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source: branches/f4grobner/termlist.lisp@ 1861

Last change on this file since 1861 was 1839, 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 (monom-append m (term-monom term))
62 :coeff (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 (monom-append (make-monom :dimension n)
71 (term-monom term))
72 :coeff (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 :monom (term-monom term) :coeff 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 (monom-mul (term-monom term1) (term-monom term2))
110 :coeff c)))))
111
112(defun term-times-termlist (ring term f)
113 (declare (type ring ring))
114 (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))
115
116(defun termlist-times-term (ring f term)
117 (declare (ring ring))
118 (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))
119
120(defun monom-times-term (m term)
121 (make-term :monom (monom-mul m (term-monom term)) :coeff (term-coeff term)))
122
123(defun monom-times-termlist (m f)
124 (cond
125 ((null f) nil)
126 (t
127 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
128
129(defun termlist-uminus (ring f)
130 (declare (ring ring))
131 (mapcar #'(lambda (x)
132 (make-term :monom (term-monom x)
133 :coeff (funcall (ring-uminus ring) (term-coeff x))))
134 f))
135
136(defun termlist-add (ring-and-order p q
137 &aux
138 (ring (ro-ring ring-and-order))
139 (order (ro-order ring-and-order)))
140 (declare (type list p q) (ring-and-order ring-and-order))
141 (do (r)
142 ((cond
143 ((endp p)
144 (setf r (revappend r q)) t)
145 ((endp q)
146 (setf r (revappend r p)) t)
147 (t
148 (multiple-value-bind
149 (lm-greater lm-equal)
150 (funcall order (termlist-lm p) (termlist-lm q))
151 (cond
152 (lm-equal
153 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
154 (unless (funcall (ring-zerop ring) s) ;check for cancellation
155 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
156 (setf p (cdr p) q (cdr q))))
157 (lm-greater
158 (setf r (cons (car p) r)
159 p (cdr p)))
160 (t (setf r (cons (car q) r)
161 q (cdr q)))))
162 nil))
163 r)))
164
165(defun termlist-sub (ring-and-order p q
166 &aux
167 (ring (ro-ring ring-and-order))
168 (order (ro-order ring-and-order)))
169 (declare (type list p q) (ring-and-order ring-and-order))
170 (do (r)
171 ((cond
172 ((endp p)
173 (setf r (revappend r (termlist-uminus ring q)))
174 t)
175 ((endp q)
176 (setf r (revappend r p))
177 t)
178 (t
179 (multiple-value-bind
180 (mgreater mequal)
181 (funcall order (termlist-lm p) (termlist-lm q))
182 (cond
183 (mequal
184 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
185 (unless (funcall (ring-zerop ring) s) ;check for cancellation
186 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
187 (setf p (cdr p) q (cdr q))))
188 (mgreater
189 (setf r (cons (car p) r)
190 p (cdr p)))
191 (t (setf r (cons (make-term :monom (termlist-lm q)
192 :coeff (funcall (ring-uminus ring) (termlist-lc q))) r)
193 q (cdr q)))))
194 nil))
195 r)))
196
197;; Multiplication of polynomials
198;; Non-destructive version
199(defun termlist-mul (ring-and-order p q
200 &aux (ring (ro-ring ring-and-order)))
201 (declare (ring-and-order ring-and-order))
202 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
203 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
204 ((endp (cdr p))
205 (term-times-termlist ring (car p) q))
206 ((endp (cdr q))
207 (termlist-times-term ring p (car q)))
208 (t
209 (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
210 (tail (termlist-add ring-and-order
211 (term-times-termlist ring (car p) (cdr q))
212 (termlist-mul ring-and-order (cdr p) q))))
213 (cond ((null head) tail)
214 ((null tail) head)
215 (t (nconc head tail)))))))
216
217(defun termlist-unit (ring dim)
218 (declare (fixnum dim) (ring ring))
219 (list (make-term :monom (make-monom :dimension dim)
220 :coeff (funcall (ring-unit ring)))))
221
222
223(defun termlist-expt (ring-and-order poly n
224 &aux
225 (ring (ro-ring ring-and-order))
226 (dim (monom-dimension (termlist-lm poly))))
227 (declare (type fixnum n dim) (ring-and-order ring-and-order))
228 (cond
229 ((minusp n) (error "termlist-expt: Negative exponent."))
230 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
231 (t
232 (do ((k 1 (ash k 1))
233 (q poly (termlist-mul ring-and-order q q)) ;keep squaring
234 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring-and-order p q) p)))
235 ((> k n) p)
236 (declare (fixnum k))))))
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