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source: branches/f4grobner/termlist.lisp@ 1945

Last change on this file since 1945 was 1945, checked in by Marek Rychlik, 9 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 (make-term :monom (monom-append (make-monom :dimension n)
73 (term-monom term))
74 :coeff (term-coeff term)))
75 p))
76
77
78;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
79;;
80;; Low-level polynomial arithmetic done on
81;; lists of terms
82;;
83;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
84
85(defmacro termlist-lt (p) `(car ,p))
86(defun termlist-lm (p) (term-monom (termlist-lt p)))
87(defun termlist-lc (p) (term-coeff (termlist-lt p)))
88
89(define-modify-macro scalar-mul (c) coeff-mul)
90
91(defun scalar-times-termlist (ring c p)
92 "Multiply scalar C by a polynomial P. This function works
93even if there are divisors of 0."
94 (declare (ring ring))
95 (mapcan
96 #'(lambda (term)
97 (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
98 (unless (funcall (ring-zerop ring) c1)
99 (list (make-term :monom (term-monom term) :coeff c1)))))
100 p))
101
102
103(defun term-mul-lst (ring term1 term2)
104 "A special version of term multiplication. Returns (LIST TERM) where
105TERM is the product of the terms TERM1 TERM2, or NIL when the product
106is 0. This definition takes care of divisors of 0 in the coefficient
107ring."
108 (declare (ring ring))
109 (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
110 (unless (funcall (ring-zerop ring) c)
111 (list (make-term :monom (monom-mul (term-monom term1) (term-monom term2))
112 :coeff c)))))
113
114(defun term-times-termlist (ring term f)
115 (declare (type ring ring))
116 (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))
117
118(defun termlist-times-term (ring f term)
119 (declare (ring ring))
120 (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))
121
122(defun monom-times-term (m term)
123 (make-term :monom (monom-mul m (term-monom term)) :coeff (term-coeff term)))
124
125(defun monom-times-termlist (m f)
126 (declare (type monom m))
127 (cond
128 ((null f) nil)
129 (t
130 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
131
132(defun termlist-uminus (ring f)
133 (declare (ring ring))
134 (mapcar #'(lambda (x)
135 (make-term :monom (term-monom x)
136 :coeff (funcall (ring-uminus ring) (term-coeff x))))
137 f))
138
139(defun termlist-add (ring-and-order p q
140 &aux
141 (ring (ro-ring ring-and-order))
142 (order (ro-order ring-and-order)))
143 (declare (ring-and-order ring-and-order) (type list p q))
144 (do (r)
145 ((cond
146 ((endp p)
147 (setf r (revappend r q)) t)
148 ((endp q)
149 (setf r (revappend r p)) t)
150 (t
151 (multiple-value-bind
152 (lm-greater lm-equal)
153 (funcall order (termlist-lm p) (termlist-lm q))
154 (cond
155 (lm-equal
156 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
157 (unless (funcall (ring-zerop ring) s) ;check for cancellation
158 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
159 (setf p (cdr p) q (cdr q))))
160 (lm-greater
161 (setf r (cons (car p) r)
162 p (cdr p)))
163 (t (setf r (cons (car q) r)
164 q (cdr q)))))
165 nil))
166 r)))
167
168(defun termlist-sub (ring-and-order p q
169 &aux
170 (ring (ro-ring ring-and-order))
171 (order (ro-order ring-and-order)))
172 (declare (ring-and-order ring-and-order) (type list p q))
173 (do (r)
174 ((cond
175 ((endp p)
176 (setf r (revappend r (termlist-uminus ring q)))
177 t)
178 ((endp q)
179 (setf r (revappend r p))
180 t)
181 (t
182 (multiple-value-bind
183 (mgreater mequal)
184 (funcall order (termlist-lm p) (termlist-lm q))
185 (cond
186 (mequal
187 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
188 (unless (funcall (ring-zerop ring) s) ;check for cancellation
189 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
190 (setf p (cdr p) q (cdr q))))
191 (mgreater
192 (setf r (cons (car p) r)
193 p (cdr p)))
194 (t (setf r (cons (make-term :monom (termlist-lm q)
195 :coeff (funcall (ring-uminus ring) (termlist-lc q))) r)
196 q (cdr q)))))
197 nil))
198 r)))
199
200;; Multiplication of polynomials
201;; Non-destructive version
202(defun termlist-mul (ring-and-order p q
203 &aux (ring (ro-ring ring-and-order)))
204 (declare (ring-and-order ring-and-order))
205 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
206 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
207 ((endp (cdr p))
208 (term-times-termlist ring (car p) q))
209 ((endp (cdr q))
210 (termlist-times-term ring p (car q)))
211 (t
212 (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
213 (tail (termlist-add ring-and-order
214 (term-times-termlist ring (car p) (cdr q))
215 (termlist-mul ring-and-order (cdr p) q))))
216 (cond ((null head) tail)
217 ((null tail) head)
218 (t (nconc head tail)))))))
219
220(defun termlist-unit (ring dim)
221 (declare (ring ring) (fixnum dim))
222 (list (make-term :monom (make-monom :dimension dim)
223 :coeff (funcall (ring-unit ring)))))
224
225
226(defun termlist-expt (ring-and-order poly n
227 &aux
228 (ring (ro-ring ring-and-order))
229 (dim (monom-dimension (termlist-lm poly))))
230 (declare (ring-and-order ring-and-order) (type fixnum n dim))
231 (cond
232 ((minusp n) (error "termlist-expt: Negative exponent."))
233 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
234 (t
235 (do ((k 1 (ash k 1))
236 (q poly (termlist-mul ring-and-order q q)) ;keep squaring
237 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring-and-order p q) p)))
238 ((> k n) p)
239 (declare (fixnum k))))))
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