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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-and-order (find-ring-and-order-by-name))
229 &aux
230 (ring (ro-ring ring-and-order)))
231 "Convert a Maxima representation of a list of polynomials to the internal form."
232 (case (caar expr)
233 (mlist (mapcar #'(lambda (p)
234 (maxima->poly p vars
235 ring order
236 primary-elimination-order
237 secondary-elimination-order))
238 (cdr expr)))
239 (otherwise (merror "Expression ~M is not a list of polynomials in variables ~M."
240 expr vars))))
241
242(defun maxima->poly-list-of-lists (poly-list-of-lists vars
243 &optional
244 (ring (find-ring-by-name $poly_coefficient_ring))
245 (order (find-order-by-name $poly_monomial_order))
246 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
247 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order)))
248 "Parse a Maxima representation of a list of lists of polynomials."
249 (mapcar #'(lambda (g) (maxima->poly-list g vars ring order primary-elimination-order secondary-elimination-order))
250 (coerce-maxima-list poly-list-of-lists)))
251
252
253
254#|
255;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
256;;
257;; Conversion from internal form to Maxima general form
258;;
259;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
260
261(defun maxima-head ()
262 (if $poly_return_term_list
263 '(mlist)
264 '(mplus)))
265
266(defun coerce-to-maxima (poly-type object vars)
267 (case poly-type
268 (:polynomial
269 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
270 (:poly-list
271 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
272 (:term
273 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
274 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
275 vars (coerce (term-monom object) 'list))))
276 ;; Assumes that Lisp and Maxima logicals coincide
277 (:logical object)
278 (otherwise
279 object)))
280
281
282;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
283;;
284;; Unary and binary operation definition facility
285;;
286;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
287
288(defmacro define-unop (maxima-name fun-name
289 &optional (documentation nil documentation-supplied-p))
290 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
291 `(defun ,maxima-name (p vars
292 &aux
293 (vars (coerce-maxima-list vars))
294 (p (parse-poly p vars)))
295 ,@(when documentation-supplied-p (list documentation))
296 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
297
298(defmacro define-binop (maxima-name fun-name
299 &optional (documentation nil documentation-supplied-p))
300 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
301 `(defmfun ,maxima-name (p q vars
302 &aux
303 (vars (coerce-maxima-list vars))
304 (p (parse-poly p vars))
305 (q (parse-poly q vars)))
306 ,@(when documentation-supplied-p (list documentation))
307 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
308
309
310;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
311;;
312;; Facilities for evaluating Grobner package expressions
313;; within a prepared environment
314;;
315;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
316
317(defmacro with-monomial-order ((order) &body body)
318 "Evaluate BODY with monomial order set to ORDER."
319 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
320 . ,body))
321
322(defmacro with-coefficient-ring ((ring) &body body)
323 "Evaluate BODY with coefficient ring set to RING."
324 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
325 . ,body))
326
327(defmacro with-ring-and-order ((ring order) &body body)
328 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
329 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
330 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
331 . ,body))
332
333(defmacro with-elimination-orders ((primary secondary elimination-order)
334 &body body)
335 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
336 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
337 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
338 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
339 . ,body))
340
341
342;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
343;;
344;; Maxima-level interface functions
345;;
346;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
347
348;; Auxillary function for removing zero polynomial
349(defun remzero (plist) (remove #'poly-zerop plist))
350
351;;Simple operators
352
353(define-binop $poly_add poly-add
354 "Adds two polynomials P and Q")
355
356(define-binop $poly_subtract poly-sub
357 "Subtracts a polynomial Q from P.")
358
359(define-binop $poly_multiply poly-mul
360 "Returns the product of polynomials P and Q.")
361
362(define-binop $poly_s_polynomial spoly
363 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
364
365(define-unop $poly_primitive_part poly-primitive-part
366 "Returns the polynomial P divided by GCD of its coefficients.")
367
368(define-unop $poly_normalize poly-normalize
369 "Returns the polynomial P divided by the leading coefficient.")
370
371;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
372;;
373;; Macro facility for writing Maxima-level wrappers for
374;; functions operating on internal representation
375;;
376;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
377
378(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
379 &key (polynomials nil)
380 (poly-lists nil)
381 (poly-list-lists nil)
382 (value-type nil))
383 &body body
384 &aux (vars (gensym))
385 (new-vars (gensym)))
386 `(let ((,vars (coerce-maxima-list ,maxima-vars))
387 ,@(when new-vars-supplied-p
388 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
389 (coerce-to-maxima
390 ,value-type
391 (with-coefficient-ring ($poly_coefficient_ring)
392 (with-monomial-order ($poly_monomial_order)
393 (with-elimination-orders ($poly_primary_elimination_order
394 $poly_secondary_elimination_order
395 $poly_elimination_order)
396 (let ,(let ((args nil))
397 (dolist (p polynomials args)
398 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
399 (dolist (p poly-lists args)
400 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
401 (dolist (p poly-list-lists args)
402 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
403 . ,body))))
404 ,(if new-vars-supplied-p
405 `(append ,vars ,new-vars)
406 vars))))
407
408
409;;Functions
410
411(defmfun $poly_expand (p vars)
412 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
413If the representation is not compatible with a polynomial in variables VARS,
414the result is an error."
415 (with-parsed-polynomials ((vars) :polynomials (p)
416 :value-type :polynomial)
417 p))
418
419(defmfun $poly_expt (p n vars)
420 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
421 (poly-expt +maxima-ring+ p n)))
422
423(defmfun $poly_content (p vars)
424 (with-parsed-polynomials ((vars) :polynomials (p))
425 (poly-content +maxima-ring+ p)))
426
427(defmfun $poly_pseudo_divide (f fl vars
428 &aux (vars (coerce-maxima-list vars))
429 (f (parse-poly f vars))
430 (fl (parse-poly-list fl vars)))
431 (multiple-value-bind (quot rem c division-count)
432 (poly-pseudo-divide +maxima-ring+ f fl)
433 `((mlist)
434 ,(coerce-to-maxima :poly-list quot vars)
435 ,(coerce-to-maxima :polynomial rem vars)
436 ,c
437 ,division-count)))
438
439(defmfun $poly_exact_divide (f g vars)
440 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
441 (poly-exact-divide +maxima-ring+ f g)))
442
443(defmfun $poly_normal_form (f fl vars)
444 (with-parsed-polynomials ((vars) :polynomials (f)
445 :poly-lists (fl)
446 :value-type :polynomial)
447 (normal-form +maxima-ring+ f (remzero fl) nil)))
448
449(defmfun $poly_buchberger_criterion (g vars)
450 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
451 (buchberger-criterion +maxima-ring+ g)))
452
453(defmfun $poly_buchberger (fl vars)
454 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
455 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
456
457(defmfun $poly_reduction (plist vars)
458 (with-parsed-polynomials ((vars) :poly-lists (plist)
459 :value-type :poly-list)
460 (reduction +maxima-ring+ plist)))
461
462(defmfun $poly_minimization (plist vars)
463 (with-parsed-polynomials ((vars) :poly-lists (plist)
464 :value-type :poly-list)
465 (minimization plist)))
466
467(defmfun $poly_normalize_list (plist vars)
468 (with-parsed-polynomials ((vars) :poly-lists (plist)
469 :value-type :poly-list)
470 (poly-normalize-list +maxima-ring+ plist)))
471
472(defmfun $poly_grobner (f vars)
473 (with-parsed-polynomials ((vars) :poly-lists (f)
474 :value-type :poly-list)
475 (grobner +maxima-ring+ (remzero f))))
476
477(defmfun $poly_reduced_grobner (f vars)
478 (with-parsed-polynomials ((vars) :poly-lists (f)
479 :value-type :poly-list)
480 (reduced-grobner +maxima-ring+ (remzero f))))
481
482(defmfun $poly_depends_p (p var mvars
483 &aux (vars (coerce-maxima-list mvars))
484 (pos (position var vars)))
485 (if (null pos)
486 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
487 (poly-depends-p (parse-poly p vars) pos)))
488
489(defmfun $poly_elimination_ideal (flist k vars)
490 (with-parsed-polynomials ((vars) :poly-lists (flist)
491 :value-type :poly-list)
492 (elimination-ideal +maxima-ring+ flist k nil 0)))
493
494(defmfun $poly_colon_ideal (f g vars)
495 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
496 (colon-ideal +maxima-ring+ f g nil)))
497
498(defmfun $poly_ideal_intersection (f g vars)
499 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
500 (ideal-intersection +maxima-ring+ f g nil)))
501
502(defmfun $poly_lcm (f g vars)
503 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
504 (poly-lcm +maxima-ring+ f g)))
505
506(defmfun $poly_gcd (f g vars)
507 ($first ($divide (m* f g) ($poly_lcm f g vars))))
508
509(defmfun $poly_grobner_equal (g1 g2 vars)
510 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
511 (grobner-equal +maxima-ring+ g1 g2)))
512
513(defmfun $poly_grobner_subsetp (g1 g2 vars)
514 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
515 (grobner-subsetp +maxima-ring+ g1 g2)))
516
517(defmfun $poly_grobner_member (p g vars)
518 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
519 (grobner-member +maxima-ring+ p g)))
520
521(defmfun $poly_ideal_saturation1 (f p vars)
522 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
523 :value-type :poly-list)
524 (ideal-saturation-1 +maxima-ring+ f p 0)))
525
526(defmfun $poly_saturation_extension (f plist vars new-vars)
527 (with-parsed-polynomials ((vars new-vars)
528 :poly-lists (f plist)
529 :value-type :poly-list)
530 (saturation-extension +maxima-ring+ f plist)))
531
532(defmfun $poly_polysaturation_extension (f plist vars new-vars)
533 (with-parsed-polynomials ((vars new-vars)
534 :poly-lists (f plist)
535 :value-type :poly-list)
536 (polysaturation-extension +maxima-ring+ f plist)))
537
538(defmfun $poly_ideal_polysaturation1 (f plist vars)
539 (with-parsed-polynomials ((vars) :poly-lists (f plist)
540 :value-type :poly-list)
541 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
542
543(defmfun $poly_ideal_saturation (f g vars)
544 (with-parsed-polynomials ((vars) :poly-lists (f g)
545 :value-type :poly-list)
546 (ideal-saturation +maxima-ring+ f g 0 nil)))
547
548(defmfun $poly_ideal_polysaturation (f ideal-list vars)
549 (with-parsed-polynomials ((vars) :poly-lists (f)
550 :poly-list-lists (ideal-list)
551 :value-type :poly-list)
552 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
553
554(defmfun $poly_lt (f vars)
555 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
556 (make-poly-from-termlist (list (poly-lt f)))))
557
558(defmfun $poly_lm (f vars)
559 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
560 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
561
562|#
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