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source: branches/f4grobner/mx-grobner.lisp@ 106

Last change on this file since 106 was 106, 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(in-package :maxima)
23
24(macsyma-module cgb-maxima)
25
26(eval-when
27 #+gcl (load eval)
28 #-gcl (:load-toplevel :execute)
29 (format t "~&Loading maxima-grobner ~a ~a~%"
30 "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
31
32;;FUNCTS is loaded because it contains the definition of LCM
33($load "functs")
34
35
36;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
37;;
38;; Maxima expression ring
39;;
40;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
41
42(defparameter *expression-ring*
43 (make-ring
44 ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
45 :parse #'(lambda (expr)
46 (when modulus (setf expr ($rat expr)))
47 expr)
48 :unit #'(lambda () (if modulus ($rat 1) 1))
49 :zerop #'(lambda (expr)
50 ;;When is exactly a maxima expression equal to 0?
51 (cond ((numberp expr)
52 (= expr 0))
53 ((atom expr) nil)
54 (t
55 (case (caar expr)
56 (mrat (eql ($ratdisrep expr) 0))
57 (otherwise (eql ($totaldisrep expr) 0))))))
58 :add #'(lambda (x y) (m+ x y))
59 :sub #'(lambda (x y) (m- x y))
60 :uminus #'(lambda (x) (m- x))
61 :mul #'(lambda (x y) (m* x y))
62 ;;(defun coeff-div (x y) (cadr ($divide x y)))
63 :div #'(lambda (x y) (m// x y))
64 :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
65 :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
66 ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
67 :gcd #'(lambda (x y) ($gcd x y))))
68
69(defvar *maxima-ring* *expression-ring*
70 "The ring of coefficients, over which all polynomials
71are assumed to be defined.")
72
73
74
75
76;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
77;;
78;; Maxima-level interface functions
79;;
80;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
81
82;; Auxillary function for removing zero polynomial
83(defun remzero (plist) (remove #'poly-zerop plist))
84
85;;Simple operators
86
87(define-binop $poly_add poly-add
88 "Adds two polynomials P and Q")
89
90(define-binop $poly_subtract poly-sub
91 "Subtracts a polynomial Q from P.")
92
93(define-binop $poly_multiply poly-mul
94 "Returns the product of polynomials P and Q.")
95
96(define-binop $poly_s_polynomial spoly
97 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
98
99(define-unop $poly_primitive_part poly-primitive-part
100 "Returns the polynomial P divided by GCD of its coefficients.")
101
102(define-unop $poly_normalize poly-normalize
103 "Returns the polynomial P divided by the leading coefficient.")
104
105;;Functions
106
107(defmfun $poly_expand (p vars)
108 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
109If the representation is not compatible with a polynomial in variables VARS,
110the result is an error."
111 (with-parsed-polynomials ((vars) :polynomials (p)
112 :value-type :polynomial)
113 p))
114
115(defmfun $poly_expt (p n vars)
116 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
117 (poly-expt *maxima-ring* p n)))
118
119(defmfun $poly_content (p vars)
120 (with-parsed-polynomials ((vars) :polynomials (p))
121 (poly-content *maxima-ring* p)))
122
123(defmfun $poly_pseudo_divide (f fl vars
124 &aux (vars (coerce-maxima-list vars))
125 (f (parse-poly f vars))
126 (fl (parse-poly-list fl vars)))
127 (multiple-value-bind (quot rem c division-count)
128 (poly-pseudo-divide *maxima-ring* f fl)
129 `((mlist)
130 ,(coerce-to-maxima :poly-list quot vars)
131 ,(coerce-to-maxima :polynomial rem vars)
132 ,c
133 ,division-count)))
134
135(defmfun $poly_exact_divide (f g vars)
136 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
137 (poly-exact-divide *maxima-ring* f g)))
138
139(defmfun $poly_normal_form (f fl vars)
140 (with-parsed-polynomials ((vars) :polynomials (f)
141 :poly-lists (fl)
142 :value-type :polynomial)
143 (normal-form *maxima-ring* f (remzero fl) nil)))
144
145(defmfun $poly_buchberger_criterion (g vars)
146 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
147 (buchberger-criterion *maxima-ring* g)))
148
149(defmfun $poly_buchberger (fl vars)
150 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
151 (buchberger *maxima-ring* (remzero fl) 0 nil)))
152
153(defmfun $poly_reduction (plist vars)
154 (with-parsed-polynomials ((vars) :poly-lists (plist)
155 :value-type :poly-list)
156 (reduction *maxima-ring* plist)))
157
158(defmfun $poly_minimization (plist vars)
159 (with-parsed-polynomials ((vars) :poly-lists (plist)
160 :value-type :poly-list)
161 (minimization plist)))
162
163(defmfun $poly_normalize_list (plist vars)
164 (with-parsed-polynomials ((vars) :poly-lists (plist)
165 :value-type :poly-list)
166 (poly-normalize-list *maxima-ring* plist)))
167
168(defmfun $poly_grobner (f vars)
169 (with-parsed-polynomials ((vars) :poly-lists (f)
170 :value-type :poly-list)
171 (grobner *maxima-ring* (remzero f))))
172
173(defmfun $poly_reduced_grobner (f vars)
174 (with-parsed-polynomials ((vars) :poly-lists (f)
175 :value-type :poly-list)
176 (reduced-grobner *maxima-ring* (remzero f))))
177
178(defmfun $poly_depends_p (p var mvars
179 &aux (vars (coerce-maxima-list mvars))
180 (pos (position var vars)))
181 (if (null pos)
182 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
183 (poly-depends-p (parse-poly p vars) pos)))
184
185(defmfun $poly_elimination_ideal (flist k vars)
186 (with-parsed-polynomials ((vars) :poly-lists (flist)
187 :value-type :poly-list)
188 (elimination-ideal *maxima-ring* flist k nil 0)))
189
190(defmfun $poly_colon_ideal (f g vars)
191 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
192 (colon-ideal *maxima-ring* f g nil)))
193
194(defmfun $poly_ideal_intersection (f g vars)
195 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
196 (ideal-intersection *maxima-ring* f g nil)))
197
198(defmfun $poly_lcm (f g vars)
199 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
200 (poly-lcm *maxima-ring* f g)))
201
202(defmfun $poly_gcd (f g vars)
203 ($first ($divide (m* f g) ($poly_lcm f g vars))))
204
205(defmfun $poly_grobner_equal (g1 g2 vars)
206 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
207 (grobner-equal *maxima-ring* g1 g2)))
208
209(defmfun $poly_grobner_subsetp (g1 g2 vars)
210 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
211 (grobner-subsetp *maxima-ring* g1 g2)))
212
213(defmfun $poly_grobner_member (p g vars)
214 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
215 (grobner-member *maxima-ring* p g)))
216
217(defmfun $poly_ideal_saturation1 (f p vars)
218 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
219 :value-type :poly-list)
220 (ideal-saturation-1 *maxima-ring* f p 0)))
221
222(defmfun $poly_saturation_extension (f plist vars new-vars)
223 (with-parsed-polynomials ((vars new-vars)
224 :poly-lists (f plist)
225 :value-type :poly-list)
226 (saturation-extension *maxima-ring* f plist)))
227
228(defmfun $poly_polysaturation_extension (f plist vars new-vars)
229 (with-parsed-polynomials ((vars new-vars)
230 :poly-lists (f plist)
231 :value-type :poly-list)
232 (polysaturation-extension *maxima-ring* f plist)))
233
234(defmfun $poly_ideal_polysaturation1 (f plist vars)
235 (with-parsed-polynomials ((vars) :poly-lists (f plist)
236 :value-type :poly-list)
237 (ideal-polysaturation-1 *maxima-ring* f plist 0 nil)))
238
239(defmfun $poly_ideal_saturation (f g vars)
240 (with-parsed-polynomials ((vars) :poly-lists (f g)
241 :value-type :poly-list)
242 (ideal-saturation *maxima-ring* f g 0 nil)))
243
244(defmfun $poly_ideal_polysaturation (f ideal-list vars)
245 (with-parsed-polynomials ((vars) :poly-lists (f)
246 :poly-list-lists (ideal-list)
247 :value-type :poly-list)
248 (ideal-polysaturation *maxima-ring* f ideal-list 0 nil)))
249
250(defmfun $poly_lt (f vars)
251 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
252 (make-poly-from-termlist (list (poly-lt f)))))
253
254(defmfun $poly_lm (f vars)
255 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
256 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *maxima-ring*)))))))
257
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