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