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1;;; -*- Mode: Lisp -*-
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
44(macsyma-module cgb-maxima)
45
46
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 $"))
52
53;;FUNCTS is loaded because it contains the definition of LCM
54($load "functs")
55#+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
56
57(use-package :ngrobner)
58
59
60;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
61;;
62;; Maxima expression ring
63;;
64;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
65;;
66;; This is how we perform operations on coefficients
67;; using Maxima functions.
68;;
69;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
70
71(defparameter +maxima-ring+
72 (make-ring
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) ($gcd x y))))
97
98;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
99;;
100;; Maxima expression parsing
101;;
102;;
103;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
104;;
105;; Functions and macros dealing with internal representation
106;; structure.
107;;
108;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
109
110(defun equal-test-p (expr1 expr2)
111 (alike1 expr1 expr2))
112
113(defun coerce-maxima-list (expr)
114 "Convert a Maxima list to Lisp list."
115 (cond
116 ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
117 (t expr)))
118
119(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
120
121;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
122;;
123;; Order utilities
124;;
125;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
126
127(defun find-ring-by-name (ring)
128 "This function returns the ring structure bases on input symbol."
129 (cond
130 ((null ring) nil)
131 ((symbolp ring)
132 (case ring
133 ((maxima-ring :maxima-ring #:maxima-ring $expression_ring #:expression_ring)
134 +maxima-ring+)
135 ((ring-of-integers :ring-of-integers #:ring-of-integers $ring_of_integers) +ring-of-integers+)
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
142(defun find-order-by-name (order)
143 "This function returns the order function bases on its name."
144 (cond
145 ((null order) nil)
146 ((symbolp order)
147 (case order
148 ((lex :lex $lex #:lex)
149 #'lex>)
150 ((grlex :grlex $grlex #:grlex)
151 #'grlex>)
152 ((grevlex :grevlex $grevlex #:grevlex)
153 #'grevlex>)
154 ((invlex :invlex $invlex #:invlex)
155 #'invlex>)
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
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
176(defun maxima->poly (expr vars
177 &optional
178 (ring-and-order (find-ring-and-order-by-name))
179 &aux
180 (ring (ro-ring ring-and-order)))
181 "Convert a maxima polynomial expression EXPR in variables VARS to
182internal form. This works by first converting the expression to Lisp,
183and then evaluating the expression using polynomial arithmetic
184implemented by the POLYNOMIAL package."
185 (labels ((parse (arg) (maxima->poly arg vars
186 ring
187 order
188 primary-elimination-order
189 secondary-elimination-order))
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)))
195 (make-poly-variable (ro-ring ring-and-order) (length vars) pos)))
196 ((free-of-vars expr vars)
197 ;;This means that variable-free CRE and Poisson forms will be converted
198 ;;to coefficients intact
199 (coerce-coeff (ro-ring ring-and-order) expr vars))
200 (t
201 (case (caar expr)
202 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
203 (mminus (poly-uminus (ro-ring ring-and-order) (parse (cadr expr))))
204 (mtimes
205 (if (endp (cddr expr)) ;unary
206 (parse (cdr expr))
207 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
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)))
213 (make-poly-variable (ro-ring ring-and-order) (length vars) pos (caddr expr))))
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)
219 (coerce-coeff (ro-ring ring-and-order) expr vars))
220 (t (poly-expt (ro-ring ring-and-order) (parse (cadr expr)) (caddr expr)))))
221 (mrat (parse ($ratdisrep expr)))
222 (mpois (parse ($outofpois expr)))
223 (otherwise
224 (coerce-coeff (ro-ring ring-and-order) expr vars)))))))
225
226(defun maxima->poly-list (expr vars
227 &optional
228 (ring (find-ring-by-name $poly_coefficient_ring))
229 (order (find-order-by-name $poly_monomial_order))
230 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
231 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order)))
232 "Convert a Maxima representation of a list of polynomials to the internal form."
233 (case (caar expr)
234 (mlist (mapcar #'(lambda (p)
235 (maxima->poly p vars
236 ring order
237 primary-elimination-order
238 secondary-elimination-order))
239 (cdr expr)))
240 (otherwise (merror "Expression ~M is not a list of polynomials in variables ~M."
241 expr vars))))
242
243(defun maxima->poly-list-of-lists (poly-list-of-lists vars
244 &optional
245 (ring (find-ring-by-name $poly_coefficient_ring))
246 (order (find-order-by-name $poly_monomial_order))
247 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
248 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order)))
249 "Parse a Maxima representation of a list of lists of polynomials."
250 (mapcar #'(lambda (g) (maxima->poly-list g vars ring order primary-elimination-order secondary-elimination-order))
251 (coerce-maxima-list poly-list-of-lists)))
252
253
254
255#|
256;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
257;;
258;; Conversion from internal form to Maxima general form
259;;
260;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
261
262(defun maxima-head ()
263 (if $poly_return_term_list
264 '(mlist)
265 '(mplus)))
266
267(defun coerce-to-maxima (poly-type object vars)
268 (case poly-type
269 (:polynomial
270 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
271 (:poly-list
272 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
273 (:term
274 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
275 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
276 vars (coerce (term-monom object) 'list))))
277 ;; Assumes that Lisp and Maxima logicals coincide
278 (:logical object)
279 (otherwise
280 object)))
281
282
283;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
284;;
285;; Unary and binary operation definition facility
286;;
287;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
288
289(defmacro define-unop (maxima-name fun-name
290 &optional (documentation nil documentation-supplied-p))
291 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
292 `(defun ,maxima-name (p vars
293 &aux
294 (vars (coerce-maxima-list vars))
295 (p (parse-poly p vars)))
296 ,@(when documentation-supplied-p (list documentation))
297 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
298
299(defmacro define-binop (maxima-name fun-name
300 &optional (documentation nil documentation-supplied-p))
301 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
302 `(defmfun ,maxima-name (p q vars
303 &aux
304 (vars (coerce-maxima-list vars))
305 (p (parse-poly p vars))
306 (q (parse-poly q vars)))
307 ,@(when documentation-supplied-p (list documentation))
308 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
309
310
311;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
312;;
313;; Facilities for evaluating Grobner package expressions
314;; within a prepared environment
315;;
316;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
317
318(defmacro with-monomial-order ((order) &body body)
319 "Evaluate BODY with monomial order set to ORDER."
320 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
321 . ,body))
322
323(defmacro with-coefficient-ring ((ring) &body body)
324 "Evaluate BODY with coefficient ring set to RING."
325 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
326 . ,body))
327
328(defmacro with-ring-and-order ((ring order) &body body)
329 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
330 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
331 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
332 . ,body))
333
334(defmacro with-elimination-orders ((primary secondary elimination-order)
335 &body body)
336 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
337 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
338 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
339 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
340 . ,body))
341
342
343;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
344;;
345;; Maxima-level interface functions
346;;
347;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
348
349;; Auxillary function for removing zero polynomial
350(defun remzero (plist) (remove #'poly-zerop plist))
351
352;;Simple operators
353
354(define-binop $poly_add poly-add
355 "Adds two polynomials P and Q")
356
357(define-binop $poly_subtract poly-sub
358 "Subtracts a polynomial Q from P.")
359
360(define-binop $poly_multiply poly-mul
361 "Returns the product of polynomials P and Q.")
362
363(define-binop $poly_s_polynomial spoly
364 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
365
366(define-unop $poly_primitive_part poly-primitive-part
367 "Returns the polynomial P divided by GCD of its coefficients.")
368
369(define-unop $poly_normalize poly-normalize
370 "Returns the polynomial P divided by the leading coefficient.")
371
372;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
373;;
374;; Macro facility for writing Maxima-level wrappers for
375;; functions operating on internal representation
376;;
377;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
378
379(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
380 &key (polynomials nil)
381 (poly-lists nil)
382 (poly-list-lists nil)
383 (value-type nil))
384 &body body
385 &aux (vars (gensym))
386 (new-vars (gensym)))
387 `(let ((,vars (coerce-maxima-list ,maxima-vars))
388 ,@(when new-vars-supplied-p
389 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
390 (coerce-to-maxima
391 ,value-type
392 (with-coefficient-ring ($poly_coefficient_ring)
393 (with-monomial-order ($poly_monomial_order)
394 (with-elimination-orders ($poly_primary_elimination_order
395 $poly_secondary_elimination_order
396 $poly_elimination_order)
397 (let ,(let ((args nil))
398 (dolist (p polynomials args)
399 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
400 (dolist (p poly-lists args)
401 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
402 (dolist (p poly-list-lists args)
403 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
404 . ,body))))
405 ,(if new-vars-supplied-p
406 `(append ,vars ,new-vars)
407 vars))))
408
409
410;;Functions
411
412(defmfun $poly_expand (p vars)
413 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
414If the representation is not compatible with a polynomial in variables VARS,
415the result is an error."
416 (with-parsed-polynomials ((vars) :polynomials (p)
417 :value-type :polynomial)
418 p))
419
420(defmfun $poly_expt (p n vars)
421 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
422 (poly-expt +maxima-ring+ p n)))
423
424(defmfun $poly_content (p vars)
425 (with-parsed-polynomials ((vars) :polynomials (p))
426 (poly-content +maxima-ring+ p)))
427
428(defmfun $poly_pseudo_divide (f fl vars
429 &aux (vars (coerce-maxima-list vars))
430 (f (parse-poly f vars))
431 (fl (parse-poly-list fl vars)))
432 (multiple-value-bind (quot rem c division-count)
433 (poly-pseudo-divide +maxima-ring+ f fl)
434 `((mlist)
435 ,(coerce-to-maxima :poly-list quot vars)
436 ,(coerce-to-maxima :polynomial rem vars)
437 ,c
438 ,division-count)))
439
440(defmfun $poly_exact_divide (f g vars)
441 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
442 (poly-exact-divide +maxima-ring+ f g)))
443
444(defmfun $poly_normal_form (f fl vars)
445 (with-parsed-polynomials ((vars) :polynomials (f)
446 :poly-lists (fl)
447 :value-type :polynomial)
448 (normal-form +maxima-ring+ f (remzero fl) nil)))
449
450(defmfun $poly_buchberger_criterion (g vars)
451 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
452 (buchberger-criterion +maxima-ring+ g)))
453
454(defmfun $poly_buchberger (fl vars)
455 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
456 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
457
458(defmfun $poly_reduction (plist vars)
459 (with-parsed-polynomials ((vars) :poly-lists (plist)
460 :value-type :poly-list)
461 (reduction +maxima-ring+ plist)))
462
463(defmfun $poly_minimization (plist vars)
464 (with-parsed-polynomials ((vars) :poly-lists (plist)
465 :value-type :poly-list)
466 (minimization plist)))
467
468(defmfun $poly_normalize_list (plist vars)
469 (with-parsed-polynomials ((vars) :poly-lists (plist)
470 :value-type :poly-list)
471 (poly-normalize-list +maxima-ring+ plist)))
472
473(defmfun $poly_grobner (f vars)
474 (with-parsed-polynomials ((vars) :poly-lists (f)
475 :value-type :poly-list)
476 (grobner +maxima-ring+ (remzero f))))
477
478(defmfun $poly_reduced_grobner (f vars)
479 (with-parsed-polynomials ((vars) :poly-lists (f)
480 :value-type :poly-list)
481 (reduced-grobner +maxima-ring+ (remzero f))))
482
483(defmfun $poly_depends_p (p var mvars
484 &aux (vars (coerce-maxima-list mvars))
485 (pos (position var vars)))
486 (if (null pos)
487 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
488 (poly-depends-p (parse-poly p vars) pos)))
489
490(defmfun $poly_elimination_ideal (flist k vars)
491 (with-parsed-polynomials ((vars) :poly-lists (flist)
492 :value-type :poly-list)
493 (elimination-ideal +maxima-ring+ flist k nil 0)))
494
495(defmfun $poly_colon_ideal (f g vars)
496 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
497 (colon-ideal +maxima-ring+ f g nil)))
498
499(defmfun $poly_ideal_intersection (f g vars)
500 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
501 (ideal-intersection +maxima-ring+ f g nil)))
502
503(defmfun $poly_lcm (f g vars)
504 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
505 (poly-lcm +maxima-ring+ f g)))
506
507(defmfun $poly_gcd (f g vars)
508 ($first ($divide (m* f g) ($poly_lcm f g vars))))
509
510(defmfun $poly_grobner_equal (g1 g2 vars)
511 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
512 (grobner-equal +maxima-ring+ g1 g2)))
513
514(defmfun $poly_grobner_subsetp (g1 g2 vars)
515 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
516 (grobner-subsetp +maxima-ring+ g1 g2)))
517
518(defmfun $poly_grobner_member (p g vars)
519 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
520 (grobner-member +maxima-ring+ p g)))
521
522(defmfun $poly_ideal_saturation1 (f p vars)
523 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
524 :value-type :poly-list)
525 (ideal-saturation-1 +maxima-ring+ f p 0)))
526
527(defmfun $poly_saturation_extension (f plist vars new-vars)
528 (with-parsed-polynomials ((vars new-vars)
529 :poly-lists (f plist)
530 :value-type :poly-list)
531 (saturation-extension +maxima-ring+ f plist)))
532
533(defmfun $poly_polysaturation_extension (f plist vars new-vars)
534 (with-parsed-polynomials ((vars new-vars)
535 :poly-lists (f plist)
536 :value-type :poly-list)
537 (polysaturation-extension +maxima-ring+ f plist)))
538
539(defmfun $poly_ideal_polysaturation1 (f plist vars)
540 (with-parsed-polynomials ((vars) :poly-lists (f plist)
541 :value-type :poly-list)
542 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
543
544(defmfun $poly_ideal_saturation (f g vars)
545 (with-parsed-polynomials ((vars) :poly-lists (f g)
546 :value-type :poly-list)
547 (ideal-saturation +maxima-ring+ f g 0 nil)))
548
549(defmfun $poly_ideal_polysaturation (f ideal-list vars)
550 (with-parsed-polynomials ((vars) :poly-lists (f)
551 :poly-list-lists (ideal-list)
552 :value-type :poly-list)
553 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
554
555(defmfun $poly_lt (f vars)
556 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
557 (make-poly-from-termlist (list (poly-lt f)))))
558
559(defmfun $poly_lm (f vars)
560 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
561 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
562
563|#
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