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source: branches/f4grobner/mx-grobner.lisp@ 111

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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;; Unary and binary operation definition facility
76;;
77;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
78
79(defmacro define-unop (maxima-name fun-name
80 &optional (documentation nil documentation-supplied-p))
81 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
82 `(defun ,maxima-name (p vars
83 &aux
84 (vars (coerce-maxima-list vars))
85 (p (parse-poly p vars)))
86 ,@(when documentation-supplied-p (list documentation))
87 (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p) vars)))
88
89(defmacro define-binop (maxima-name fun-name
90 &optional (documentation nil documentation-supplied-p))
91 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
92 `(defmfun ,maxima-name (p q vars
93 &aux
94 (vars (coerce-maxima-list vars))
95 (p (parse-poly p vars))
96 (q (parse-poly q vars)))
97 ,@(when documentation-supplied-p (list documentation))
98 (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p q) vars)))
99
100
101
102
103;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
104;;
105;; Maxima-level interface functions
106;;
107;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
108
109;; Auxillary function for removing zero polynomial
110(defun remzero (plist) (remove #'poly-zerop plist))
111
112;;Simple operators
113
114(define-binop $poly_add poly-add
115 "Adds two polynomials P and Q")
116
117(define-binop $poly_subtract poly-sub
118 "Subtracts a polynomial Q from P.")
119
120(define-binop $poly_multiply poly-mul
121 "Returns the product of polynomials P and Q.")
122
123(define-binop $poly_s_polynomial spoly
124 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
125
126(define-unop $poly_primitive_part poly-primitive-part
127 "Returns the polynomial P divided by GCD of its coefficients.")
128
129(define-unop $poly_normalize poly-normalize
130 "Returns the polynomial P divided by the leading coefficient.")
131
132;;Functions
133
134(defmfun $poly_expand (p vars)
135 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
136If the representation is not compatible with a polynomial in variables VARS,
137the result is an error."
138 (with-parsed-polynomials ((vars) :polynomials (p)
139 :value-type :polynomial)
140 p))
141
142(defmfun $poly_expt (p n vars)
143 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
144 (poly-expt *maxima-ring* p n)))
145
146(defmfun $poly_content (p vars)
147 (with-parsed-polynomials ((vars) :polynomials (p))
148 (poly-content *maxima-ring* p)))
149
150(defmfun $poly_pseudo_divide (f fl vars
151 &aux (vars (coerce-maxima-list vars))
152 (f (parse-poly f vars))
153 (fl (parse-poly-list fl vars)))
154 (multiple-value-bind (quot rem c division-count)
155 (poly-pseudo-divide *maxima-ring* f fl)
156 `((mlist)
157 ,(coerce-to-maxima :poly-list quot vars)
158 ,(coerce-to-maxima :polynomial rem vars)
159 ,c
160 ,division-count)))
161
162(defmfun $poly_exact_divide (f g vars)
163 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
164 (poly-exact-divide *maxima-ring* f g)))
165
166(defmfun $poly_normal_form (f fl vars)
167 (with-parsed-polynomials ((vars) :polynomials (f)
168 :poly-lists (fl)
169 :value-type :polynomial)
170 (normal-form *maxima-ring* f (remzero fl) nil)))
171
172(defmfun $poly_buchberger_criterion (g vars)
173 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
174 (buchberger-criterion *maxima-ring* g)))
175
176(defmfun $poly_buchberger (fl vars)
177 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
178 (buchberger *maxima-ring* (remzero fl) 0 nil)))
179
180(defmfun $poly_reduction (plist vars)
181 (with-parsed-polynomials ((vars) :poly-lists (plist)
182 :value-type :poly-list)
183 (reduction *maxima-ring* plist)))
184
185(defmfun $poly_minimization (plist vars)
186 (with-parsed-polynomials ((vars) :poly-lists (plist)
187 :value-type :poly-list)
188 (minimization plist)))
189
190(defmfun $poly_normalize_list (plist vars)
191 (with-parsed-polynomials ((vars) :poly-lists (plist)
192 :value-type :poly-list)
193 (poly-normalize-list *maxima-ring* plist)))
194
195(defmfun $poly_grobner (f vars)
196 (with-parsed-polynomials ((vars) :poly-lists (f)
197 :value-type :poly-list)
198 (grobner *maxima-ring* (remzero f))))
199
200(defmfun $poly_reduced_grobner (f vars)
201 (with-parsed-polynomials ((vars) :poly-lists (f)
202 :value-type :poly-list)
203 (reduced-grobner *maxima-ring* (remzero f))))
204
205(defmfun $poly_depends_p (p var mvars
206 &aux (vars (coerce-maxima-list mvars))
207 (pos (position var vars)))
208 (if (null pos)
209 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
210 (poly-depends-p (parse-poly p vars) pos)))
211
212(defmfun $poly_elimination_ideal (flist k vars)
213 (with-parsed-polynomials ((vars) :poly-lists (flist)
214 :value-type :poly-list)
215 (elimination-ideal *maxima-ring* flist k nil 0)))
216
217(defmfun $poly_colon_ideal (f g vars)
218 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
219 (colon-ideal *maxima-ring* f g nil)))
220
221(defmfun $poly_ideal_intersection (f g vars)
222 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
223 (ideal-intersection *maxima-ring* f g nil)))
224
225(defmfun $poly_lcm (f g vars)
226 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
227 (poly-lcm *maxima-ring* f g)))
228
229(defmfun $poly_gcd (f g vars)
230 ($first ($divide (m* f g) ($poly_lcm f g vars))))
231
232(defmfun $poly_grobner_equal (g1 g2 vars)
233 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
234 (grobner-equal *maxima-ring* g1 g2)))
235
236(defmfun $poly_grobner_subsetp (g1 g2 vars)
237 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
238 (grobner-subsetp *maxima-ring* g1 g2)))
239
240(defmfun $poly_grobner_member (p g vars)
241 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
242 (grobner-member *maxima-ring* p g)))
243
244(defmfun $poly_ideal_saturation1 (f p vars)
245 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
246 :value-type :poly-list)
247 (ideal-saturation-1 *maxima-ring* f p 0)))
248
249(defmfun $poly_saturation_extension (f plist vars new-vars)
250 (with-parsed-polynomials ((vars new-vars)
251 :poly-lists (f plist)
252 :value-type :poly-list)
253 (saturation-extension *maxima-ring* f plist)))
254
255(defmfun $poly_polysaturation_extension (f plist vars new-vars)
256 (with-parsed-polynomials ((vars new-vars)
257 :poly-lists (f plist)
258 :value-type :poly-list)
259 (polysaturation-extension *maxima-ring* f plist)))
260
261(defmfun $poly_ideal_polysaturation1 (f plist vars)
262 (with-parsed-polynomials ((vars) :poly-lists (f plist)
263 :value-type :poly-list)
264 (ideal-polysaturation-1 *maxima-ring* f plist 0 nil)))
265
266(defmfun $poly_ideal_saturation (f g vars)
267 (with-parsed-polynomials ((vars) :poly-lists (f g)
268 :value-type :poly-list)
269 (ideal-saturation *maxima-ring* f g 0 nil)))
270
271(defmfun $poly_ideal_polysaturation (f ideal-list vars)
272 (with-parsed-polynomials ((vars) :poly-lists (f)
273 :poly-list-lists (ideal-list)
274 :value-type :poly-list)
275 (ideal-polysaturation *maxima-ring* f ideal-list 0 nil)))
276
277(defmfun $poly_lt (f vars)
278 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
279 (make-poly-from-termlist (list (poly-lt f)))))
280
281(defmfun $poly_lm (f vars)
282 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
283 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *maxima-ring*)))))))
284
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