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source: branches/f4grobner/termlist.lisp@ 1950

Last change on this file since 1950 was 1950, checked in by Marek Rychlik, 10 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 "TERMLIST"
23 (:use :cl :monom :ring :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(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
48
49(defun termlist-sugar (p &aux (sugar -1))
50 (declare (fixnum sugar))
51 (dolist (term p sugar)
52 (setf sugar (max sugar (term-sugar term)))))
53
54(defun termlist-contract (p &optional (k 1))
55 "Eliminate first K variables from a polynomial P."
56 (mapcar #'(lambda (term) (make-term :monom (monom-contract (term-monom term) k)
57 :coeff (term-coeff term)))
58 p))
59
60(defun termlist-extend (p &optional (m (make-monom :dimension 1)))
61 "Extend every monomial in a polynomial P by inserting at the
62beginning of every monomial the list of powers M."
63 (mapcar #'(lambda (term) (make-term :monom (monom-append m (term-monom term))
64 :coeff (term-coeff term)))
65 p))
66
67(defun termlist-add-variables (p n)
68 "Add N variables to a polynomial P by inserting zero powers
69at the beginning of each monomial."
70 (declare (fixnum n))
71 (mapcar #'(lambda (term)
72 (declare (type term term))
73 (make-term :monom (monom-append (make-monom :dimension n)
74 (term-monom term))
75 :coeff (term-coeff term)))
76 p))
77
78
79;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
80;;
81;; Low-level polynomial arithmetic done on
82;; lists of terms
83;;
84;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
85
86(defmacro termlist-lt (p) `(car ,p))
87(defun termlist-lm (p) (term-monom (termlist-lt p)))
88(defun termlist-lc (p) (term-coeff (termlist-lt p)))
89
90(define-modify-macro scalar-mul (c) coeff-mul)
91
92(defun scalar-times-termlist (ring c p)
93 "Multiply scalar C by a polynomial P. This function works
94even if there are divisors of 0."
95 (declare (ring ring))
96 (mapcan
97 #'(lambda (term)
98 (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
99 (unless (funcall (ring-zerop ring) c1)
100 (list (make-term :monom (term-monom term) :coeff c1)))))
101 p))
102
103
104(defun term-mul-lst (ring term1 term2)
105 "A special version of term multiplication. Returns (LIST TERM) where
106TERM is the product of the terms TERM1 TERM2, or NIL when the product
107is 0. This definition takes care of divisors of 0 in the coefficient
108ring."
109 (declare (ring ring) (type term1 term2))
110 (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
111 (unless (funcall (ring-zerop ring) c)
112 (list (make-term :monom (monom-mul (term-monom term1) (term-monom term2))
113 :coeff c)))))
114
115(defun term-times-termlist (ring term f)
116 (declare (type ring ring) (type term term))
117 (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))
118
119(defun termlist-times-term (ring f term)
120 (declare (ring ring) (type term term))
121 (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))
122
123(defun monom-times-term (m term)
124 (declare (type monom m) (type term term))
125 (make-term :monom (monom-mul m (term-monom term)) :coeff (term-coeff term)))
126
127(defun monom-times-termlist (m f)
128 (declare (type monom m))
129 (cond
130 ((null f) nil)
131 (t
132 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
133
134(defun termlist-uminus (ring f)
135 (declare (ring ring))
136 (mapcar #'(lambda (x)
137 (make-term :monom (term-monom x)
138 :coeff (funcall (ring-uminus ring) (term-coeff x))))
139 f))
140
141(defun termlist-add (ring-and-order p q
142 &aux
143 (ring (ro-ring ring-and-order))
144 (order (ro-order ring-and-order)))
145 (declare (ring-and-order ring-and-order) (type list p q))
146 (do (r)
147 ((cond
148 ((endp p)
149 (setf r (revappend r q)) t)
150 ((endp q)
151 (setf r (revappend r p)) t)
152 (t
153 (multiple-value-bind
154 (lm-greater lm-equal)
155 (funcall order (termlist-lm p) (termlist-lm q))
156 (cond
157 (lm-equal
158 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
159 (unless (funcall (ring-zerop ring) s) ;check for cancellation
160 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
161 (setf p (cdr p) q (cdr q))))
162 (lm-greater
163 (setf r (cons (car p) r)
164 p (cdr p)))
165 (t (setf r (cons (car q) r)
166 q (cdr q)))))
167 nil))
168 r)))
169
170(defun termlist-sub (ring-and-order p q
171 &aux
172 (ring (ro-ring ring-and-order))
173 (order (ro-order ring-and-order)))
174 (declare (ring-and-order ring-and-order) (type list p q))
175 (do (r)
176 ((cond
177 ((endp p)
178 (setf r (revappend r (termlist-uminus ring q)))
179 t)
180 ((endp q)
181 (setf r (revappend r p))
182 t)
183 (t
184 (multiple-value-bind
185 (mgreater mequal)
186 (funcall order (termlist-lm p) (termlist-lm q))
187 (cond
188 (mequal
189 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
190 (unless (funcall (ring-zerop ring) s) ;check for cancellation
191 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
192 (setf p (cdr p) q (cdr q))))
193 (mgreater
194 (setf r (cons (car p) r)
195 p (cdr p)))
196 (t (setf r (cons (make-term :monom (termlist-lm q)
197 :coeff (funcall (ring-uminus ring) (termlist-lc q))) r)
198 q (cdr q)))))
199 nil))
200 r)))
201
202;; Multiplication of polynomials
203;; Non-destructive version
204(defun termlist-mul (ring-and-order p q
205 &aux (ring (ro-ring ring-and-order)))
206 (declare (ring-and-order ring-and-order))
207 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
208 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
209 ((endp (cdr p))
210 (term-times-termlist ring (car p) q))
211 ((endp (cdr q))
212 (termlist-times-term ring p (car q)))
213 (t
214 (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
215 (tail (termlist-add ring-and-order
216 (term-times-termlist ring (car p) (cdr q))
217 (termlist-mul ring-and-order (cdr p) q))))
218 (cond ((null head) tail)
219 ((null tail) head)
220 (t (nconc head tail)))))))
221
222(defun termlist-unit (ring dim)
223 (declare (ring ring) (fixnum dim))
224 (list (make-term :monom (make-monom :dimension dim)
225 :coeff (funcall (ring-unit ring)))))
226
227
228(defun termlist-expt (ring-and-order poly n
229 &aux
230 (ring (ro-ring ring-and-order))
231 (dim (monom-dimension (termlist-lm poly))))
232 (declare (ring-and-order ring-and-order) (type fixnum n dim))
233 (cond
234 ((minusp n) (error "termlist-expt: Negative exponent."))
235 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
236 (t
237 (do ((k 1 (ash k 1))
238 (q poly (termlist-mul ring-and-order q q)) ;keep squaring
239 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring-and-order p q) p)))
240 ((> k n) p)
241 (declare (fixnum k))))))
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