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source: branches/f4grobner/mx-grobner.lisp@ 566

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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#+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
43
44
45
46(eval-when
47 #+gcl (load eval)
48 #-gcl (:load-toplevel :execute)
49 (defpackage "MAXIMA" (:use :cl))
50 (setf *features* (remove :maxima *features*)))
51
52(in-package :maxima)
53(use-package :ngrobner)
54
55#+maxima(macsyma-module cgb-maxima)
56
57(eval-when
58 #+gcl (load eval)
59 #-gcl (:load-toplevel :execute)
60 (format t "~&Loading maxima-grobner ~a ~a~%"
61 "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
62
63;;FUNCTS is loaded because it contains the definition of LCM
64#+maxima($load "functs")
65
66
67
68;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
69;;
70;; Maxima expression ring
71;;
72;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
73;;
74;; This is how we perform operations on coefficients
75;; using Maxima functions.
76;;
77;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
78
79(defparameter *maxima-ring*
80 (make-ring
81 ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
82 :parse #'(lambda (expr)
83 (when modulus (setf expr ($rat expr)))
84 expr)
85 :unit #'(lambda () (if modulus ($rat 1) 1))
86 :zerop #'(lambda (expr)
87 ;;When is exactly a maxima expression equal to 0?
88 (cond ((numberp expr)
89 (= expr 0))
90 ((atom expr) nil)
91 (t
92 (case (caar expr)
93 (mrat (eql ($ratdisrep expr) 0))
94 (otherwise (eql ($totaldisrep expr) 0))))))
95 :add #'(lambda (x y) (m+ x y))
96 :sub #'(lambda (x y) (m- x y))
97 :uminus #'(lambda (x) (m- x))
98 :mul #'(lambda (x y) (m* x y))
99 ;;(defun coeff-div (x y) (cadr ($divide x y)))
100 :div #'(lambda (x y) (m// x y))
101 :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
102 :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
103 ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
104 :gcd #'(lambda (x y) ($gcd x y))))
105
106;; Rebind some global variables for Maxima environment
107(setf *expression-ring* *maxima-ring* ; Coefficient arithmetic done by Maxima
108 *ratdisrep-fun* '$ratdisrep ; Coefficients are converted to general form
109 )
110
111;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
112;;
113;; Maxima expression parsing
114;;
115;;
116;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
117;;
118;; Functions and macros dealing with internal representation
119;; structure.
120;;
121;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
122
123(defun equal-test-p (expr1 expr2)
124 (alike1 expr1 expr2))
125
126(defun coerce-maxima-list (expr)
127 "Convert a Maxima list to Lisp list."
128 (cond
129 ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
130 (t expr)))
131
132(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
133
134(defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
135 "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
136 (labels ((parse (arg) (parse-poly arg vars))
137 (parse-list (args) (mapcar #'parse args)))
138 (cond
139 ((eql expr 0) (make-poly-zero))
140 ((member expr vars :test #'equal-test-p)
141 (let ((pos (position expr vars :test #'equal-test-p)))
142 (make-variable *expression-ring* (length vars) pos)))
143 ((free-of-vars expr vars)
144 ;;This means that variable-free CRE and Poisson forms will be converted
145 ;;to coefficients intact
146 (coerce-coeff *expression-ring* expr vars))
147 (t
148 (case (caar expr)
149 (mplus (reduce #'(lambda (x y) (poly-add *expression-ring* x y)) (parse-list (cdr expr))))
150 (mminus (poly-uminus *expression-ring* (parse (cadr expr))))
151 (mtimes
152 (if (endp (cddr expr)) ;unary
153 (parse (cdr expr))
154 (reduce #'(lambda (p q) (poly-mul *expression-ring* p q)) (parse-list (cdr expr)))))
155 (mexpt
156 (cond
157 ((member (cadr expr) vars :test #'equal-test-p)
158 ;;Special handling of (expt var pow)
159 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
160 (make-variable *expression-ring* (length vars) pos (caddr expr))))
161 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
162 ;; Negative power means division in coefficient ring
163 ;; Non-integer power means non-polynomial coefficient
164 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
165 expr)
166 (coerce-coeff *expression-ring* expr vars))
167 (t (poly-expt *expression-ring* (parse (cadr expr)) (caddr expr)))))
168 (mrat (parse ($ratdisrep expr)))
169 (mpois (parse ($outofpois expr)))
170 (otherwise
171 (coerce-coeff *expression-ring* expr vars)))))))
172
173(defun parse-poly-list (expr vars)
174 (case (caar expr)
175 (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
176 (t (merror "Expression ~M is not a list of polynomials in variables ~M."
177 expr vars))))
178(defun parse-poly-list-list (poly-list-list vars)
179 (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
180
181
182;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
183;;
184;; Conversion from internal form to Maxima general form
185;;
186;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
187
188(defun maxima-head ()
189 (if $poly_return_term_list
190 '(mlist)
191 '(mplus)))
192
193(defun coerce-to-maxima (poly-type object vars)
194 (case poly-type
195 (:polynomial
196 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
197 (:poly-list
198 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
199 (:term
200 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
201 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
202 vars (monom-exponents (term-monom object)))))
203 ;; Assumes that Lisp and Maxima logicals coincide
204 (:logical object)
205 (otherwise
206 object)))
207
208
209;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
210;;
211;; Unary and binary operation definition facility
212;;
213;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
214
215(defmacro define-unop (maxima-name fun-name
216 &optional (documentation nil documentation-supplied-p))
217 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
218 `(defun ,maxima-name (p vars
219 &aux
220 (vars (coerce-maxima-list vars))
221 (p (parse-poly p vars)))
222 ,@(when documentation-supplied-p (list documentation))
223 (coerce-to-maxima :polynomial (,fun-name *expression-ring* p) vars)))
224
225(defmacro define-binop (maxima-name fun-name
226 &optional (documentation nil documentation-supplied-p))
227 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
228 `(defmfun ,maxima-name (p q vars
229 &aux
230 (vars (coerce-maxima-list vars))
231 (p (parse-poly p vars))
232 (q (parse-poly q vars)))
233 ,@(when documentation-supplied-p (list documentation))
234 (coerce-to-maxima :polynomial (,fun-name *expression-ring* p q) vars)))
235
236
237;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
238;;
239;; Facilities for evaluating Grobner package expressions
240;; within a prepared environment
241;;
242;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
243
244(defmacro with-monomial-order ((order) &body body)
245 "Evaluate BODY with monomial order set to ORDER."
246 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
247 . ,body))
248
249(defmacro with-coefficient-ring ((ring) &body body)
250 "Evaluate BODY with coefficient ring set to RING."
251 `(let ((*expression-ring* (or (find-ring ,ring) *expression-ring*)))
252 . ,body))
253
254(defmacro with-elimination-orders ((primary secondary elimination-order)
255 &body body)
256 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
257 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
258 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
259 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
260 . ,body))
261
262
263;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
264;;
265;; Maxima-level interface functions
266;;
267;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
268
269;; Auxillary function for removing zero polynomial
270(defun remzero (plist) (remove #'poly-zerop plist))
271
272;;Simple operators
273
274(define-binop $poly_add poly-add
275 "Adds two polynomials P and Q")
276
277(define-binop $poly_subtract poly-sub
278 "Subtracts a polynomial Q from P.")
279
280(define-binop $poly_multiply poly-mul
281 "Returns the product of polynomials P and Q.")
282
283(define-binop $poly_s_polynomial spoly
284 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
285
286(define-unop $poly_primitive_part poly-primitive-part
287 "Returns the polynomial P divided by GCD of its coefficients.")
288
289(define-unop $poly_normalize poly-normalize
290 "Returns the polynomial P divided by the leading coefficient.")
291
292;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
293;;
294;; Macro facility for writing Maxima-level wrappers for
295;; functions operating on internal representation
296;;
297;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
298
299(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
300 &key (polynomials nil)
301 (poly-lists nil)
302 (poly-list-lists nil)
303 (value-type nil))
304 &body body
305 &aux (vars (gensym))
306 (new-vars (gensym)))
307 `(let ((,vars (coerce-maxima-list ,maxima-vars))
308 ,@(when new-vars-supplied-p
309 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
310 (coerce-to-maxima
311 ,value-type
312 (with-coefficient-ring ($poly_coefficient_ring)
313 (with-monomial-order ($poly_monomial_order)
314 (with-elimination-orders ($poly_primary_elimination_order
315 $poly_secondary_elimination_order
316 $poly_elimination_order)
317 (let ,(let ((args nil))
318 (dolist (p polynomials args)
319 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
320 (dolist (p poly-lists args)
321 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
322 (dolist (p poly-list-lists args)
323 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
324 . ,body))))
325 ,(if new-vars-supplied-p
326 `(append ,vars ,new-vars)
327 vars))))
328
329
330;;Functions
331
332(defmfun $poly_expand (p vars)
333 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
334If the representation is not compatible with a polynomial in variables VARS,
335the result is an error."
336 (with-parsed-polynomials ((vars) :polynomials (p)
337 :value-type :polynomial)
338 p))
339
340(defmfun $poly_expt (p n vars)
341 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
342 (poly-expt *expression-ring* p n)))
343
344(defmfun $poly_content (p vars)
345 (with-parsed-polynomials ((vars) :polynomials (p))
346 (poly-content *expression-ring* p)))
347
348(defmfun $poly_pseudo_divide (f fl vars
349 &aux (vars (coerce-maxima-list vars))
350 (f (parse-poly f vars))
351 (fl (parse-poly-list fl vars)))
352 (multiple-value-bind (quot rem c division-count)
353 (poly-pseudo-divide *expression-ring* f fl)
354 `((mlist)
355 ,(coerce-to-maxima :poly-list quot vars)
356 ,(coerce-to-maxima :polynomial rem vars)
357 ,c
358 ,division-count)))
359
360(defmfun $poly_exact_divide (f g vars)
361 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
362 (poly-exact-divide *expression-ring* f g)))
363
364(defmfun $poly_normal_form (f fl vars)
365 (with-parsed-polynomials ((vars) :polynomials (f)
366 :poly-lists (fl)
367 :value-type :polynomial)
368 (normal-form *expression-ring* f (remzero fl) nil)))
369
370(defmfun $poly_buchberger_criterion (g vars)
371 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
372 (buchberger-criterion *expression-ring* g)))
373
374(defmfun $poly_buchberger (fl vars)
375 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
376 (buchberger *expression-ring* (remzero fl) 0 nil)))
377
378(defmfun $poly_reduction (plist vars)
379 (with-parsed-polynomials ((vars) :poly-lists (plist)
380 :value-type :poly-list)
381 (reduction *expression-ring* plist)))
382
383(defmfun $poly_minimization (plist vars)
384 (with-parsed-polynomials ((vars) :poly-lists (plist)
385 :value-type :poly-list)
386 (minimization plist)))
387
388(defmfun $poly_normalize_list (plist vars)
389 (with-parsed-polynomials ((vars) :poly-lists (plist)
390 :value-type :poly-list)
391 (poly-normalize-list *expression-ring* plist)))
392
393(defmfun $poly_grobner (f vars)
394 (with-parsed-polynomials ((vars) :poly-lists (f)
395 :value-type :poly-list)
396 (grobner *expression-ring* (remzero f))))
397
398(defmfun $poly_reduced_grobner (f vars)
399 (with-parsed-polynomials ((vars) :poly-lists (f)
400 :value-type :poly-list)
401 (reduced-grobner *expression-ring* (remzero f))))
402
403(defmfun $poly_depends_p (p var mvars
404 &aux (vars (coerce-maxima-list mvars))
405 (pos (position var vars)))
406 (if (null pos)
407 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
408 (poly-depends-p (parse-poly p vars) pos)))
409
410(defmfun $poly_elimination_ideal (flist k vars)
411 (with-parsed-polynomials ((vars) :poly-lists (flist)
412 :value-type :poly-list)
413 (elimination-ideal *expression-ring* flist k nil 0)))
414
415(defmfun $poly_colon_ideal (f g vars)
416 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
417 (colon-ideal *expression-ring* f g nil)))
418
419(defmfun $poly_ideal_intersection (f g vars)
420 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
421 (ideal-intersection *expression-ring* f g nil)))
422
423(defmfun $poly_lcm (f g vars)
424 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
425 (poly-lcm *expression-ring* f g)))
426
427(defmfun $poly_gcd (f g vars)
428 ($first ($divide (m* f g) ($poly_lcm f g vars))))
429
430(defmfun $poly_grobner_equal (g1 g2 vars)
431 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
432 (grobner-equal *expression-ring* g1 g2)))
433
434(defmfun $poly_grobner_subsetp (g1 g2 vars)
435 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
436 (grobner-subsetp *expression-ring* g1 g2)))
437
438(defmfun $poly_grobner_member (p g vars)
439 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
440 (grobner-member *expression-ring* p g)))
441
442(defmfun $poly_ideal_saturation1 (f p vars)
443 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
444 :value-type :poly-list)
445 (ideal-saturation-1 *expression-ring* f p 0)))
446
447(defmfun $poly_saturation_extension (f plist vars new-vars)
448 (with-parsed-polynomials ((vars new-vars)
449 :poly-lists (f plist)
450 :value-type :poly-list)
451 (saturation-extension *expression-ring* f plist)))
452
453(defmfun $poly_polysaturation_extension (f plist vars new-vars)
454 (with-parsed-polynomials ((vars new-vars)
455 :poly-lists (f plist)
456 :value-type :poly-list)
457 (polysaturation-extension *expression-ring* f plist)))
458
459(defmfun $poly_ideal_polysaturation1 (f plist vars)
460 (with-parsed-polynomials ((vars) :poly-lists (f plist)
461 :value-type :poly-list)
462 (ideal-polysaturation-1 *expression-ring* f plist 0 nil)))
463
464(defmfun $poly_ideal_saturation (f g vars)
465 (with-parsed-polynomials ((vars) :poly-lists (f g)
466 :value-type :poly-list)
467 (ideal-saturation *expression-ring* f g 0 nil)))
468
469(defmfun $poly_ideal_polysaturation (f ideal-list vars)
470 (with-parsed-polynomials ((vars) :poly-lists (f)
471 :poly-list-lists (ideal-list)
472 :value-type :poly-list)
473 (ideal-polysaturation *expression-ring* f ideal-list 0 nil)))
474
475(defmfun $poly_lt (f vars)
476 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
477 (make-poly-from-termlist (list (poly-lt f)))))
478
479(defmfun $poly_lm (f vars)
480 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
481 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *expression-ring*)))))))
482
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