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source: branches/f4grobner/mx-grobner.lisp@ 202

Last change on this file since 202 was 202, 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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
24;; Load this file into Maxima to bootstrap the Grobner package
25;;
26;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
27
28(in-package :maxima)
29
30(macsyma-module cgb-maxima)
31
32(eval-when
33 #+gcl (load eval)
34 #-gcl (:load-toplevel :execute)
35 (format t "~&Loading maxima-grobner ~a ~a~%"
36 "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
37
38;;FUNCTS is loaded because it contains the definition of LCM
39($load "functs")
40
41#+gcl (unless (macro-function 'with-compilation-unit)
42 (defmacro with-compilation-unit (a &rest b) `(progn ,@b)))
43
44($load "ngrobner-package")
45($load "utils")
46($load "ngrobner")
47($load "monomial")
48($load "order")
49($load "order-mk")
50($load "term")
51($load "termlist")
52($load "polynomial")
53($load "priority-queue")
54($load "pair-queue")
55($load "division")
56($load "criterion")
57($load "buchberger")
58($load "gebauer-moeller")
59($load "gb-postprocessing")
60($load "ideal")
61
62;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
63;;
64;; Maxima expression ring
65;;
66;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
67
68(defparameter *expression-ring*
69 (make-ring
70 ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
71 :parse #'(lambda (expr)
72 (when modulus (setf expr ($rat expr)))
73 expr)
74 :unit #'(lambda () (if modulus ($rat 1) 1))
75 :zerop #'(lambda (expr)
76 ;;When is exactly a maxima expression equal to 0?
77 (cond ((numberp expr)
78 (= expr 0))
79 ((atom expr) nil)
80 (t
81 (case (caar expr)
82 (mrat (eql ($ratdisrep expr) 0))
83 (otherwise (eql ($totaldisrep expr) 0))))))
84 :add #'(lambda (x y) (m+ x y))
85 :sub #'(lambda (x y) (m- x y))
86 :uminus #'(lambda (x) (m- x))
87 :mul #'(lambda (x y) (m* x y))
88 ;;(defun coeff-div (x y) (cadr ($divide x y)))
89 :div #'(lambda (x y) (m// x y))
90 :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
91 :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
92 ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
93 :gcd #'(lambda (x y) ($gcd x y))))
94
95;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
96;;
97;; Maxima expression parsing
98;;
99;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
100
101(defun equal-test-p (expr1 expr2)
102 (alike1 expr1 expr2))
103
104(defun coerce-maxima-list (expr)
105 "convert a maxima list to lisp list."
106 (cond
107 ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
108 (t expr)))
109
110(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
111
112(defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
113 "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
114 (labels ((parse (arg) (parse-poly arg vars))
115 (parse-list (args) (mapcar #'parse args)))
116 (cond
117 ((eql expr 0) (make-poly-zero))
118 ((member expr vars :test #'equal-test-p)
119 (let ((pos (position expr vars :test #'equal-test-p)))
120 (make-variable *maxima-ring* (length vars) pos)))
121 ((free-of-vars expr vars)
122 ;;This means that variable-free CRE and Poisson forms will be converted
123 ;;to coefficients intact
124 (coerce-coeff *maxima-ring* expr vars))
125 (t
126 (case (caar expr)
127 (mplus (reduce #'(lambda (x y) (poly-add *maxima-ring* x y)) (parse-list (cdr expr))))
128 (mminus (poly-uminus *maxima-ring* (parse (cadr expr))))
129 (mtimes
130 (if (endp (cddr expr)) ;unary
131 (parse (cdr expr))
132 (reduce #'(lambda (p q) (poly-mul *maxima-ring* p q)) (parse-list (cdr expr)))))
133 (mexpt
134 (cond
135 ((member (cadr expr) vars :test #'equal-test-p)
136 ;;Special handling of (expt var pow)
137 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
138 (make-variable *maxima-ring* (length vars) pos (caddr expr))))
139 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
140 ;; Negative power means division in coefficient ring
141 ;; Non-integer power means non-polynomial coefficient
142 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
143 expr)
144 (coerce-coeff *maxima-ring* expr vars))
145 (t (poly-expt *maxima-ring* (parse (cadr expr)) (caddr expr)))))
146 (mrat (parse ($ratdisrep expr)))
147 (mpois (parse ($outofpois expr)))
148 (otherwise
149 (coerce-coeff *maxima-ring* expr vars)))))))
150
151(defun parse-poly-list (expr vars)
152 (case (caar expr)
153 (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
154 (t (merror "Expression ~M is not a list of polynomials in variables ~M."
155 expr vars))))
156(defun parse-poly-list-list (poly-list-list vars)
157 (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
158
159
160;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
161;;
162;; Unary and binary operation definition facility
163;;
164;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
165
166(defmacro define-unop (maxima-name fun-name
167 &optional (documentation nil documentation-supplied-p))
168 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
169 `(defun ,maxima-name (p vars
170 &aux
171 (vars (coerce-maxima-list vars))
172 (p (parse-poly p vars)))
173 ,@(when documentation-supplied-p (list documentation))
174 (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p) vars)))
175
176(defmacro define-binop (maxima-name fun-name
177 &optional (documentation nil documentation-supplied-p))
178 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
179 `(defmfun ,maxima-name (p q vars
180 &aux
181 (vars (coerce-maxima-list vars))
182 (p (parse-poly p vars))
183 (q (parse-poly q vars)))
184 ,@(when documentation-supplied-p (list documentation))
185 (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p q) vars)))
186
187
188;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
189;;
190;; Maxima-level interface functions
191;;
192;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
193
194;; Auxillary function for removing zero polynomial
195(defun remzero (plist) (remove #'poly-zerop plist))
196
197;;Simple operators
198
199(define-binop $poly_add poly-add
200 "Adds two polynomials P and Q")
201
202(define-binop $poly_subtract poly-sub
203 "Subtracts a polynomial Q from P.")
204
205(define-binop $poly_multiply poly-mul
206 "Returns the product of polynomials P and Q.")
207
208(define-binop $poly_s_polynomial spoly
209 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
210
211(define-unop $poly_primitive_part poly-primitive-part
212 "Returns the polynomial P divided by GCD of its coefficients.")
213
214(define-unop $poly_normalize poly-normalize
215 "Returns the polynomial P divided by the leading coefficient.")
216
217;;Functions
218
219(defmfun $poly_expand (p vars)
220 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
221If the representation is not compatible with a polynomial in variables VARS,
222the result is an error."
223 (with-parsed-polynomials ((vars) :polynomials (p)
224 :value-type :polynomial)
225 p))
226
227(defmfun $poly_expt (p n vars)
228 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
229 (poly-expt *maxima-ring* p n)))
230
231(defmfun $poly_content (p vars)
232 (with-parsed-polynomials ((vars) :polynomials (p))
233 (poly-content *maxima-ring* p)))
234
235(defmfun $poly_pseudo_divide (f fl vars
236 &aux (vars (coerce-maxima-list vars))
237 (f (parse-poly f vars))
238 (fl (parse-poly-list fl vars)))
239 (multiple-value-bind (quot rem c division-count)
240 (poly-pseudo-divide *maxima-ring* f fl)
241 `((mlist)
242 ,(coerce-to-maxima :poly-list quot vars)
243 ,(coerce-to-maxima :polynomial rem vars)
244 ,c
245 ,division-count)))
246
247(defmfun $poly_exact_divide (f g vars)
248 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
249 (poly-exact-divide *maxima-ring* f g)))
250
251(defmfun $poly_normal_form (f fl vars)
252 (with-parsed-polynomials ((vars) :polynomials (f)
253 :poly-lists (fl)
254 :value-type :polynomial)
255 (normal-form *maxima-ring* f (remzero fl) nil)))
256
257(defmfun $poly_buchberger_criterion (g vars)
258 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
259 (buchberger-criterion *maxima-ring* g)))
260
261(defmfun $poly_buchberger (fl vars)
262 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
263 (buchberger *maxima-ring* (remzero fl) 0 nil)))
264
265(defmfun $poly_reduction (plist vars)
266 (with-parsed-polynomials ((vars) :poly-lists (plist)
267 :value-type :poly-list)
268 (reduction *maxima-ring* plist)))
269
270(defmfun $poly_minimization (plist vars)
271 (with-parsed-polynomials ((vars) :poly-lists (plist)
272 :value-type :poly-list)
273 (minimization plist)))
274
275(defmfun $poly_normalize_list (plist vars)
276 (with-parsed-polynomials ((vars) :poly-lists (plist)
277 :value-type :poly-list)
278 (poly-normalize-list *maxima-ring* plist)))
279
280(defmfun $poly_grobner (f vars)
281 (with-parsed-polynomials ((vars) :poly-lists (f)
282 :value-type :poly-list)
283 (grobner *maxima-ring* (remzero f))))
284
285(defmfun $poly_reduced_grobner (f vars)
286 (with-parsed-polynomials ((vars) :poly-lists (f)
287 :value-type :poly-list)
288 (reduced-grobner *maxima-ring* (remzero f))))
289
290(defmfun $poly_depends_p (p var mvars
291 &aux (vars (coerce-maxima-list mvars))
292 (pos (position var vars)))
293 (if (null pos)
294 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
295 (poly-depends-p (parse-poly p vars) pos)))
296
297(defmfun $poly_elimination_ideal (flist k vars)
298 (with-parsed-polynomials ((vars) :poly-lists (flist)
299 :value-type :poly-list)
300 (elimination-ideal *maxima-ring* flist k nil 0)))
301
302(defmfun $poly_colon_ideal (f g vars)
303 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
304 (colon-ideal *maxima-ring* f g nil)))
305
306(defmfun $poly_ideal_intersection (f g vars)
307 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
308 (ideal-intersection *maxima-ring* f g nil)))
309
310(defmfun $poly_lcm (f g vars)
311 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
312 (poly-lcm *maxima-ring* f g)))
313
314(defmfun $poly_gcd (f g vars)
315 ($first ($divide (m* f g) ($poly_lcm f g vars))))
316
317(defmfun $poly_grobner_equal (g1 g2 vars)
318 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
319 (grobner-equal *maxima-ring* g1 g2)))
320
321(defmfun $poly_grobner_subsetp (g1 g2 vars)
322 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
323 (grobner-subsetp *maxima-ring* g1 g2)))
324
325(defmfun $poly_grobner_member (p g vars)
326 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
327 (grobner-member *maxima-ring* p g)))
328
329(defmfun $poly_ideal_saturation1 (f p vars)
330 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
331 :value-type :poly-list)
332 (ideal-saturation-1 *maxima-ring* f p 0)))
333
334(defmfun $poly_saturation_extension (f plist vars new-vars)
335 (with-parsed-polynomials ((vars new-vars)
336 :poly-lists (f plist)
337 :value-type :poly-list)
338 (saturation-extension *maxima-ring* f plist)))
339
340(defmfun $poly_polysaturation_extension (f plist vars new-vars)
341 (with-parsed-polynomials ((vars new-vars)
342 :poly-lists (f plist)
343 :value-type :poly-list)
344 (polysaturation-extension *maxima-ring* f plist)))
345
346(defmfun $poly_ideal_polysaturation1 (f plist vars)
347 (with-parsed-polynomials ((vars) :poly-lists (f plist)
348 :value-type :poly-list)
349 (ideal-polysaturation-1 *maxima-ring* f plist 0 nil)))
350
351(defmfun $poly_ideal_saturation (f g vars)
352 (with-parsed-polynomials ((vars) :poly-lists (f g)
353 :value-type :poly-list)
354 (ideal-saturation *maxima-ring* f g 0 nil)))
355
356(defmfun $poly_ideal_polysaturation (f ideal-list vars)
357 (with-parsed-polynomials ((vars) :poly-lists (f)
358 :poly-list-lists (ideal-list)
359 :value-type :poly-list)
360 (ideal-polysaturation *maxima-ring* f ideal-list 0 nil)))
361
362(defmfun $poly_lt (f vars)
363 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
364 (make-poly-from-termlist (list (poly-lt f)))))
365
366(defmfun $poly_lm (f vars)
367 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
368 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *maxima-ring*)))))))
369
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