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source: branches/f4grobner/termlist.lisp@ 1829

Last change on this file since 1829 was 1829, 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(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 (monom-contract (term-monom term) k)
55 :coeff (term-coeff term)))
56 p))
57
58(defun termlist-extend (p &optional (m (make-monom :dimension 1)))
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 :dimension n)
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 (declare (ring ring))
93 (mapcan
94 #'(lambda (term)
95 (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
96 (unless (funcall (ring-zerop ring) c1)
97 (list (make-term (term-monom term) c1)))))
98 p))
99
100
101(defun term-mul-lst (ring term1 term2)
102 "A special version of term multiplication. Returns (LIST TERM) where
103TERM is the product of the terms TERM1 TERM2, or NIL when the product
104is 0. This definition takes care of divisors of 0 in the coefficient
105ring."
106 (declare (ring ring))
107 (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
108 (unless (funcall (ring-zerop ring) c)
109 (list (make-term (monom-mul (term-monom term1) (term-monom term2)) c)))))
110
111(defun term-times-termlist (ring term f)
112 (declare (type ring ring))
113 (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))
114
115(defun termlist-times-term (ring f term)
116 (declare (ring ring))
117 (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))
118
119(defun monom-times-term (m term)
120 (make-term (monom-mul m (term-monom term)) (term-coeff term)))
121
122(defun monom-times-termlist (m f)
123 (cond
124 ((null f) nil)
125 (t
126 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
127
128(defun termlist-uminus (ring f)
129 (declare (ring ring))
130 (mapcar #'(lambda (x)
131 (make-term (term-monom x) (funcall (ring-uminus ring) (term-coeff x))))
132 f))
133
134(defun termlist-add (ring-and-order p q
135 &aux
136 (ring (ro-ring ring-and-order))
137 (order (ro-order ring-and-order)))
138 (declare (type list p q) (ring-and-order ring-and-order))
139 (do (r)
140 ((cond
141 ((endp p)
142 (setf r (revappend r q)) t)
143 ((endp q)
144 (setf r (revappend r p)) t)
145 (t
146 (multiple-value-bind
147 (lm-greater lm-equal)
148 (funcall order (termlist-lm p) (termlist-lm q))
149 (cond
150 (lm-equal
151 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
152 (unless (funcall (ring-zerop ring) s) ;check for cancellation
153 (setf r (cons (make-term (termlist-lm p) s) r)))
154 (setf p (cdr p) q (cdr q))))
155 (lm-greater
156 (setf r (cons (car p) r)
157 p (cdr p)))
158 (t (setf r (cons (car q) r)
159 q (cdr q)))))
160 nil))
161 r)))
162
163(defun termlist-sub (ring-and-order p q
164 &aux
165 (ring (ro-ring ring-and-order))
166 (order (ro-order ring-and-order)))
167 (declare (type list p q) (ring-and-order ring-and-order))
168 (do (r)
169 ((cond
170 ((endp p)
171 (setf r (revappend r (termlist-uminus ring q)))
172 t)
173 ((endp q)
174 (setf r (revappend r p))
175 t)
176 (t
177 (multiple-value-bind
178 (mgreater mequal)
179 (funcall order (termlist-lm p) (termlist-lm q))
180 (cond
181 (mequal
182 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
183 (unless (funcall (ring-zerop ring) s) ;check for cancellation
184 (setf r (cons (make-term (termlist-lm p) s) r)))
185 (setf p (cdr p) q (cdr q))))
186 (mgreater
187 (setf r (cons (car p) r)
188 p (cdr p)))
189 (t (setf r (cons (make-term (termlist-lm q)
190 (funcall (ring-uminus ring) (termlist-lc q))) r)
191 q (cdr q)))))
192 nil))
193 r)))
194
195;; Multiplication of polynomials
196;; Non-destructive version
197(defun termlist-mul (ring-and-order p q
198 &aux (ring (ro-ring ring-and-order)))
199 (declare (ring-and-order ring-and-order))
200 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
201 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
202 ((endp (cdr p))
203 (term-times-termlist ring (car p) q))
204 ((endp (cdr q))
205 (termlist-times-term ring p (car q)))
206 (t
207 (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
208 (tail (termlist-add ring-and-order
209 (term-times-termlist ring (car p) (cdr q))
210 (termlist-mul ring-and-order (cdr p) q))))
211 (cond ((null head) tail)
212 ((null tail) head)
213 (t (nconc head tail)))))))
214
215(defun termlist-unit (ring dim)
216 (declare (fixnum dim) (ring ring))
217 (list (make-term (make-monom :dimension dim) (funcall (ring-unit ring)))))
218
219
220(defun termlist-expt (ring-and-order poly n
221 &aux
222 (ring (ro-ring ring-and-order))
223 (dim (monom-dimension (termlist-lm poly))))
224 (declare (type fixnum n dim) (ring-and-order ring-and-order))
225 (cond
226 ((minusp n) (error "termlist-expt: Negative exponent."))
227 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
228 (t
229 (do ((k 1 (ash k 1))
230 (q poly (termlist-mul ring-and-order q q)) ;keep squaring
231 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring-and-order p q) p)))
232 ((> k n) p)
233 (declare (fixnum k))))))
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