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source: branches/f4grobner/mx-grobner.lisp@ 1687

Last change on this file since 1687 was 1687, checked in by Marek Rychlik, 9 years ago

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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 maxima->poly (expr vars
163 &optional
164 (ring (find-ring-by-name $poly_coefficient_ring))
165 (order (find-order-by-name $poly_monomial_order))
166 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
167 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order))
168 &aux
169 (vars (coerce-maxima-list vars))
170 (ring-and-order (make-ring-and-order
171 :ring ring
172 :order order
173 :primary-elimination-order primary-elimination-order
174 :secondary-elimination-order secondary-elimination-order))
175 (ring (ro-ring ring-and-order)))
176 "Convert a maxima polynomial expression EXPR in variables VARS to
177internal form. This works by first converting the expression to Lisp,
178and then evaluating the expression using polynomial arithmetic
179implemented by the POLYNOMIAL package."
180 (labels ((parse (arg) (maxima->poly arg vars
181 ring
182 order
183 primary-elimination-order
184 secondary-elimination-order))
185 (parse-list (args) (mapcar #'parse args)))
186 (cond
187 ((eql expr 0) (make-poly-zero))
188 ((member expr vars :test #'equal-test-p)
189 (let ((pos (position expr vars :test #'equal-test-p)))
190 (make-poly-variable (ro-ring ring-and-order) (length vars) pos)))
191 ((free-of-vars expr vars)
192 ;;This means that variable-free CRE and Poisson forms will be converted
193 ;;to coefficients intact
194 (coerce-coeff (ro-ring ring-and-order) expr vars))
195 (t
196 (case (caar expr)
197 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
198 (mminus (poly-uminus (ro-ring ring-and-order) (parse (cadr expr))))
199 (mtimes
200 (if (endp (cddr expr)) ;unary
201 (parse (cdr expr))
202 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
203 (mexpt
204 (cond
205 ((member (cadr expr) vars :test #'equal-test-p)
206 ;;Special handling of (expt var pow)
207 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
208 (make-poly-variable (ro-ring ring-and-order) (length vars) pos (caddr expr))))
209 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
210 ;; Negative power means division in coefficient ring
211 ;; Non-integer power means non-polynomial coefficient
212 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
213 expr)
214 (coerce-coeff (ro-ring ring-and-order) expr vars))
215 (t (poly-expt (ro-ring ring-and-order) (parse (cadr expr)) (caddr expr)))))
216 (mrat (parse ($ratdisrep expr)))
217 (mpois (parse ($outofpois expr)))
218 (otherwise
219 (coerce-coeff (ro-ring ring-and-order) expr vars)))))))
220
221#|
222
223(defun parse-poly-list (expr vars)
224 "Parse a Maxima representation of a list of polynomials."
225 (case (caar expr)
226 (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
227 (t (merror "Expression ~M is not a list of polynomials in variables ~M."
228 expr vars))))
229
230(defun parse-poly-list-list (poly-list-list vars)
231 "Parse a Maxima representation of a list of lists of polynomials."
232 (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
233
234
235;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
236;;
237;; Conversion from internal form to Maxima general form
238;;
239;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
240
241(defun maxima-head ()
242 (if $poly_return_term_list
243 '(mlist)
244 '(mplus)))
245
246(defun coerce-to-maxima (poly-type object vars)
247 (case poly-type
248 (:polynomial
249 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
250 (:poly-list
251 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
252 (:term
253 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
254 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
255 vars (coerce (term-monom object) 'list))))
256 ;; Assumes that Lisp and Maxima logicals coincide
257 (:logical object)
258 (otherwise
259 object)))
260
261
262;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
263;;
264;; Unary and binary operation definition facility
265;;
266;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
267
268(defmacro define-unop (maxima-name fun-name
269 &optional (documentation nil documentation-supplied-p))
270 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
271 `(defun ,maxima-name (p vars
272 &aux
273 (vars (coerce-maxima-list vars))
274 (p (parse-poly p vars)))
275 ,@(when documentation-supplied-p (list documentation))
276 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
277
278(defmacro define-binop (maxima-name fun-name
279 &optional (documentation nil documentation-supplied-p))
280 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
281 `(defmfun ,maxima-name (p q vars
282 &aux
283 (vars (coerce-maxima-list vars))
284 (p (parse-poly p vars))
285 (q (parse-poly q vars)))
286 ,@(when documentation-supplied-p (list documentation))
287 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
288
289
290;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
291;;
292;; Facilities for evaluating Grobner package expressions
293;; within a prepared environment
294;;
295;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
296
297(defmacro with-monomial-order ((order) &body body)
298 "Evaluate BODY with monomial order set to ORDER."
299 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
300 . ,body))
301
302(defmacro with-coefficient-ring ((ring) &body body)
303 "Evaluate BODY with coefficient ring set to RING."
304 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
305 . ,body))
306
307(defmacro with-ring-and-order ((ring order) &body body)
308 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
309 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
310 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
311 . ,body))
312
313(defmacro with-elimination-orders ((primary secondary elimination-order)
314 &body body)
315 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
316 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
317 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
318 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
319 . ,body))
320
321
322;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
323;;
324;; Maxima-level interface functions
325;;
326;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
327
328;; Auxillary function for removing zero polynomial
329(defun remzero (plist) (remove #'poly-zerop plist))
330
331;;Simple operators
332
333(define-binop $poly_add poly-add
334 "Adds two polynomials P and Q")
335
336(define-binop $poly_subtract poly-sub
337 "Subtracts a polynomial Q from P.")
338
339(define-binop $poly_multiply poly-mul
340 "Returns the product of polynomials P and Q.")
341
342(define-binop $poly_s_polynomial spoly
343 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
344
345(define-unop $poly_primitive_part poly-primitive-part
346 "Returns the polynomial P divided by GCD of its coefficients.")
347
348(define-unop $poly_normalize poly-normalize
349 "Returns the polynomial P divided by the leading coefficient.")
350
351;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
352;;
353;; Macro facility for writing Maxima-level wrappers for
354;; functions operating on internal representation
355;;
356;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
357
358(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
359 &key (polynomials nil)
360 (poly-lists nil)
361 (poly-list-lists nil)
362 (value-type nil))
363 &body body
364 &aux (vars (gensym))
365 (new-vars (gensym)))
366 `(let ((,vars (coerce-maxima-list ,maxima-vars))
367 ,@(when new-vars-supplied-p
368 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
369 (coerce-to-maxima
370 ,value-type
371 (with-coefficient-ring ($poly_coefficient_ring)
372 (with-monomial-order ($poly_monomial_order)
373 (with-elimination-orders ($poly_primary_elimination_order
374 $poly_secondary_elimination_order
375 $poly_elimination_order)
376 (let ,(let ((args nil))
377 (dolist (p polynomials args)
378 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
379 (dolist (p poly-lists args)
380 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
381 (dolist (p poly-list-lists args)
382 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
383 . ,body))))
384 ,(if new-vars-supplied-p
385 `(append ,vars ,new-vars)
386 vars))))
387
388
389;;Functions
390
391(defmfun $poly_expand (p vars)
392 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
393If the representation is not compatible with a polynomial in variables VARS,
394the result is an error."
395 (with-parsed-polynomials ((vars) :polynomials (p)
396 :value-type :polynomial)
397 p))
398
399(defmfun $poly_expt (p n vars)
400 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
401 (poly-expt +maxima-ring+ p n)))
402
403(defmfun $poly_content (p vars)
404 (with-parsed-polynomials ((vars) :polynomials (p))
405 (poly-content +maxima-ring+ p)))
406
407(defmfun $poly_pseudo_divide (f fl vars
408 &aux (vars (coerce-maxima-list vars))
409 (f (parse-poly f vars))
410 (fl (parse-poly-list fl vars)))
411 (multiple-value-bind (quot rem c division-count)
412 (poly-pseudo-divide +maxima-ring+ f fl)
413 `((mlist)
414 ,(coerce-to-maxima :poly-list quot vars)
415 ,(coerce-to-maxima :polynomial rem vars)
416 ,c
417 ,division-count)))
418
419(defmfun $poly_exact_divide (f g vars)
420 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
421 (poly-exact-divide +maxima-ring+ f g)))
422
423(defmfun $poly_normal_form (f fl vars)
424 (with-parsed-polynomials ((vars) :polynomials (f)
425 :poly-lists (fl)
426 :value-type :polynomial)
427 (normal-form +maxima-ring+ f (remzero fl) nil)))
428
429(defmfun $poly_buchberger_criterion (g vars)
430 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
431 (buchberger-criterion +maxima-ring+ g)))
432
433(defmfun $poly_buchberger (fl vars)
434 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
435 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
436
437(defmfun $poly_reduction (plist vars)
438 (with-parsed-polynomials ((vars) :poly-lists (plist)
439 :value-type :poly-list)
440 (reduction +maxima-ring+ plist)))
441
442(defmfun $poly_minimization (plist vars)
443 (with-parsed-polynomials ((vars) :poly-lists (plist)
444 :value-type :poly-list)
445 (minimization plist)))
446
447(defmfun $poly_normalize_list (plist vars)
448 (with-parsed-polynomials ((vars) :poly-lists (plist)
449 :value-type :poly-list)
450 (poly-normalize-list +maxima-ring+ plist)))
451
452(defmfun $poly_grobner (f vars)
453 (with-parsed-polynomials ((vars) :poly-lists (f)
454 :value-type :poly-list)
455 (grobner +maxima-ring+ (remzero f))))
456
457(defmfun $poly_reduced_grobner (f vars)
458 (with-parsed-polynomials ((vars) :poly-lists (f)
459 :value-type :poly-list)
460 (reduced-grobner +maxima-ring+ (remzero f))))
461
462(defmfun $poly_depends_p (p var mvars
463 &aux (vars (coerce-maxima-list mvars))
464 (pos (position var vars)))
465 (if (null pos)
466 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
467 (poly-depends-p (parse-poly p vars) pos)))
468
469(defmfun $poly_elimination_ideal (flist k vars)
470 (with-parsed-polynomials ((vars) :poly-lists (flist)
471 :value-type :poly-list)
472 (elimination-ideal +maxima-ring+ flist k nil 0)))
473
474(defmfun $poly_colon_ideal (f g vars)
475 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
476 (colon-ideal +maxima-ring+ f g nil)))
477
478(defmfun $poly_ideal_intersection (f g vars)
479 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
480 (ideal-intersection +maxima-ring+ f g nil)))
481
482(defmfun $poly_lcm (f g vars)
483 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
484 (poly-lcm +maxima-ring+ f g)))
485
486(defmfun $poly_gcd (f g vars)
487 ($first ($divide (m* f g) ($poly_lcm f g vars))))
488
489(defmfun $poly_grobner_equal (g1 g2 vars)
490 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
491 (grobner-equal +maxima-ring+ g1 g2)))
492
493(defmfun $poly_grobner_subsetp (g1 g2 vars)
494 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
495 (grobner-subsetp +maxima-ring+ g1 g2)))
496
497(defmfun $poly_grobner_member (p g vars)
498 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
499 (grobner-member +maxima-ring+ p g)))
500
501(defmfun $poly_ideal_saturation1 (f p vars)
502 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
503 :value-type :poly-list)
504 (ideal-saturation-1 +maxima-ring+ f p 0)))
505
506(defmfun $poly_saturation_extension (f plist vars new-vars)
507 (with-parsed-polynomials ((vars new-vars)
508 :poly-lists (f plist)
509 :value-type :poly-list)
510 (saturation-extension +maxima-ring+ f plist)))
511
512(defmfun $poly_polysaturation_extension (f plist vars new-vars)
513 (with-parsed-polynomials ((vars new-vars)
514 :poly-lists (f plist)
515 :value-type :poly-list)
516 (polysaturation-extension +maxima-ring+ f plist)))
517
518(defmfun $poly_ideal_polysaturation1 (f plist vars)
519 (with-parsed-polynomials ((vars) :poly-lists (f plist)
520 :value-type :poly-list)
521 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
522
523(defmfun $poly_ideal_saturation (f g vars)
524 (with-parsed-polynomials ((vars) :poly-lists (f g)
525 :value-type :poly-list)
526 (ideal-saturation +maxima-ring+ f g 0 nil)))
527
528(defmfun $poly_ideal_polysaturation (f ideal-list vars)
529 (with-parsed-polynomials ((vars) :poly-lists (f)
530 :poly-list-lists (ideal-list)
531 :value-type :poly-list)
532 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
533
534(defmfun $poly_lt (f vars)
535 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
536 (make-poly-from-termlist (list (poly-lt f)))))
537
538(defmfun $poly_lm (f vars)
539 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
540 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
541
542|#
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