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