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source: branches/f4grobner/mx-grobner.lisp@ 1681

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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 (print "Its a symbol!!!~A%" ring)
133 (case ring
134 ((maxima-ring :maxima-ring #:maxima-ring $expression_ring #:expression_ring)
135 +maxima-ring+)
136 ((ring-of-integers :ring-of-integers #:ring-of-integers $ring_of_integers) +ring-of-integers+)
137 (otherwise
138 (mtell "~%Warning: Ring ~M not found. Using default.~%" ring))))
139 (t
140 (mtell "~%Ring specification ~M is not recognized. Using default.~%" ring)
141 nil)))
142
143(defun find-order-by-name (order)
144 "This function returns the order function bases on its name."
145 (cond
146 ((null order) nil)
147 ((symbolp order)
148 (case order
149 ((lex :lex $lex #:lex)
150 #'lex>)
151 ((grlex :grlex $grlex #:grlex)
152 #'grlex>)
153 ((grevlex :grevlex $grevlex #:grevlex)
154 #'grevlex>)
155 ((invlex :invlex $invlex #:invlex)
156 #'invlex>)
157 (otherwise
158 (mtell "~%Warning: Order ~M not found. Using default.~%" order))))
159 (t
160 (mtell "~%Order specification ~M is not recognized. Using default.~%" order)
161 nil)))
162
163(defun maxima->poly (expr vars
164 &optional
165 (ring (find-ring-by-name $poly_coefficient_ring))
166 (order (find-order-by-name $poly_monomial_order))
167 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
168 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order))
169 &aux
170 (vars (coerce-maxima-list vars))
171 (ring-and-order (make-ring-and-order
172 :ring ring
173 :order order
174 :primary-elimination-order primary-elimination-order
175 :secondary-elimination-order secondary-elimination-order))
176 (ring (ro-ring ring-and-order)))
177 "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
178 (labels ((parse (arg) (maxima->poly arg vars ring order primary-elimination-order secondary-elimination-order))
179 (parse-list (args) (mapcar #'parse args)))
180 (cond
181 ((eql expr 0) (make-poly-zero))
182 ((member expr vars :test #'equal-test-p)
183 (let ((pos (position expr vars :test #'equal-test-p)))
184 (make-poly-variable (ro-ring ring-and-order) (length vars) pos)))
185 ((free-of-vars expr vars)
186 ;;This means that variable-free CRE and Poisson forms will be converted
187 ;;to coefficients intact
188 (coerce-coeff (ro-ring ring-and-order) expr vars))
189 (t
190 (case (caar expr)
191 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
192 (mminus (poly-uminus (ro-ring ring-and-order) (parse (cadr expr))))
193 (mtimes
194 (if (endp (cddr expr)) ;unary
195 (parse (cdr expr))
196 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
197 (mexpt
198 (cond
199 ((member (cadr expr) vars :test #'equal-test-p)
200 ;;Special handling of (expt var pow)
201 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
202 (make-poly-variable (ro-ring ring-and-order) (length vars) pos (caddr expr))))
203 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
204 ;; Negative power means division in coefficient ring
205 ;; Non-integer power means non-polynomial coefficient
206 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
207 expr)
208 (coerce-coeff (ro-ring ring-and-order) expr vars))
209 (t (poly-expt (ro-ring ring-and-order) (parse (cadr expr)) (caddr expr)))))
210 (mrat (parse ($ratdisrep expr)))
211 (mpois (parse ($outofpois expr)))
212 (otherwise
213 (coerce-coeff (ro-ring ring-and-order) expr vars)))))))
214
215#|
216
217(defun parse-poly-list (expr vars)
218 "Parse a Maxima representation of a list of polynomials."
219 (case (caar expr)
220 (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
221 (t (merror "Expression ~M is not a list of polynomials in variables ~M."
222 expr vars))))
223
224(defun parse-poly-list-list (poly-list-list vars)
225 "Parse a Maxima representation of a list of lists of polynomials."
226 (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
227
228
229;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
230;;
231;; Conversion from internal form to Maxima general form
232;;
233;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
234
235(defun maxima-head ()
236 (if $poly_return_term_list
237 '(mlist)
238 '(mplus)))
239
240(defun coerce-to-maxima (poly-type object vars)
241 (case poly-type
242 (:polynomial
243 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
244 (:poly-list
245 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
246 (:term
247 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
248 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
249 vars (coerce (term-monom object) 'list))))
250 ;; Assumes that Lisp and Maxima logicals coincide
251 (:logical object)
252 (otherwise
253 object)))
254
255
256;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
257;;
258;; Unary and binary operation definition facility
259;;
260;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
261
262(defmacro define-unop (maxima-name fun-name
263 &optional (documentation nil documentation-supplied-p))
264 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
265 `(defun ,maxima-name (p vars
266 &aux
267 (vars (coerce-maxima-list vars))
268 (p (parse-poly p vars)))
269 ,@(when documentation-supplied-p (list documentation))
270 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
271
272(defmacro define-binop (maxima-name fun-name
273 &optional (documentation nil documentation-supplied-p))
274 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
275 `(defmfun ,maxima-name (p q vars
276 &aux
277 (vars (coerce-maxima-list vars))
278 (p (parse-poly p vars))
279 (q (parse-poly q vars)))
280 ,@(when documentation-supplied-p (list documentation))
281 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
282
283
284;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
285;;
286;; Facilities for evaluating Grobner package expressions
287;; within a prepared environment
288;;
289;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
290
291(defmacro with-monomial-order ((order) &body body)
292 "Evaluate BODY with monomial order set to ORDER."
293 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
294 . ,body))
295
296(defmacro with-coefficient-ring ((ring) &body body)
297 "Evaluate BODY with coefficient ring set to RING."
298 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
299 . ,body))
300
301(defmacro with-ring-and-order ((ring order) &body body)
302 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
303 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
304 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
305 . ,body))
306
307(defmacro with-elimination-orders ((primary secondary elimination-order)
308 &body body)
309 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
310 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
311 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
312 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
313 . ,body))
314
315
316;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
317;;
318;; Maxima-level interface functions
319;;
320;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
321
322;; Auxillary function for removing zero polynomial
323(defun remzero (plist) (remove #'poly-zerop plist))
324
325;;Simple operators
326
327(define-binop $poly_add poly-add
328 "Adds two polynomials P and Q")
329
330(define-binop $poly_subtract poly-sub
331 "Subtracts a polynomial Q from P.")
332
333(define-binop $poly_multiply poly-mul
334 "Returns the product of polynomials P and Q.")
335
336(define-binop $poly_s_polynomial spoly
337 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
338
339(define-unop $poly_primitive_part poly-primitive-part
340 "Returns the polynomial P divided by GCD of its coefficients.")
341
342(define-unop $poly_normalize poly-normalize
343 "Returns the polynomial P divided by the leading coefficient.")
344
345;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
346;;
347;; Macro facility for writing Maxima-level wrappers for
348;; functions operating on internal representation
349;;
350;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
351
352(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
353 &key (polynomials nil)
354 (poly-lists nil)
355 (poly-list-lists nil)
356 (value-type nil))
357 &body body
358 &aux (vars (gensym))
359 (new-vars (gensym)))
360 `(let ((,vars (coerce-maxima-list ,maxima-vars))
361 ,@(when new-vars-supplied-p
362 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
363 (coerce-to-maxima
364 ,value-type
365 (with-coefficient-ring ($poly_coefficient_ring)
366 (with-monomial-order ($poly_monomial_order)
367 (with-elimination-orders ($poly_primary_elimination_order
368 $poly_secondary_elimination_order
369 $poly_elimination_order)
370 (let ,(let ((args nil))
371 (dolist (p polynomials args)
372 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
373 (dolist (p poly-lists args)
374 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
375 (dolist (p poly-list-lists args)
376 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
377 . ,body))))
378 ,(if new-vars-supplied-p
379 `(append ,vars ,new-vars)
380 vars))))
381
382
383;;Functions
384
385(defmfun $poly_expand (p vars)
386 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
387If the representation is not compatible with a polynomial in variables VARS,
388the result is an error."
389 (with-parsed-polynomials ((vars) :polynomials (p)
390 :value-type :polynomial)
391 p))
392
393(defmfun $poly_expt (p n vars)
394 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
395 (poly-expt +maxima-ring+ p n)))
396
397(defmfun $poly_content (p vars)
398 (with-parsed-polynomials ((vars) :polynomials (p))
399 (poly-content +maxima-ring+ p)))
400
401(defmfun $poly_pseudo_divide (f fl vars
402 &aux (vars (coerce-maxima-list vars))
403 (f (parse-poly f vars))
404 (fl (parse-poly-list fl vars)))
405 (multiple-value-bind (quot rem c division-count)
406 (poly-pseudo-divide +maxima-ring+ f fl)
407 `((mlist)
408 ,(coerce-to-maxima :poly-list quot vars)
409 ,(coerce-to-maxima :polynomial rem vars)
410 ,c
411 ,division-count)))
412
413(defmfun $poly_exact_divide (f g vars)
414 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
415 (poly-exact-divide +maxima-ring+ f g)))
416
417(defmfun $poly_normal_form (f fl vars)
418 (with-parsed-polynomials ((vars) :polynomials (f)
419 :poly-lists (fl)
420 :value-type :polynomial)
421 (normal-form +maxima-ring+ f (remzero fl) nil)))
422
423(defmfun $poly_buchberger_criterion (g vars)
424 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
425 (buchberger-criterion +maxima-ring+ g)))
426
427(defmfun $poly_buchberger (fl vars)
428 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
429 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
430
431(defmfun $poly_reduction (plist vars)
432 (with-parsed-polynomials ((vars) :poly-lists (plist)
433 :value-type :poly-list)
434 (reduction +maxima-ring+ plist)))
435
436(defmfun $poly_minimization (plist vars)
437 (with-parsed-polynomials ((vars) :poly-lists (plist)
438 :value-type :poly-list)
439 (minimization plist)))
440
441(defmfun $poly_normalize_list (plist vars)
442 (with-parsed-polynomials ((vars) :poly-lists (plist)
443 :value-type :poly-list)
444 (poly-normalize-list +maxima-ring+ plist)))
445
446(defmfun $poly_grobner (f vars)
447 (with-parsed-polynomials ((vars) :poly-lists (f)
448 :value-type :poly-list)
449 (grobner +maxima-ring+ (remzero f))))
450
451(defmfun $poly_reduced_grobner (f vars)
452 (with-parsed-polynomials ((vars) :poly-lists (f)
453 :value-type :poly-list)
454 (reduced-grobner +maxima-ring+ (remzero f))))
455
456(defmfun $poly_depends_p (p var mvars
457 &aux (vars (coerce-maxima-list mvars))
458 (pos (position var vars)))
459 (if (null pos)
460 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
461 (poly-depends-p (parse-poly p vars) pos)))
462
463(defmfun $poly_elimination_ideal (flist k vars)
464 (with-parsed-polynomials ((vars) :poly-lists (flist)
465 :value-type :poly-list)
466 (elimination-ideal +maxima-ring+ flist k nil 0)))
467
468(defmfun $poly_colon_ideal (f g vars)
469 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
470 (colon-ideal +maxima-ring+ f g nil)))
471
472(defmfun $poly_ideal_intersection (f g vars)
473 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
474 (ideal-intersection +maxima-ring+ f g nil)))
475
476(defmfun $poly_lcm (f g vars)
477 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
478 (poly-lcm +maxima-ring+ f g)))
479
480(defmfun $poly_gcd (f g vars)
481 ($first ($divide (m* f g) ($poly_lcm f g vars))))
482
483(defmfun $poly_grobner_equal (g1 g2 vars)
484 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
485 (grobner-equal +maxima-ring+ g1 g2)))
486
487(defmfun $poly_grobner_subsetp (g1 g2 vars)
488 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
489 (grobner-subsetp +maxima-ring+ g1 g2)))
490
491(defmfun $poly_grobner_member (p g vars)
492 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
493 (grobner-member +maxima-ring+ p g)))
494
495(defmfun $poly_ideal_saturation1 (f p vars)
496 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
497 :value-type :poly-list)
498 (ideal-saturation-1 +maxima-ring+ f p 0)))
499
500(defmfun $poly_saturation_extension (f plist vars new-vars)
501 (with-parsed-polynomials ((vars new-vars)
502 :poly-lists (f plist)
503 :value-type :poly-list)
504 (saturation-extension +maxima-ring+ f plist)))
505
506(defmfun $poly_polysaturation_extension (f plist vars new-vars)
507 (with-parsed-polynomials ((vars new-vars)
508 :poly-lists (f plist)
509 :value-type :poly-list)
510 (polysaturation-extension +maxima-ring+ f plist)))
511
512(defmfun $poly_ideal_polysaturation1 (f plist vars)
513 (with-parsed-polynomials ((vars) :poly-lists (f plist)
514 :value-type :poly-list)
515 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
516
517(defmfun $poly_ideal_saturation (f g vars)
518 (with-parsed-polynomials ((vars) :poly-lists (f g)
519 :value-type :poly-list)
520 (ideal-saturation +maxima-ring+ f g 0 nil)))
521
522(defmfun $poly_ideal_polysaturation (f ideal-list vars)
523 (with-parsed-polynomials ((vars) :poly-lists (f)
524 :poly-list-lists (ideal-list)
525 :value-type :poly-list)
526 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
527
528(defmfun $poly_lt (f vars)
529 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
530 (make-poly-from-termlist (list (poly-lt f)))))
531
532(defmfun $poly_lm (f vars)
533 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
534 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
535
536|#
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