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