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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;; NOTE: This file does use symbols defined by Maxima, so it
26;; will not work when loaded in Common Lisp.
27;;
28;; DETAILS: This file implements an interface between the Grobner
29;; basis package NGROBNER, which is a pure Common Lisp package, and
30;; Maxima. NGROBNER for efficiency uses its own representation of
31;; polynomials. Thus, it is necessary to convert Maxima representation
32;; to the internal representation and back. The facilities to do so
33;; are implemented in this file.
34;;
35;; Also, since the NGROBNER package consists of many Lisp files, it is
36;; necessary to load the files. It is possible and preferrable to use
37;; ASDF for this purpose. The default is ASDF. It is also possible to
38;; simply used LOAD and COMPILE-FILE to accomplish this task.
39;;
40;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
41
42(eval-when
43 #+gcl (load eval)
44 #-gcl (:load-toplevel :execute)
45 (defpackage "MAXIMA" (:use :cl)))
46
47(in-package :maxima)
48
49(macsyma-module cgb-maxima)
50
51(eval-when
52 #+gcl (load eval)
53 #-gcl (:load-toplevel :execute)
54 (format t "~&Loading maxima-grobner ~a ~a~%"
55 "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
56
57;;FUNCTS is loaded because it contains the definition of LCM
58($load "functs")
59
60#+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
61
62(use-package :ngrobner)
63
64;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
65;;
66;; Maxima expression ring
67;;
68;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
69;;
70;; This is how we perform operations on coefficients
71;; using Maxima functions.
72;;
73;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
74
75(defparameter *maxima-ring*
76 (make-ring
77 ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
78 :parse #'(lambda (expr)
79 (when modulus (setf expr ($rat expr)))
80 expr)
81 :unit #'(lambda () (if modulus ($rat 1) 1))
82 :zerop #'(lambda (expr)
83 ;;When is exactly a maxima expression equal to 0?
84 (cond ((numberp expr)
85 (= expr 0))
86 ((atom expr) nil)
87 (t
88 (case (caar expr)
89 (mrat (eql ($ratdisrep expr) 0))
90 (otherwise (eql ($totaldisrep expr) 0))))))
91 :add #'(lambda (x y) (m+ x y))
92 :sub #'(lambda (x y) (m- x y))
93 :uminus #'(lambda (x) (m- x))
94 :mul #'(lambda (x y) (m* x y))
95 ;;(defun coeff-div (x y) (cadr ($divide x y)))
96 :div #'(lambda (x y) (m// x y))
97 :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
98 :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
99 ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
100 :gcd #'(lambda (x y) ($gcd x y))))
101
102;; Rebind some global variables for Maxima environment
103(setf *expression-ring* *maxima-ring* ; Coefficient arithmetic done by Maxima
104 *ratdisrep-fun* '$ratdisrep ; Coefficients are converted to general form
105 )
106
107;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
108;;
109;; Maxima expression parsing
110;;
111;;
112;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
113;;
114;; Functions and macros dealing with internal representation
115;; structure.
116;;
117;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
118
119(defun equal-test-p (expr1 expr2)
120 (alike1 expr1 expr2))
121
122(defun coerce-maxima-list (expr)
123 "Convert a Maxima list to Lisp list."
124 (cond
125 ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
126 (t expr)))
127
128(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
129
130(defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
131 "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
132 (labels ((parse (arg) (parse-poly arg vars))
133 (parse-list (args) (mapcar #'parse args)))
134 (cond
135 ((eql expr 0) (make-poly-zero))
136 ((member expr vars :test #'equal-test-p)
137 (let ((pos (position expr vars :test #'equal-test-p)))
138 (make-variable *expression-ring* (length vars) pos)))
139 ((free-of-vars expr vars)
140 ;;This means that variable-free CRE and Poisson forms will be converted
141 ;;to coefficients intact
142 (coerce-coeff *expression-ring* expr vars))
143 (t
144 (case (caar expr)
145 (mplus (reduce #'(lambda (x y) (poly-add *expression-ring* x y)) (parse-list (cdr expr))))
146 (mminus (poly-uminus *expression-ring* (parse (cadr expr))))
147 (mtimes
148 (if (endp (cddr expr)) ;unary
149 (parse (cdr expr))
150 (reduce #'(lambda (p q) (poly-mul *expression-ring* p q)) (parse-list (cdr expr)))))
151 (mexpt
152 (cond
153 ((member (cadr expr) vars :test #'equal-test-p)
154 ;;Special handling of (expt var pow)
155 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
156 (make-variable *expression-ring* (length vars) pos (caddr expr))))
157 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
158 ;; Negative power means division in coefficient ring
159 ;; Non-integer power means non-polynomial coefficient
160 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
161 expr)
162 (coerce-coeff *expression-ring* expr vars))
163 (t (poly-expt *expression-ring* (parse (cadr expr)) (caddr expr)))))
164 (mrat (parse ($ratdisrep expr)))
165 (mpois (parse ($outofpois expr)))
166 (otherwise
167 (coerce-coeff *expression-ring* expr vars)))))))
168
169(defun parse-poly-list (expr vars)
170 (case (caar expr)
171 (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
172 (t (merror "Expression ~M is not a list of polynomials in variables ~M."
173 expr vars))))
174(defun parse-poly-list-list (poly-list-list vars)
175 (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
176
177
178;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
179;;
180;; Conversion from internal form to Maxima general form
181;;
182;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
183
184(defun maxima-head ()
185 (if $poly_return_term_list
186 '(mlist)
187 '(mplus)))
188
189(defun coerce-to-maxima (poly-type object vars)
190 (case poly-type
191 (:polynomial
192 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
193 (:poly-list
194 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
195 (:term
196 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
197 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
198 vars (monom-exponents (term-monom object)))))
199 ;; Assumes that Lisp and Maxima logicals coincide
200 (:logical object)
201 (otherwise
202 object)))
203
204
205;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
206;;
207;; Unary and binary operation definition facility
208;;
209;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
210
211(defmacro define-unop (maxima-name fun-name
212 &optional (documentation nil documentation-supplied-p))
213 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
214 `(defun ,maxima-name (p vars
215 &aux
216 (vars (coerce-maxima-list vars))
217 (p (parse-poly p vars)))
218 ,@(when documentation-supplied-p (list documentation))
219 (coerce-to-maxima :polynomial (,fun-name *expression-ring* p) vars)))
220
221(defmacro define-binop (maxima-name fun-name
222 &optional (documentation nil documentation-supplied-p))
223 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
224 `(defmfun ,maxima-name (p q vars
225 &aux
226 (vars (coerce-maxima-list vars))
227 (p (parse-poly p vars))
228 (q (parse-poly q vars)))
229 ,@(when documentation-supplied-p (list documentation))
230 (coerce-to-maxima :polynomial (,fun-name *expression-ring* p q) vars)))
231
232
233;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
234;;
235;; Facilities for evaluating Grobner package expressions
236;; within a prepared environment
237;;
238;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
239
240(defmacro with-monomial-order ((order) &body body)
241 "Evaluate BODY with monomial order set to ORDER."
242 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
243 . ,body))
244
245(defmacro with-coefficient-ring ((ring) &body body)
246 "Evaluate BODY with coefficient ring set to RING."
247 `(let ((*expression-ring* (or (find-ring ,ring) *expression-ring*)))
248 . ,body))
249
250(defmacro with-elimination-orders ((primary secondary elimination-order)
251 &body body)
252 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
253 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
254 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
255 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
256 . ,body))
257
258
259;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
260;;
261;; Maxima-level interface functions
262;;
263;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
264
265;; Auxillary function for removing zero polynomial
266(defun remzero (plist) (remove #'poly-zerop plist))
267
268;;Simple operators
269
270(define-binop $poly_add poly-add
271 "Adds two polynomials P and Q")
272
273(define-binop $poly_subtract poly-sub
274 "Subtracts a polynomial Q from P.")
275
276(define-binop $poly_multiply poly-mul
277 "Returns the product of polynomials P and Q.")
278
279(define-binop $poly_s_polynomial spoly
280 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
281
282(define-unop $poly_primitive_part poly-primitive-part
283 "Returns the polynomial P divided by GCD of its coefficients.")
284
285(define-unop $poly_normalize poly-normalize
286 "Returns the polynomial P divided by the leading coefficient.")
287
288;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
289;;
290;; Macro facility for writing Maxima-level wrappers for
291;; functions operating on internal representation
292;;
293;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
294
295(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
296 &key (polynomials nil)
297 (poly-lists nil)
298 (poly-list-lists nil)
299 (value-type nil))
300 &body body
301 &aux (vars (gensym))
302 (new-vars (gensym)))
303 `(let ((,vars (coerce-maxima-list ,maxima-vars))
304 ,@(when new-vars-supplied-p
305 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
306 (coerce-to-maxima
307 ,value-type
308 (with-coefficient-ring ($poly_coefficient_ring)
309 (with-monomial-order ($poly_monomial_order)
310 (with-elimination-orders ($poly_primary_elimination_order
311 $poly_secondary_elimination_order
312 $poly_elimination_order)
313 (let ,(let ((args nil))
314 (dolist (p polynomials args)
315 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
316 (dolist (p poly-lists args)
317 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
318 (dolist (p poly-list-lists args)
319 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
320 . ,body))))
321 ,(if new-vars-supplied-p
322 `(append ,vars ,new-vars)
323 vars))))
324
325
326;;Functions
327
328(defmfun $poly_expand (p vars)
329 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
330If the representation is not compatible with a polynomial in variables VARS,
331the result is an error."
332 (with-parsed-polynomials ((vars) :polynomials (p)
333 :value-type :polynomial)
334 p))
335
336(defmfun $poly_expt (p n vars)
337 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
338 (poly-expt *expression-ring* p n)))
339
340(defmfun $poly_content (p vars)
341 (with-parsed-polynomials ((vars) :polynomials (p))
342 (poly-content *expression-ring* p)))
343
344(defmfun $poly_pseudo_divide (f fl vars
345 &aux (vars (coerce-maxima-list vars))
346 (f (parse-poly f vars))
347 (fl (parse-poly-list fl vars)))
348 (multiple-value-bind (quot rem c division-count)
349 (poly-pseudo-divide *expression-ring* f fl)
350 `((mlist)
351 ,(coerce-to-maxima :poly-list quot vars)
352 ,(coerce-to-maxima :polynomial rem vars)
353 ,c
354 ,division-count)))
355
356(defmfun $poly_exact_divide (f g vars)
357 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
358 (poly-exact-divide *expression-ring* f g)))
359
360(defmfun $poly_normal_form (f fl vars)
361 (with-parsed-polynomials ((vars) :polynomials (f)
362 :poly-lists (fl)
363 :value-type :polynomial)
364 (normal-form *expression-ring* f (remzero fl) nil)))
365
366(defmfun $poly_buchberger_criterion (g vars)
367 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
368 (buchberger-criterion *expression-ring* g)))
369
370(defmfun $poly_buchberger (fl vars)
371 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
372 (buchberger *expression-ring* (remzero fl) 0 nil)))
373
374(defmfun $poly_reduction (plist vars)
375 (with-parsed-polynomials ((vars) :poly-lists (plist)
376 :value-type :poly-list)
377 (reduction *expression-ring* plist)))
378
379(defmfun $poly_minimization (plist vars)
380 (with-parsed-polynomials ((vars) :poly-lists (plist)
381 :value-type :poly-list)
382 (minimization plist)))
383
384(defmfun $poly_normalize_list (plist vars)
385 (with-parsed-polynomials ((vars) :poly-lists (plist)
386 :value-type :poly-list)
387 (poly-normalize-list *expression-ring* plist)))
388
389(defmfun $poly_grobner (f vars)
390 (with-parsed-polynomials ((vars) :poly-lists (f)
391 :value-type :poly-list)
392 (grobner *expression-ring* (remzero f))))
393
394(defmfun $poly_reduced_grobner (f vars)
395 (with-parsed-polynomials ((vars) :poly-lists (f)
396 :value-type :poly-list)
397 (reduced-grobner *expression-ring* (remzero f))))
398
399(defmfun $poly_depends_p (p var mvars
400 &aux (vars (coerce-maxima-list mvars))
401 (pos (position var vars)))
402 (if (null pos)
403 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
404 (poly-depends-p (parse-poly p vars) pos)))
405
406(defmfun $poly_elimination_ideal (flist k vars)
407 (with-parsed-polynomials ((vars) :poly-lists (flist)
408 :value-type :poly-list)
409 (elimination-ideal *expression-ring* flist k nil 0)))
410
411(defmfun $poly_colon_ideal (f g vars)
412 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
413 (colon-ideal *expression-ring* f g nil)))
414
415(defmfun $poly_ideal_intersection (f g vars)
416 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
417 (ideal-intersection *expression-ring* f g nil)))
418
419(defmfun $poly_lcm (f g vars)
420 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
421 (poly-lcm *expression-ring* f g)))
422
423(defmfun $poly_gcd (f g vars)
424 ($first ($divide (m* f g) ($poly_lcm f g vars))))
425
426(defmfun $poly_grobner_equal (g1 g2 vars)
427 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
428 (grobner-equal *expression-ring* g1 g2)))
429
430(defmfun $poly_grobner_subsetp (g1 g2 vars)
431 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
432 (grobner-subsetp *expression-ring* g1 g2)))
433
434(defmfun $poly_grobner_member (p g vars)
435 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
436 (grobner-member *expression-ring* p g)))
437
438(defmfun $poly_ideal_saturation1 (f p vars)
439 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
440 :value-type :poly-list)
441 (ideal-saturation-1 *expression-ring* f p 0)))
442
443(defmfun $poly_saturation_extension (f plist vars new-vars)
444 (with-parsed-polynomials ((vars new-vars)
445 :poly-lists (f plist)
446 :value-type :poly-list)
447 (saturation-extension *expression-ring* f plist)))
448
449(defmfun $poly_polysaturation_extension (f plist vars new-vars)
450 (with-parsed-polynomials ((vars new-vars)
451 :poly-lists (f plist)
452 :value-type :poly-list)
453 (polysaturation-extension *expression-ring* f plist)))
454
455(defmfun $poly_ideal_polysaturation1 (f plist vars)
456 (with-parsed-polynomials ((vars) :poly-lists (f plist)
457 :value-type :poly-list)
458 (ideal-polysaturation-1 *expression-ring* f plist 0 nil)))
459
460(defmfun $poly_ideal_saturation (f g vars)
461 (with-parsed-polynomials ((vars) :poly-lists (f g)
462 :value-type :poly-list)
463 (ideal-saturation *expression-ring* f g 0 nil)))
464
465(defmfun $poly_ideal_polysaturation (f ideal-list vars)
466 (with-parsed-polynomials ((vars) :poly-lists (f)
467 :poly-list-lists (ideal-list)
468 :value-type :poly-list)
469 (ideal-polysaturation *expression-ring* f ideal-list 0 nil)))
470
471(defmfun $poly_lt (f vars)
472 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
473 (make-poly-from-termlist (list (poly-lt f)))))
474
475(defmfun $poly_lm (f vars)
476 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
477 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *expression-ring*)))))))
478
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