFF) ...)."
152 (poly->alist (string->poly str vars order coefficient-class)))
153
154(defun poly-equal-no-sugar-p (p q)
155 "Compare polynomials for equality, ignoring sugar."
156 (declare (type poly p q))
157 (equalp (poly-termlist p) (poly-termlist q)))
158
159(defun poly-set-equal-no-sugar-p (p q)
160 "Compare polynomial sets P and Q for equality, ignoring sugar."
161 (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
162
163(defun poly-list-equal-no-sugar-p (p q)
164 "Compare polynomial lists P and Q for equality, ignoring sugar."
165 (every #'poly-equal-no-sugar-p p q))
166
167(defmethod ->sexp :around ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))
168 "Convert a symbolic polynomial SELF to infix form, using variables VARS. The default
169value of VARS is the corresponding slot value of SELF."
170 (call-next-method self vars))
171
172(defgeneric poly->string (self &optional vars)
173 (:documentation "Render polynomial SELF as a string, using symbolic variables VARS.")
174 (:method ((self list) &optional (vars nil vars-p))
175 (assert (eql (car self) :[))
176 (cond (vars-p
177 (format nil "[~{~a~^, ~}]" (mapcar #'(lambda (p) (poly->string p vars)) (cdr self))))
178 (t
179 (format nil "[~{~a~^, ~}]" (mapcar #'(lambda (p) (poly->string p)) (cdr self))))))
180 (:method ((self poly) &optional (vars nil))
181 ;; Ensure that the number of variables matches the dimension
182 (assert (= (length vars) (poly-dimension self)))
183 (infix-print-to-string (->sexp self vars)))
184 (:method ((self symbolic-poly) &optional (vars (symbolic-poly-vars self)))
185 (infix-print-to-string (->sexp self vars))))
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