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source: branches/f4grobner/termlist.lisp@ 705

Last change on this file since 705 was 705, 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 :monomial :ring-and-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 (declare (ring ring))
106 (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
107 (unless (funcall (ring-zerop ring) c)
108 (list (make-term (monom-mul (term-monom term1) (term-monom term2)) c)))))
109
110(defun term-times-termlist (ring term f)
111 (declare (type ring ring))
112 (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))
113
114(defun termlist-times-term (ring f term)
115 (declare (ring ring))
116 (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))
117
118(defun monom-times-term (m term)
119 (make-term (monom-mul m (term-monom term)) (term-coeff term)))
120
121(defun monom-times-termlist (m f)
122 (cond
123 ((null f) nil)
124 (t
125 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
126
127(defun termlist-uminus (ring f)
128 (declare (ring ring))
129 (mapcar #'(lambda (x)
130 (make-term (term-monom x) (funcall (ring-uminus ring) (term-coeff x))))
131 f))
132
133(defun termlist-add (ring p q)
134 (declare (type list p q) (ring ring))
135 (do (r)
136 ((cond
137 ((endp p)
138 (setf r (revappend r q)) t)
139 ((endp q)
140 (setf r (revappend r p)) t)
141 (t
142 (multiple-value-bind
143 (lm-greater lm-equal)
144 (funcall (ro-order ring) (termlist-lm p) (termlist-lm q))
145 (cond
146 (lm-equal
147 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
148 (unless (funcall (ring-zerop ring) s) ;check for cancellation
149 (setf r (cons (make-term (termlist-lm p) s) r)))
150 (setf p (cdr p) q (cdr q))))
151 (lm-greater
152 (setf r (cons (car p) r)
153 p (cdr p)))
154 (t (setf r (cons (car q) r)
155 q (cdr q)))))
156 nil))
157 r)))
158
159(defun termlist-sub (ring p q)
160 (declare (type list p q) (ring ring))
161 (do (r)
162 ((cond
163 ((endp p)
164 (setf r (revappend r (termlist-uminus ring q)))
165 t)
166 ((endp q)
167 (setf r (revappend r p))
168 t)
169 (t
170 (multiple-value-bind
171 (mgreater mequal)
172 (funcall (ro-order ring) (termlist-lm p) (termlist-lm q))
173 (cond
174 (mequal
175 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
176 (unless (funcall (ring-zerop ring) s) ;check for cancellation
177 (setf r (cons (make-term (termlist-lm p) s) r)))
178 (setf p (cdr p) q (cdr q))))
179 (mgreater
180 (setf r (cons (car p) r)
181 p (cdr p)))
182 (t (setf r (cons (make-term (termlist-lm q) (funcall (ring-uminus ring) (termlist-lc q))) r)
183 q (cdr q)))))
184 nil))
185 r)))
186
187;; Multiplication of polynomials
188;; Non-destructive version
189(defun termlist-mul (ring p q)
190 (declare (ring ring))
191 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
192 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
193 ((endp (cdr p))
194 (term-times-termlist ring (car p) q))
195 ((endp (cdr q))
196 (termlist-times-term ring p (car q)))
197 (t
198 (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
199 (tail (termlist-add ring (term-times-termlist ring (car p) (cdr q))
200 (termlist-mul ring (cdr p) q))))
201 (cond ((null head) tail)
202 ((null tail) head)
203 (t (nconc head tail)))))))
204
205(defun termlist-unit (ring dimension)
206 (declare (fixnum dimension) (ring ring))
207 (list (make-term (make-monom dimension :initial-element 0)
208 (funcall (ring-unit ring)))))
209
210(defun termlist-expt (ring poly n &aux (dim (monom-dimension (termlist-lm poly))))
211 (declare (type fixnum n dim) (ring ring))
212 (cond
213 ((minusp n) (error "termlist-expt: Negative exponent."))
214 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
215 (t
216 (do ((k 1 (ash k 1))
217 (q poly (termlist-mul ring q q)) ;keep squaring
218 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring p q) p)))
219 ((> k n) p)
220 (declare (fixnum k))))))
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