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source: branches/f4grobner/mx-grobner.lisp@ 105

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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) ($gcd x y))))
68
69(defvar *maxima-ring* *expression-ring*
70 "The ring of coefficients, over which all polynomials
71are assumed to be defined.")
72
73
74
75
76;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
77;;
78;; Macro facility for writing Maxima-level wrappers for
79;; functions operating on internal representation
80;;
81;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
82
83(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
84 &key (polynomials nil)
85 (poly-lists nil)
86 (poly-list-lists nil)
87 (value-type nil))
88 &body body
89 &aux (vars (gensym))
90 (new-vars (gensym)))
91 `(let ((,vars (coerce-maxima-list ,maxima-vars))
92 ,@(when new-vars-supplied-p
93 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
94 (coerce-to-maxima
95 ,value-type
96 (with-coefficient-ring ($poly_coefficient_ring)
97 (with-monomial-order ($poly_monomial_order)
98 (with-elimination-orders ($poly_primary_elimination_order
99 $poly_secondary_elimination_order
100 $poly_elimination_order)
101 (let ,(let ((args nil))
102 (dolist (p polynomials args)
103 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
104 (dolist (p poly-lists args)
105 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
106 (dolist (p poly-list-lists args)
107 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
108 . ,body))))
109 ,(if new-vars-supplied-p
110 `(append ,vars ,new-vars)
111 vars))))
112
113(defmacro define-unop (maxima-name fun-name
114 &optional (documentation nil documentation-supplied-p))
115 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
116 `(defun ,maxima-name (p vars
117 &aux
118 (vars (coerce-maxima-list vars))
119 (p (parse-poly p vars)))
120 ,@(when documentation-supplied-p (list documentation))
121 (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p) vars)))
122
123(defmacro define-binop (maxima-name fun-name
124 &optional (documentation nil documentation-supplied-p))
125 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
126 `(defmfun ,maxima-name (p q vars
127 &aux
128 (vars (coerce-maxima-list vars))
129 (p (parse-poly p vars))
130 (q (parse-poly q vars)))
131 ,@(when documentation-supplied-p (list documentation))
132 (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p q) vars)))
133
134
135
136;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
137;;
138;; Maxima-level interface functions
139;;
140;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
141
142;; Auxillary function for removing zero polynomial
143(defun remzero (plist) (remove #'poly-zerop plist))
144
145;;Simple operators
146
147(define-binop $poly_add poly-add
148 "Adds two polynomials P and Q")
149
150(define-binop $poly_subtract poly-sub
151 "Subtracts a polynomial Q from P.")
152
153(define-binop $poly_multiply poly-mul
154 "Returns the product of polynomials P and Q.")
155
156(define-binop $poly_s_polynomial spoly
157 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
158
159(define-unop $poly_primitive_part poly-primitive-part
160 "Returns the polynomial P divided by GCD of its coefficients.")
161
162(define-unop $poly_normalize poly-normalize
163 "Returns the polynomial P divided by the leading coefficient.")
164
165;;Functions
166
167(defmfun $poly_expand (p vars)
168 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
169If the representation is not compatible with a polynomial in variables VARS,
170the result is an error."
171 (with-parsed-polynomials ((vars) :polynomials (p)
172 :value-type :polynomial)
173 p))
174
175(defmfun $poly_expt (p n vars)
176 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
177 (poly-expt *maxima-ring* p n)))
178
179(defmfun $poly_content (p vars)
180 (with-parsed-polynomials ((vars) :polynomials (p))
181 (poly-content *maxima-ring* p)))
182
183(defmfun $poly_pseudo_divide (f fl vars
184 &aux (vars (coerce-maxima-list vars))
185 (f (parse-poly f vars))
186 (fl (parse-poly-list fl vars)))
187 (multiple-value-bind (quot rem c division-count)
188 (poly-pseudo-divide *maxima-ring* f fl)
189 `((mlist)
190 ,(coerce-to-maxima :poly-list quot vars)
191 ,(coerce-to-maxima :polynomial rem vars)
192 ,c
193 ,division-count)))
194
195(defmfun $poly_exact_divide (f g vars)
196 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
197 (poly-exact-divide *maxima-ring* f g)))
198
199(defmfun $poly_normal_form (f fl vars)
200 (with-parsed-polynomials ((vars) :polynomials (f)
201 :poly-lists (fl)
202 :value-type :polynomial)
203 (normal-form *maxima-ring* f (remzero fl) nil)))
204
205(defmfun $poly_buchberger_criterion (g vars)
206 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
207 (buchberger-criterion *maxima-ring* g)))
208
209(defmfun $poly_buchberger (fl vars)
210 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
211 (buchberger *maxima-ring* (remzero fl) 0 nil)))
212
213(defmfun $poly_reduction (plist vars)
214 (with-parsed-polynomials ((vars) :poly-lists (plist)
215 :value-type :poly-list)
216 (reduction *maxima-ring* plist)))
217
218(defmfun $poly_minimization (plist vars)
219 (with-parsed-polynomials ((vars) :poly-lists (plist)
220 :value-type :poly-list)
221 (minimization plist)))
222
223(defmfun $poly_normalize_list (plist vars)
224 (with-parsed-polynomials ((vars) :poly-lists (plist)
225 :value-type :poly-list)
226 (poly-normalize-list *maxima-ring* plist)))
227
228(defmfun $poly_grobner (f vars)
229 (with-parsed-polynomials ((vars) :poly-lists (f)
230 :value-type :poly-list)
231 (grobner *maxima-ring* (remzero f))))
232
233(defmfun $poly_reduced_grobner (f vars)
234 (with-parsed-polynomials ((vars) :poly-lists (f)
235 :value-type :poly-list)
236 (reduced-grobner *maxima-ring* (remzero f))))
237
238(defmfun $poly_depends_p (p var mvars
239 &aux (vars (coerce-maxima-list mvars))
240 (pos (position var vars)))
241 (if (null pos)
242 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
243 (poly-depends-p (parse-poly p vars) pos)))
244
245(defmfun $poly_elimination_ideal (flist k vars)
246 (with-parsed-polynomials ((vars) :poly-lists (flist)
247 :value-type :poly-list)
248 (elimination-ideal *maxima-ring* flist k nil 0)))
249
250(defmfun $poly_colon_ideal (f g vars)
251 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
252 (colon-ideal *maxima-ring* f g nil)))
253
254(defmfun $poly_ideal_intersection (f g vars)
255 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
256 (ideal-intersection *maxima-ring* f g nil)))
257
258(defmfun $poly_lcm (f g vars)
259 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
260 (poly-lcm *maxima-ring* f g)))
261
262(defmfun $poly_gcd (f g vars)
263 ($first ($divide (m* f g) ($poly_lcm f g vars))))
264
265(defmfun $poly_grobner_equal (g1 g2 vars)
266 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
267 (grobner-equal *maxima-ring* g1 g2)))
268
269(defmfun $poly_grobner_subsetp (g1 g2 vars)
270 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
271 (grobner-subsetp *maxima-ring* g1 g2)))
272
273(defmfun $poly_grobner_member (p g vars)
274 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
275 (grobner-member *maxima-ring* p g)))
276
277(defmfun $poly_ideal_saturation1 (f p vars)
278 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
279 :value-type :poly-list)
280 (ideal-saturation-1 *maxima-ring* f p 0)))
281
282(defmfun $poly_saturation_extension (f plist vars new-vars)
283 (with-parsed-polynomials ((vars new-vars)
284 :poly-lists (f plist)
285 :value-type :poly-list)
286 (saturation-extension *maxima-ring* f plist)))
287
288(defmfun $poly_polysaturation_extension (f plist vars new-vars)
289 (with-parsed-polynomials ((vars new-vars)
290 :poly-lists (f plist)
291 :value-type :poly-list)
292 (polysaturation-extension *maxima-ring* f plist)))
293
294(defmfun $poly_ideal_polysaturation1 (f plist vars)
295 (with-parsed-polynomials ((vars) :poly-lists (f plist)
296 :value-type :poly-list)
297 (ideal-polysaturation-1 *maxima-ring* f plist 0 nil)))
298
299(defmfun $poly_ideal_saturation (f g vars)
300 (with-parsed-polynomials ((vars) :poly-lists (f g)
301 :value-type :poly-list)
302 (ideal-saturation *maxima-ring* f g 0 nil)))
303
304(defmfun $poly_ideal_polysaturation (f ideal-list vars)
305 (with-parsed-polynomials ((vars) :poly-lists (f)
306 :poly-list-lists (ideal-list)
307 :value-type :poly-list)
308 (ideal-polysaturation *maxima-ring* f ideal-list 0 nil)))
309
310(defmfun $poly_lt (f vars)
311 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
312 (make-poly-from-termlist (list (poly-lt f)))))
313
314(defmfun $poly_lm (f vars)
315 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
316 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *maxima-ring*)))))))
317
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