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source: branches/f4grobner/mx-grobner.lisp@ 1724

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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 (elimination-order (find-order-by-name $poly_elimination_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 (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 "Build RING-AND-ORDER structure. The defaults are determined by various Maxima-level switches,
175which are names of ring and orders."
176 ring-and-order)
177
178(defun maxima->poly (expr vars
179 &optional
180 (ring-and-order (find-ring-and-order-by-name))
181 &aux
182 (vars (coerce-maxima-list vars))
183 (ring (ro-ring ring-and-order)))
184 "Convert a maxima polynomial expression EXPR in variables VARS to
185internal form. This works by first converting the expression to Lisp,
186and then evaluating the expression using polynomial arithmetic
187implemented by the POLYNOMIAL package."
188 (labels ((parse (arg) (maxima->poly arg vars ring-and-order))
189 (parse-list (args) (mapcar #'parse args)))
190 (cond
191 ((eql expr 0) (make-poly-zero))
192 ((member expr vars :test #'equal-test-p)
193 (let ((pos (position expr vars :test #'equal-test-p)))
194 (make-poly-variable ring (length vars) pos)))
195 ((free-of-vars expr vars)
196 ;;This means that variable-free CRE and Poisson forms will be converted
197 ;;to coefficients intact
198 (coerce-coeff ring expr vars))
199 (t
200 (case (caar expr)
201 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
202 (mminus (poly-uminus ring (parse (cadr expr))))
203 (mtimes
204 (if (endp (cddr expr)) ;unary
205 (parse (cdr expr))
206 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
207 (mexpt
208 (cond
209 ((member (cadr expr) vars :test #'equal-test-p)
210 ;;Special handling of (expt var pow)
211 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
212 (make-poly-variable ring (length vars) pos (caddr expr))))
213 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
214 ;; Negative power means division in coefficient ring
215 ;; Non-integer power means non-polynomial coefficient
216 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
217 expr)
218 (coerce-coeff ring expr vars))
219 (t (poly-expt ring (parse (cadr expr)) (caddr expr)))))
220 (mrat (parse ($ratdisrep expr)))
221 (mpois (parse ($outofpois expr)))
222 (otherwise
223 (coerce-coeff ring expr vars)))))))
224
225(defun maxima->poly-list (expr vars
226 &optional
227 (ring-and-order (find-ring-and-order-by-name)))
228 "Convert a Maxima representation of a list of polynomials to the internal form."
229 (case (caar expr)
230 (mlist (mapcar #'(lambda (p)
231 (maxima->poly p vars ring-and-order))
232 (cdr expr)))
233 (otherwise (merror "Expression ~M is not a list of polynomials in variables ~M."
234 expr vars))))
235
236(defun maxima->poly-list-of-lists (poly-list-of-lists vars
237 &optional
238 (ring-and-order (find-ring-and-order-by-name)))
239 "Parse a Maxima representation of a list of lists of polynomials."
240 (mapcar #'(lambda (g) (maxima->poly-list g vars ring-and-order))
241 (coerce-maxima-list poly-list-of-lists)))
242
243
244
245;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
246;;
247;; Conversion from internal form to Maxima general form
248;;
249;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
250
251(defun maxima-head ()
252 (if $poly_return_term_list
253 '(mlist)
254 '(mplus)))
255
256(defun poly->maxima (poly-type object vars)
257 (case poly-type
258 (:poly
259 `(,(maxima-head) ,@(mapcar #'(lambda (term) (poly->maxima :term term vars)) (poly-termlist object))))
260 (:poly-list
261 `((mlist) ,@(mapcar #'(lambda (p) ($ratdisrep (poly->maxima :polynomial p vars))) object)))
262 (:term
263 `((mtimes) ,($ratdisrep (term-coeff object))
264 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
265 vars (monom->list (term-monom object)))))
266 ;; Assumes that Lisp and Maxima logicals coincide
267 (:logical object)
268 (otherwise
269 object)))
270
271
272;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
273;;
274;; Unary and binary operation definition facility
275;;
276;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
277
278(defmacro define-unop (maxima-name fun-name
279 &optional (documentation nil documentation-supplied-p))
280 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
281 `(defun ,maxima-name (p vars
282 &aux
283 (vars (coerce-maxima-list vars))
284 (p (parse-poly p vars)))
285 ,@(when documentation-supplied-p (list documentation))
286 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
287
288(defmacro define-binop (maxima-name fun-name
289 &optional (documentation nil documentation-supplied-p))
290 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
291 `(defmfun ,maxima-name (p q vars
292 &aux
293 (vars (coerce-maxima-list vars))
294 (p (parse-poly p vars))
295 (q (parse-poly q vars)))
296 ,@(when documentation-supplied-p (list documentation))
297 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
298
299
300(defvar *ring-and-order* nil)
301
302;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
303;;
304;; Facilities for evaluating Grobner package expressions
305;; within a prepared environment
306;;
307;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
308
309#|
310(defmacro with-monomial-order ((order) &body body)
311 "Evaluate BODY with monomial order set to ORDER."
312 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
313 . ,body))
314
315(defmacro with-coefficient-ring ((ring) &body body)
316 "Evaluate BODY with coefficient ring set to RING."
317 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
318 . ,body))
319
320(defmacro with-ring-and-order ((ring order) &body body)
321 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
322 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
323 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
324 . ,body))
325
326(defmacro with-elimination-orders ((primary secondary elimination-order)
327 &body body)
328 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
329 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
330 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
331 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
332 . ,body))
333
334|#
335
336
337;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
338;;
339;; Maxima-level interface functions
340;;
341;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
342
343;; Auxillary function for removing zero polynomial
344(defun remzero (plist) (remove #'poly-zerop plist))
345
346;;Simple operators
347
348(define-binop $poly_add poly-add
349 "Adds two polynomials P and Q")
350
351(define-binop $poly_subtract poly-sub
352 "Subtracts a polynomial Q from P.")
353
354(define-binop $poly_multiply poly-mul
355 "Returns the product of polynomials P and Q.")
356
357(define-binop $poly_s_polynomial spoly
358 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
359
360(define-unop $poly_primitive_part poly-primitive-part
361 "Returns the polynomial P divided by GCD of its coefficients.")
362
363(define-unop $poly_normalize poly-normalize
364 "Returns the polynomial P divided by the leading coefficient.")
365
366;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
367;;
368;; Macro facility for writing Maxima-level wrappers for
369;; functions operating on internal representation
370;;
371;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
372
373(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
374 &key (polynomials nil)
375 (poly-lists nil)
376 (poly-list-lists nil)
377 (value-type nil))
378 &body body
379 &aux (vars (gensym))
380 (new-vars (gensym)))
381 `(let ((,vars (coerce-maxima-list ,maxima-vars))
382 ,@(when new-vars-supplied-p
383 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
384 (coerce-to-maxima
385 ,value-type
386 (let ((*ring-and-order* ,(find-ring-and-order-by-name
387 :ring ,$poly_coefficient_ring
388 :order ,$poly_monomial_order
389 :elimination-order ,$poly_primary_elimination_order
390 :primary-elimination-order ,$poly_secondary_elimination_order
391 :secondary-elimination-order ,$poly_elimination_order)))
392 (let ,(let ((args nil))
393 (dolist (p polynomials args)
394 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
395 (dolist (p poly-lists args)
396 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
397 (dolist (p poly-list-lists args)
398 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
399 . ,body))))
400 ,(if new-vars-supplied-p
401 `(append ,vars ,new-vars)
402 vars))))
403
404
405;;Functions
406
407(defmfun $poly_expand (p vars)
408 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
409If the representation is not compatible with a polynomial in variables VARS,
410the result is an error."
411 (with-parsed-polynomials ((vars) :polynomials (p)
412 :value-type :polynomial)
413 p))
414
415#|
416
417(defmfun $poly_expt (p n vars)
418 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
419 (poly-expt +maxima-ring+ p n)))
420
421(defmfun $poly_content (p vars)
422 (with-parsed-polynomials ((vars) :polynomials (p))
423 (poly-content +maxima-ring+ p)))
424
425(defmfun $poly_pseudo_divide (f fl vars
426 &aux (vars (coerce-maxima-list vars))
427 (f (parse-poly f vars))
428 (fl (parse-poly-list fl vars)))
429 (multiple-value-bind (quot rem c division-count)
430 (poly-pseudo-divide +maxima-ring+ f fl)
431 `((mlist)
432 ,(coerce-to-maxima :poly-list quot vars)
433 ,(coerce-to-maxima :polynomial rem vars)
434 ,c
435 ,division-count)))
436
437(defmfun $poly_exact_divide (f g vars)
438 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
439 (poly-exact-divide +maxima-ring+ f g)))
440
441(defmfun $poly_normal_form (f fl vars)
442 (with-parsed-polynomials ((vars) :polynomials (f)
443 :poly-lists (fl)
444 :value-type :polynomial)
445 (normal-form +maxima-ring+ f (remzero fl) nil)))
446
447(defmfun $poly_buchberger_criterion (g vars)
448 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
449 (buchberger-criterion +maxima-ring+ g)))
450
451(defmfun $poly_buchberger (fl vars)
452 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
453 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
454
455(defmfun $poly_reduction (plist vars)
456 (with-parsed-polynomials ((vars) :poly-lists (plist)
457 :value-type :poly-list)
458 (reduction +maxima-ring+ plist)))
459
460(defmfun $poly_minimization (plist vars)
461 (with-parsed-polynomials ((vars) :poly-lists (plist)
462 :value-type :poly-list)
463 (minimization plist)))
464
465(defmfun $poly_normalize_list (plist vars)
466 (with-parsed-polynomials ((vars) :poly-lists (plist)
467 :value-type :poly-list)
468 (poly-normalize-list +maxima-ring+ plist)))
469
470(defmfun $poly_grobner (f vars)
471 (with-parsed-polynomials ((vars) :poly-lists (f)
472 :value-type :poly-list)
473 (grobner +maxima-ring+ (remzero f))))
474
475(defmfun $poly_reduced_grobner (f vars)
476 (with-parsed-polynomials ((vars) :poly-lists (f)
477 :value-type :poly-list)
478 (reduced-grobner +maxima-ring+ (remzero f))))
479
480(defmfun $poly_depends_p (p var mvars
481 &aux (vars (coerce-maxima-list mvars))
482 (pos (position var vars)))
483 (if (null pos)
484 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
485 (poly-depends-p (parse-poly p vars) pos)))
486
487(defmfun $poly_elimination_ideal (flist k vars)
488 (with-parsed-polynomials ((vars) :poly-lists (flist)
489 :value-type :poly-list)
490 (elimination-ideal +maxima-ring+ flist k nil 0)))
491
492(defmfun $poly_colon_ideal (f g vars)
493 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
494 (colon-ideal +maxima-ring+ f g nil)))
495
496(defmfun $poly_ideal_intersection (f g vars)
497 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
498 (ideal-intersection +maxima-ring+ f g nil)))
499
500(defmfun $poly_lcm (f g vars)
501 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
502 (poly-lcm +maxima-ring+ f g)))
503
504(defmfun $poly_gcd (f g vars)
505 ($first ($divide (m* f g) ($poly_lcm f g vars))))
506
507(defmfun $poly_grobner_equal (g1 g2 vars)
508 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
509 (grobner-equal +maxima-ring+ g1 g2)))
510
511(defmfun $poly_grobner_subsetp (g1 g2 vars)
512 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
513 (grobner-subsetp +maxima-ring+ g1 g2)))
514
515(defmfun $poly_grobner_member (p g vars)
516 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
517 (grobner-member +maxima-ring+ p g)))
518
519(defmfun $poly_ideal_saturation1 (f p vars)
520 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
521 :value-type :poly-list)
522 (ideal-saturation-1 +maxima-ring+ f p 0)))
523
524(defmfun $poly_saturation_extension (f plist vars new-vars)
525 (with-parsed-polynomials ((vars new-vars)
526 :poly-lists (f plist)
527 :value-type :poly-list)
528 (saturation-extension +maxima-ring+ f plist)))
529
530(defmfun $poly_polysaturation_extension (f plist vars new-vars)
531 (with-parsed-polynomials ((vars new-vars)
532 :poly-lists (f plist)
533 :value-type :poly-list)
534 (polysaturation-extension +maxima-ring+ f plist)))
535
536(defmfun $poly_ideal_polysaturation1 (f plist vars)
537 (with-parsed-polynomials ((vars) :poly-lists (f plist)
538 :value-type :poly-list)
539 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
540
541(defmfun $poly_ideal_saturation (f g vars)
542 (with-parsed-polynomials ((vars) :poly-lists (f g)
543 :value-type :poly-list)
544 (ideal-saturation +maxima-ring+ f g 0 nil)))
545
546(defmfun $poly_ideal_polysaturation (f ideal-list vars)
547 (with-parsed-polynomials ((vars) :poly-lists (f)
548 :poly-list-lists (ideal-list)
549 :value-type :poly-list)
550 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
551
552(defmfun $poly_lt (f vars)
553 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
554 (make-poly-from-termlist (list (poly-lt f)))))
555
556(defmfun $poly_lm (f vars)
557 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
558 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
559
560|#
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