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[1201]1;;; -*- Mode: Lisp -*-
[98]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
[133]22;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
[268]24;; Load this file into Maxima to bootstrap the Grobner package.
[390]25;; NOTE: This file does use symbols defined by Maxima, so it
26;; will not work when loaded in Common Lisp.
[133]27;;
[268]28;; DETAILS: This file implements an interface between the Grobner
[374]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.
[268]34;;
[270]35;; Also, since the NGROBNER package consists of many Lisp files, it is
[375]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.
[270]39;;
[133]40;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
41
[98]42(in-package :maxima)
43
[568]44(macsyma-module cgb-maxima)
[98]45
[568]46
[98]47(eval-when
48 #+gcl (load eval)
49 #-gcl (:load-toplevel :execute)
50 (format t "~&Loading maxima-grobner ~a ~a~%"
51 "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
52
53;;FUNCTS is loaded because it contains the definition of LCM
[995]54($load "functs")
[568]55#+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
[152]56
[571]57(use-package :ngrobner)
[274]58
[571]59
[98]60;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
61;;
62;; Maxima expression ring
63;;
64;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
[521]65;;
66;; This is how we perform operations on coefficients
67;; using Maxima functions.
68;;
69;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
70
[1669]71(defparameter +maxima-ring+
[230]72 (make-ring
[98]73 ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
74 :parse #'(lambda (expr)
75 (when modulus (setf expr ($rat expr)))
76 expr)
77 :unit #'(lambda () (if modulus ($rat 1) 1))
78 :zerop #'(lambda (expr)
79 ;;When is exactly a maxima expression equal to 0?
80 (cond ((numberp expr)
81 (= expr 0))
82 ((atom expr) nil)
83 (t
84 (case (caar expr)
85 (mrat (eql ($ratdisrep expr) 0))
86 (otherwise (eql ($totaldisrep expr) 0))))))
87 :add #'(lambda (x y) (m+ x y))
88 :sub #'(lambda (x y) (m- x y))
89 :uminus #'(lambda (x) (m- x))
90 :mul #'(lambda (x y) (m* x y))
91 ;;(defun coeff-div (x y) (cadr ($divide x y)))
92 :div #'(lambda (x y) (m// x y))
93 :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
94 :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
95 ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
96 :gcd #'(lambda (x y) ($gcd x y))))
97
[619]98;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
99;;
100;; Maxima expression parsing
101;;
102;;
103;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
104;;
105;; Functions and macros dealing with internal representation
106;; structure.
107;;
108;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
[114]109
[619]110(defun equal-test-p (expr1 expr2)
111 (alike1 expr1 expr2))
112
113(defun coerce-maxima-list (expr)
114 "Convert a Maxima list to Lisp list."
115 (cond
116 ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
117 (t expr)))
118
119(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
120
[1642]121;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
122;;
123;; Order utilities
124;;
125;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
126
[1674]127(defun find-ring-by-name (ring)
[1644]128 "This function returns the ring structure bases on input symbol."
129 (cond
130 ((null ring) nil)
131 ((symbolp ring)
132 (case ring
[1650]133 ((maxima-ring :maxima-ring #:maxima-ring $expression_ring #:expression_ring)
[1669]134 +maxima-ring+)
135 ((ring-of-integers :ring-of-integers #:ring-of-integers $ring_of_integers) +ring-of-integers+)
[1644]136 (otherwise
137 (mtell "~%Warning: Ring ~M not found. Using default.~%" ring))))
138 (t
139 (mtell "~%Ring specification ~M is not recognized. Using default.~%" ring)
140 nil)))
141
[1674]142(defun find-order-by-name (order)
[1642]143 "This function returns the order function bases on its name."
144 (cond
145 ((null order) nil)
146 ((symbolp order)
147 (case order
[1650]148 ((lex :lex $lex #:lex)
[1649]149 #'lex>)
[1650]150 ((grlex :grlex $grlex #:grlex)
[1649]151 #'grlex>)
152 ((grevlex :grevlex $grevlex #:grevlex)
153 #'grevlex>)
[1650]154 ((invlex :invlex $invlex #:invlex)
[1649]155 #'invlex>)
[1642]156 (otherwise
157 (mtell "~%Warning: Order ~M not found. Using default.~%" order))))
158 (t
159 (mtell "~%Order specification ~M is not recognized. Using default.~%" order)
160 nil)))
161
[1703]162(defun find-ring-and-order-by-name (&optional
163 (ring (find-ring-by-name $poly_coefficient_ring))
164 (order (find-order-by-name $poly_monomial_order))
165 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
166 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order))
167 &aux
168 (vars (coerce-maxima-list vars))
169 (ring-and-order (make-ring-and-order
170 :ring ring
171 :order order
172 :primary-elimination-order primary-elimination-order
173 :secondary-elimination-order secondary-elimination-order)))
174 ring-and-order)
175
[1644]176(defun maxima->poly (expr vars
[1703]177 &optional
178 (ring-and-order (find-ring-and-order-by-name))
179 &aux
[1673]180 (ring (ro-ring ring-and-order)))
[1683]181 "Convert a maxima polynomial expression EXPR in variables VARS to
182internal form. This works by first converting the expression to Lisp,
[1685]183and then evaluating the expression using polynomial arithmetic
184implemented by the POLYNOMIAL package."
[1687]185 (labels ((parse (arg) (maxima->poly arg vars
186 ring
187 order
[1686]188 primary-elimination-order
189 secondary-elimination-order))
[619]190 (parse-list (args) (mapcar #'parse args)))
191 (cond
192 ((eql expr 0) (make-poly-zero))
193 ((member expr vars :test #'equal-test-p)
194 (let ((pos (position expr vars :test #'equal-test-p)))
[1672]195 (make-poly-variable (ro-ring ring-and-order) (length vars) pos)))
[619]196 ((free-of-vars expr vars)
197 ;;This means that variable-free CRE and Poisson forms will be converted
198 ;;to coefficients intact
[1672]199 (coerce-coeff (ro-ring ring-and-order) expr vars))
[619]200 (t
201 (case (caar expr)
[1654]202 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
[1672]203 (mminus (poly-uminus (ro-ring ring-and-order) (parse (cadr expr))))
[619]204 (mtimes
205 (if (endp (cddr expr)) ;unary
206 (parse (cdr expr))
[1655]207 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
[619]208 (mexpt
209 (cond
210 ((member (cadr expr) vars :test #'equal-test-p)
211 ;;Special handling of (expt var pow)
212 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
[1672]213 (make-poly-variable (ro-ring ring-and-order) (length vars) pos (caddr expr))))
[619]214 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
215 ;; Negative power means division in coefficient ring
216 ;; Non-integer power means non-polynomial coefficient
217 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
218 expr)
[1672]219 (coerce-coeff (ro-ring ring-and-order) expr vars))
220 (t (poly-expt (ro-ring ring-and-order) (parse (cadr expr)) (caddr expr)))))
[619]221 (mrat (parse ($ratdisrep expr)))
222 (mpois (parse ($outofpois expr)))
223 (otherwise
[1673]224 (coerce-coeff (ro-ring ring-and-order) expr vars)))))))
[619]225
[1696]226(defun maxima->poly-list (expr vars
[1704]227 &optional
228 (ring-and-order (find-ring-and-order-by-name))
229 &aux
230 (ring (ro-ring ring-and-order)))
[1693]231 "Convert a Maxima representation of a list of polynomials to the internal form."
[619]232 (case (caar expr)
[1688]233 (mlist (mapcar #'(lambda (p)
[1692]234 (maxima->poly p vars
235 ring order
236 primary-elimination-order
237 secondary-elimination-order))
[1688]238 (cdr expr)))
[1691]239 (otherwise (merror "Expression ~M is not a list of polynomials in variables ~M."
240 expr vars))))
[619]241
[1700]242(defun maxima->poly-list-of-lists (poly-list-of-lists vars
[1705]243 &optional
244 (ring-and-order (find-ring-and-order-by-name))
245 &aux
246 (ring (ro-ring ring-and-order)))
[619]247 "Parse a Maxima representation of a list of lists of polynomials."
[1705]248 (mapcar #'(lambda (g) (maxima->poly-list g vars ring order))
[1700]249 (coerce-maxima-list poly-list-of-lists)))
[619]250
251
[1688]252
[1701]253#|
[111]254;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
255;;
[241]256;; Conversion from internal form to Maxima general form
257;;
258;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
259
260(defun maxima-head ()
261 (if $poly_return_term_list
262 '(mlist)
263 '(mplus)))
264
265(defun coerce-to-maxima (poly-type object vars)
266 (case poly-type
267 (:polynomial
268 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
269 (:poly-list
270 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
271 (:term
272 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
273 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
[882]274 vars (coerce (term-monom object) 'list))))
[241]275 ;; Assumes that Lisp and Maxima logicals coincide
276 (:logical object)
277 (otherwise
278 object)))
279
280
281;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
282;;
[111]283;; Unary and binary operation definition facility
284;;
285;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
[98]286
[111]287(defmacro define-unop (maxima-name fun-name
288 &optional (documentation nil documentation-supplied-p))
289 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
290 `(defun ,maxima-name (p vars
291 &aux
292 (vars (coerce-maxima-list vars))
293 (p (parse-poly p vars)))
294 ,@(when documentation-supplied-p (list documentation))
[1669]295 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
[111]296
297(defmacro define-binop (maxima-name fun-name
298 &optional (documentation nil documentation-supplied-p))
299 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
300 `(defmfun ,maxima-name (p q vars
301 &aux
302 (vars (coerce-maxima-list vars))
303 (p (parse-poly p vars))
304 (q (parse-poly q vars)))
305 ,@(when documentation-supplied-p (list documentation))
[1669]306 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
[111]307
308
[219]309;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
310;;
311;; Facilities for evaluating Grobner package expressions
312;; within a prepared environment
313;;
314;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
315
316(defmacro with-monomial-order ((order) &body body)
317 "Evaluate BODY with monomial order set to ORDER."
318 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
319 . ,body))
320
321(defmacro with-coefficient-ring ((ring) &body body)
322 "Evaluate BODY with coefficient ring set to RING."
[1669]323 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
[219]324 . ,body))
325
[863]326(defmacro with-ring-and-order ((ring order) &body body)
[830]327 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
328 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
[1669]329 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
[830]330 . ,body))
331
[219]332(defmacro with-elimination-orders ((primary secondary elimination-order)
333 &body body)
334 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
335 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
336 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
337 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
338 . ,body))
339
340
[98]341;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
342;;
343;; Maxima-level interface functions
344;;
345;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
346
347;; Auxillary function for removing zero polynomial
348(defun remzero (plist) (remove #'poly-zerop plist))
349
350;;Simple operators
351
352(define-binop $poly_add poly-add
353 "Adds two polynomials P and Q")
354
355(define-binop $poly_subtract poly-sub
356 "Subtracts a polynomial Q from P.")
357
358(define-binop $poly_multiply poly-mul
359 "Returns the product of polynomials P and Q.")
360
361(define-binop $poly_s_polynomial spoly
362 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
363
364(define-unop $poly_primitive_part poly-primitive-part
365 "Returns the polynomial P divided by GCD of its coefficients.")
366
367(define-unop $poly_normalize poly-normalize
368 "Returns the polynomial P divided by the leading coefficient.")
369
[222]370;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
371;;
372;; Macro facility for writing Maxima-level wrappers for
373;; functions operating on internal representation
374;;
375;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
376
377(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
378 &key (polynomials nil)
[1288]379 (poly-lists nil)
380 (poly-list-lists nil)
381 (value-type nil))
[222]382 &body body
383 &aux (vars (gensym))
[1288]384 (new-vars (gensym)))
[222]385 `(let ((,vars (coerce-maxima-list ,maxima-vars))
386 ,@(when new-vars-supplied-p
[1288]387 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
[222]388 (coerce-to-maxima
389 ,value-type
390 (with-coefficient-ring ($poly_coefficient_ring)
391 (with-monomial-order ($poly_monomial_order)
392 (with-elimination-orders ($poly_primary_elimination_order
393 $poly_secondary_elimination_order
394 $poly_elimination_order)
395 (let ,(let ((args nil))
[1288]396 (dolist (p polynomials args)
397 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
398 (dolist (p poly-lists args)
399 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
400 (dolist (p poly-list-lists args)
401 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
[222]402 . ,body))))
403 ,(if new-vars-supplied-p
404 `(append ,vars ,new-vars)
[1288]405 vars))))
[222]406
407
[98]408;;Functions
409
410(defmfun $poly_expand (p vars)
411 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
412If the representation is not compatible with a polynomial in variables VARS,
413the result is an error."
414 (with-parsed-polynomials ((vars) :polynomials (p)
415 :value-type :polynomial)
416 p))
417
418(defmfun $poly_expt (p n vars)
419 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
[1669]420 (poly-expt +maxima-ring+ p n)))
[98]421
422(defmfun $poly_content (p vars)
423 (with-parsed-polynomials ((vars) :polynomials (p))
[1669]424 (poly-content +maxima-ring+ p)))
[98]425
426(defmfun $poly_pseudo_divide (f fl vars
427 &aux (vars (coerce-maxima-list vars))
428 (f (parse-poly f vars))
429 (fl (parse-poly-list fl vars)))
430 (multiple-value-bind (quot rem c division-count)
[1669]431 (poly-pseudo-divide +maxima-ring+ f fl)
[98]432 `((mlist)
433 ,(coerce-to-maxima :poly-list quot vars)
434 ,(coerce-to-maxima :polynomial rem vars)
435 ,c
436 ,division-count)))
437
438(defmfun $poly_exact_divide (f g vars)
439 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
[1669]440 (poly-exact-divide +maxima-ring+ f g)))
[98]441
442(defmfun $poly_normal_form (f fl vars)
443 (with-parsed-polynomials ((vars) :polynomials (f)
444 :poly-lists (fl)
445 :value-type :polynomial)
[1669]446 (normal-form +maxima-ring+ f (remzero fl) nil)))
[98]447
448(defmfun $poly_buchberger_criterion (g vars)
449 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
[1669]450 (buchberger-criterion +maxima-ring+ g)))
[98]451
452(defmfun $poly_buchberger (fl vars)
453 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
[1669]454 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
[98]455
456(defmfun $poly_reduction (plist vars)
457 (with-parsed-polynomials ((vars) :poly-lists (plist)
458 :value-type :poly-list)
[1669]459 (reduction +maxima-ring+ plist)))
[98]460
461(defmfun $poly_minimization (plist vars)
462 (with-parsed-polynomials ((vars) :poly-lists (plist)
463 :value-type :poly-list)
464 (minimization plist)))
465
466(defmfun $poly_normalize_list (plist vars)
467 (with-parsed-polynomials ((vars) :poly-lists (plist)
468 :value-type :poly-list)
[1669]469 (poly-normalize-list +maxima-ring+ plist)))
[98]470
471(defmfun $poly_grobner (f vars)
472 (with-parsed-polynomials ((vars) :poly-lists (f)
473 :value-type :poly-list)
[1669]474 (grobner +maxima-ring+ (remzero f))))
[98]475
476(defmfun $poly_reduced_grobner (f vars)
477 (with-parsed-polynomials ((vars) :poly-lists (f)
478 :value-type :poly-list)
[1669]479 (reduced-grobner +maxima-ring+ (remzero f))))
[98]480
481(defmfun $poly_depends_p (p var mvars
482 &aux (vars (coerce-maxima-list mvars))
483 (pos (position var vars)))
484 (if (null pos)
485 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
486 (poly-depends-p (parse-poly p vars) pos)))
487
488(defmfun $poly_elimination_ideal (flist k vars)
489 (with-parsed-polynomials ((vars) :poly-lists (flist)
490 :value-type :poly-list)
[1669]491 (elimination-ideal +maxima-ring+ flist k nil 0)))
[98]492
493(defmfun $poly_colon_ideal (f g vars)
494 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
[1669]495 (colon-ideal +maxima-ring+ f g nil)))
[98]496
497(defmfun $poly_ideal_intersection (f g vars)
498 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
[1669]499 (ideal-intersection +maxima-ring+ f g nil)))
[98]500
501(defmfun $poly_lcm (f g vars)
502 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
[1669]503 (poly-lcm +maxima-ring+ f g)))
[98]504
505(defmfun $poly_gcd (f g vars)
506 ($first ($divide (m* f g) ($poly_lcm f g vars))))
507
508(defmfun $poly_grobner_equal (g1 g2 vars)
509 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
[1669]510 (grobner-equal +maxima-ring+ g1 g2)))
[98]511
512(defmfun $poly_grobner_subsetp (g1 g2 vars)
513 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
[1669]514 (grobner-subsetp +maxima-ring+ g1 g2)))
[98]515
516(defmfun $poly_grobner_member (p g vars)
517 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
[1669]518 (grobner-member +maxima-ring+ p g)))
[98]519
520(defmfun $poly_ideal_saturation1 (f p vars)
521 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
522 :value-type :poly-list)
[1669]523 (ideal-saturation-1 +maxima-ring+ f p 0)))
[98]524
525(defmfun $poly_saturation_extension (f plist vars new-vars)
526 (with-parsed-polynomials ((vars new-vars)
527 :poly-lists (f plist)
528 :value-type :poly-list)
[1669]529 (saturation-extension +maxima-ring+ f plist)))
[98]530
531(defmfun $poly_polysaturation_extension (f plist vars new-vars)
532 (with-parsed-polynomials ((vars new-vars)
533 :poly-lists (f plist)
534 :value-type :poly-list)
[1669]535 (polysaturation-extension +maxima-ring+ f plist)))
[98]536
537(defmfun $poly_ideal_polysaturation1 (f plist vars)
538 (with-parsed-polynomials ((vars) :poly-lists (f plist)
539 :value-type :poly-list)
[1669]540 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
[98]541
542(defmfun $poly_ideal_saturation (f g vars)
543 (with-parsed-polynomials ((vars) :poly-lists (f g)
544 :value-type :poly-list)
[1669]545 (ideal-saturation +maxima-ring+ f g 0 nil)))
[98]546
547(defmfun $poly_ideal_polysaturation (f ideal-list vars)
548 (with-parsed-polynomials ((vars) :poly-lists (f)
549 :poly-list-lists (ideal-list)
550 :value-type :poly-list)
[1669]551 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
[98]552
553(defmfun $poly_lt (f vars)
554 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
555 (make-poly-from-termlist (list (poly-lt f)))))
556
557(defmfun $poly_lm (f vars)
558 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
[1669]559 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
[98]560
[1640]561|#
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