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source: branches/f4grobner/termlist.lisp@ 545

Last change on this file since 545 was 445, checked in by Marek Rychlik, 9 years ago

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1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
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 "TERMLIST"
23 (:use :cl :ring :monomial :order :term)
24 (:export "TERMLIST-SUGAR"
25 "TERMLIST-CONTRACT"
26 "TERMLIST-EXTEND"
27 "TERMLIST-ADD-VARIABLES"
28 "TERMLIST-LT"
29 "TERMLIST-LM"
30 "TERMLIST-LC"
31 "SCALAR-MUL"
32 "SCALAR-TIMES-TERMLIST"
33 "TERM-MUL-LST"
34 "TERMLIST-TIMES-TERM"
35 "TERM-TIMES-TERMLIST"
36 "MONOM-TIMES-TERM"
37 "MONOM-TIMES-TERMLIST"
38 "TERMLIST-UMINUS"
39 "TERMLIST-ADD"
40 "TERMLIST-SUB"
41 "TERMLIST-MUL"
42 "TERMLIST-UNIT"
43 "TERMLIST-EXPT"))
44
45(in-package :termlist)
46
47(defun termlist-sugar (p &aux (sugar -1))
48 (declare (fixnum sugar))
49 (dolist (term p sugar)
50 (setf sugar (max sugar (term-sugar term)))))
51
52(defun termlist-contract (p &optional (k 1))
53 "Eliminate first K variables from a polynomial P."
54 (mapcar #'(lambda (term) (make-term (monom-contract k (term-monom term))
55 (term-coeff term)))
56 p))
57
58(defun termlist-extend (p &optional (m (make-monom 1 :initial-element 0)))
59 "Extend every monomial in a polynomial P by inserting at the
60beginning of every monomial the list of powers M."
61 (mapcar #'(lambda (term) (make-term (monom-append m (term-monom term))
62 (term-coeff term)))
63 p))
64
65(defun termlist-add-variables (p n)
66 "Add N variables to a polynomial P by inserting zero powers
67at the beginning of each monomial."
68 (declare (fixnum n))
69 (mapcar #'(lambda (term)
70 (make-term (monom-append (make-monom n :initial-element 0)
71 (term-monom term))
72 (term-coeff term)))
73 p))
74
75
76;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
77;;
78;; Low-level polynomial arithmetic done on
79;; lists of terms
80;;
81;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
82
83(defmacro termlist-lt (p) `(car ,p))
84(defun termlist-lm (p) (term-monom (termlist-lt p)))
85(defun termlist-lc (p) (term-coeff (termlist-lt p)))
86
87(define-modify-macro scalar-mul (c) coeff-mul)
88
89(defun scalar-times-termlist (ring c p)
90 "Multiply scalar C by a polynomial P. This function works
91even if there are divisors of 0."
92 (mapcan
93 #'(lambda (term)
94 (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
95 (unless (funcall (ring-zerop ring) c1)
96 (list (make-term (term-monom term) c1)))))
97 p))
98
99
100(defun term-mul-lst (ring term1 term2)
101 "A special version of term multiplication. Returns (LIST TERM) where
102TERM is the product of the terms TERM1 TERM2, or NIL when the product
103is 0. This definition takes care of divisors of 0 in the coefficient
104ring."
105 (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
106 (unless (funcall (ring-zerop ring) c)
107 (list (make-term (monom-mul (term-monom term1) (term-monom term2)) c)))))
108
109(defun term-times-termlist (ring term f)
110 (declare (type ring ring))
111 (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))
112
113(defun termlist-times-term (ring f term)
114 (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))
115
116(defun monom-times-term (m term)
117 (make-term (monom-mul m (term-monom term)) (term-coeff term)))
118
119(defun monom-times-termlist (m f)
120 (cond
121 ((null f) nil)
122 (t
123 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
124
125(defun termlist-uminus (ring f)
126 (mapcar #'(lambda (x)
127 (make-term (term-monom x) (funcall (ring-uminus ring) (term-coeff x))))
128 f))
129
130(defun termlist-add (ring p q)
131 (declare (type list p q))
132 (do (r)
133 ((cond
134 ((endp p)
135 (setf r (revappend r q)) t)
136 ((endp q)
137 (setf r (revappend r p)) t)
138 (t
139 (multiple-value-bind
140 (lm-greater lm-equal)
141 (monomial-order (termlist-lm p) (termlist-lm q))
142 (cond
143 (lm-equal
144 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
145 (unless (funcall (ring-zerop ring) s) ;check for cancellation
146 (setf r (cons (make-term (termlist-lm p) s) r)))
147 (setf p (cdr p) q (cdr q))))
148 (lm-greater
149 (setf r (cons (car p) r)
150 p (cdr p)))
151 (t (setf r (cons (car q) r)
152 q (cdr q)))))
153 nil))
154 r)))
155
156(defun termlist-sub (ring p q)
157 (declare (type list p q))
158 (do (r)
159 ((cond
160 ((endp p)
161 (setf r (revappend r (termlist-uminus ring q)))
162 t)
163 ((endp q)
164 (setf r (revappend r p))
165 t)
166 (t
167 (multiple-value-bind
168 (mgreater mequal)
169 (monomial-order (termlist-lm p) (termlist-lm q))
170 (cond
171 (mequal
172 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
173 (unless (funcall (ring-zerop ring) s) ;check for cancellation
174 (setf r (cons (make-term (termlist-lm p) s) r)))
175 (setf p (cdr p) q (cdr q))))
176 (mgreater
177 (setf r (cons (car p) r)
178 p (cdr p)))
179 (t (setf r (cons (make-term (termlist-lm q) (funcall (ring-uminus ring) (termlist-lc q))) r)
180 q (cdr q)))))
181 nil))
182 r)))
183
184;; Multiplication of polynomials
185;; Non-destructive version
186(defun termlist-mul (ring p q)
187 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
188 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
189 ((endp (cdr p))
190 (term-times-termlist ring (car p) q))
191 ((endp (cdr q))
192 (termlist-times-term ring p (car q)))
193 (t
194 (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
195 (tail (termlist-add ring (term-times-termlist ring (car p) (cdr q))
196 (termlist-mul ring (cdr p) q))))
197 (cond ((null head) tail)
198 ((null tail) head)
199 (t (nconc head tail)))))))
200
201(defun termlist-unit (ring dimension)
202 (declare (fixnum dimension))
203 (list (make-term (make-monom dimension :initial-element 0)
204 (funcall (ring-unit ring)))))
205
206(defun termlist-expt (ring poly n &aux (dim (monom-dimension (termlist-lm poly))))
207 (declare (type fixnum n dim))
208 (cond
209 ((minusp n) (error "termlist-expt: Negative exponent."))
210 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
211 (t
212 (do ((k 1 (ash k 1))
213 (q poly (termlist-mul ring q q)) ;keep squaring
214 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring p q) p)))
215 ((> k n) p)
216 (declare (fixnum k))))))
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