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source: branches/f4grobner/mx-grobner.lisp@ 1685

Last change on this file since 1685 was 1685, checked in by Marek Rychlik, 10 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 ring order primary-elimination-order secondary-elimination-order))
181 (parse-list (args) (mapcar #'parse args)))
182 (cond
183 ((eql expr 0) (make-poly-zero))
184 ((member expr vars :test #'equal-test-p)
185 (let ((pos (position expr vars :test #'equal-test-p)))
186 (make-poly-variable (ro-ring ring-and-order) (length vars) pos)))
187 ((free-of-vars expr vars)
188 ;;This means that variable-free CRE and Poisson forms will be converted
189 ;;to coefficients intact
190 (coerce-coeff (ro-ring ring-and-order) expr vars))
191 (t
192 (case (caar expr)
193 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
194 (mminus (poly-uminus (ro-ring ring-and-order) (parse (cadr expr))))
195 (mtimes
196 (if (endp (cddr expr)) ;unary
197 (parse (cdr expr))
198 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
199 (mexpt
200 (cond
201 ((member (cadr expr) vars :test #'equal-test-p)
202 ;;Special handling of (expt var pow)
203 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
204 (make-poly-variable (ro-ring ring-and-order) (length vars) pos (caddr expr))))
205 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
206 ;; Negative power means division in coefficient ring
207 ;; Non-integer power means non-polynomial coefficient
208 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
209 expr)
210 (coerce-coeff (ro-ring ring-and-order) expr vars))
211 (t (poly-expt (ro-ring ring-and-order) (parse (cadr expr)) (caddr expr)))))
212 (mrat (parse ($ratdisrep expr)))
213 (mpois (parse ($outofpois expr)))
214 (otherwise
215 (coerce-coeff (ro-ring ring-and-order) expr vars)))))))
216
217#|
218
219(defun parse-poly-list (expr vars)
220 "Parse a Maxima representation of a list of polynomials."
221 (case (caar expr)
222 (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
223 (t (merror "Expression ~M is not a list of polynomials in variables ~M."
224 expr vars))))
225
226(defun parse-poly-list-list (poly-list-list vars)
227 "Parse a Maxima representation of a list of lists of polynomials."
228 (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
229
230
231;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
232;;
233;; Conversion from internal form to Maxima general form
234;;
235;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
236
237(defun maxima-head ()
238 (if $poly_return_term_list
239 '(mlist)
240 '(mplus)))
241
242(defun coerce-to-maxima (poly-type object vars)
243 (case poly-type
244 (:polynomial
245 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
246 (:poly-list
247 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
248 (:term
249 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
250 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
251 vars (coerce (term-monom object) 'list))))
252 ;; Assumes that Lisp and Maxima logicals coincide
253 (:logical object)
254 (otherwise
255 object)))
256
257
258;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
259;;
260;; Unary and binary operation definition facility
261;;
262;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
263
264(defmacro define-unop (maxima-name fun-name
265 &optional (documentation nil documentation-supplied-p))
266 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
267 `(defun ,maxima-name (p vars
268 &aux
269 (vars (coerce-maxima-list vars))
270 (p (parse-poly p vars)))
271 ,@(when documentation-supplied-p (list documentation))
272 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
273
274(defmacro define-binop (maxima-name fun-name
275 &optional (documentation nil documentation-supplied-p))
276 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
277 `(defmfun ,maxima-name (p q vars
278 &aux
279 (vars (coerce-maxima-list vars))
280 (p (parse-poly p vars))
281 (q (parse-poly q vars)))
282 ,@(when documentation-supplied-p (list documentation))
283 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
284
285
286;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
287;;
288;; Facilities for evaluating Grobner package expressions
289;; within a prepared environment
290;;
291;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
292
293(defmacro with-monomial-order ((order) &body body)
294 "Evaluate BODY with monomial order set to ORDER."
295 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
296 . ,body))
297
298(defmacro with-coefficient-ring ((ring) &body body)
299 "Evaluate BODY with coefficient ring set to RING."
300 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
301 . ,body))
302
303(defmacro with-ring-and-order ((ring order) &body body)
304 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
305 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
306 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
307 . ,body))
308
309(defmacro with-elimination-orders ((primary secondary elimination-order)
310 &body body)
311 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
312 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
313 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
314 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
315 . ,body))
316
317
318;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
319;;
320;; Maxima-level interface functions
321;;
322;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
323
324;; Auxillary function for removing zero polynomial
325(defun remzero (plist) (remove #'poly-zerop plist))
326
327;;Simple operators
328
329(define-binop $poly_add poly-add
330 "Adds two polynomials P and Q")
331
332(define-binop $poly_subtract poly-sub
333 "Subtracts a polynomial Q from P.")
334
335(define-binop $poly_multiply poly-mul
336 "Returns the product of polynomials P and Q.")
337
338(define-binop $poly_s_polynomial spoly
339 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
340
341(define-unop $poly_primitive_part poly-primitive-part
342 "Returns the polynomial P divided by GCD of its coefficients.")
343
344(define-unop $poly_normalize poly-normalize
345 "Returns the polynomial P divided by the leading coefficient.")
346
347;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
348;;
349;; Macro facility for writing Maxima-level wrappers for
350;; functions operating on internal representation
351;;
352;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
353
354(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
355 &key (polynomials nil)
356 (poly-lists nil)
357 (poly-list-lists nil)
358 (value-type nil))
359 &body body
360 &aux (vars (gensym))
361 (new-vars (gensym)))
362 `(let ((,vars (coerce-maxima-list ,maxima-vars))
363 ,@(when new-vars-supplied-p
364 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
365 (coerce-to-maxima
366 ,value-type
367 (with-coefficient-ring ($poly_coefficient_ring)
368 (with-monomial-order ($poly_monomial_order)
369 (with-elimination-orders ($poly_primary_elimination_order
370 $poly_secondary_elimination_order
371 $poly_elimination_order)
372 (let ,(let ((args nil))
373 (dolist (p polynomials args)
374 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
375 (dolist (p poly-lists args)
376 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
377 (dolist (p poly-list-lists args)
378 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
379 . ,body))))
380 ,(if new-vars-supplied-p
381 `(append ,vars ,new-vars)
382 vars))))
383
384
385;;Functions
386
387(defmfun $poly_expand (p vars)
388 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
389If the representation is not compatible with a polynomial in variables VARS,
390the result is an error."
391 (with-parsed-polynomials ((vars) :polynomials (p)
392 :value-type :polynomial)
393 p))
394
395(defmfun $poly_expt (p n vars)
396 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
397 (poly-expt +maxima-ring+ p n)))
398
399(defmfun $poly_content (p vars)
400 (with-parsed-polynomials ((vars) :polynomials (p))
401 (poly-content +maxima-ring+ p)))
402
403(defmfun $poly_pseudo_divide (f fl vars
404 &aux (vars (coerce-maxima-list vars))
405 (f (parse-poly f vars))
406 (fl (parse-poly-list fl vars)))
407 (multiple-value-bind (quot rem c division-count)
408 (poly-pseudo-divide +maxima-ring+ f fl)
409 `((mlist)
410 ,(coerce-to-maxima :poly-list quot vars)
411 ,(coerce-to-maxima :polynomial rem vars)
412 ,c
413 ,division-count)))
414
415(defmfun $poly_exact_divide (f g vars)
416 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
417 (poly-exact-divide +maxima-ring+ f g)))
418
419(defmfun $poly_normal_form (f fl vars)
420 (with-parsed-polynomials ((vars) :polynomials (f)
421 :poly-lists (fl)
422 :value-type :polynomial)
423 (normal-form +maxima-ring+ f (remzero fl) nil)))
424
425(defmfun $poly_buchberger_criterion (g vars)
426 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
427 (buchberger-criterion +maxima-ring+ g)))
428
429(defmfun $poly_buchberger (fl vars)
430 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
431 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
432
433(defmfun $poly_reduction (plist vars)
434 (with-parsed-polynomials ((vars) :poly-lists (plist)
435 :value-type :poly-list)
436 (reduction +maxima-ring+ plist)))
437
438(defmfun $poly_minimization (plist vars)
439 (with-parsed-polynomials ((vars) :poly-lists (plist)
440 :value-type :poly-list)
441 (minimization plist)))
442
443(defmfun $poly_normalize_list (plist vars)
444 (with-parsed-polynomials ((vars) :poly-lists (plist)
445 :value-type :poly-list)
446 (poly-normalize-list +maxima-ring+ plist)))
447
448(defmfun $poly_grobner (f vars)
449 (with-parsed-polynomials ((vars) :poly-lists (f)
450 :value-type :poly-list)
451 (grobner +maxima-ring+ (remzero f))))
452
453(defmfun $poly_reduced_grobner (f vars)
454 (with-parsed-polynomials ((vars) :poly-lists (f)
455 :value-type :poly-list)
456 (reduced-grobner +maxima-ring+ (remzero f))))
457
458(defmfun $poly_depends_p (p var mvars
459 &aux (vars (coerce-maxima-list mvars))
460 (pos (position var vars)))
461 (if (null pos)
462 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
463 (poly-depends-p (parse-poly p vars) pos)))
464
465(defmfun $poly_elimination_ideal (flist k vars)
466 (with-parsed-polynomials ((vars) :poly-lists (flist)
467 :value-type :poly-list)
468 (elimination-ideal +maxima-ring+ flist k nil 0)))
469
470(defmfun $poly_colon_ideal (f g vars)
471 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
472 (colon-ideal +maxima-ring+ f g nil)))
473
474(defmfun $poly_ideal_intersection (f g vars)
475 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
476 (ideal-intersection +maxima-ring+ f g nil)))
477
478(defmfun $poly_lcm (f g vars)
479 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
480 (poly-lcm +maxima-ring+ f g)))
481
482(defmfun $poly_gcd (f g vars)
483 ($first ($divide (m* f g) ($poly_lcm f g vars))))
484
485(defmfun $poly_grobner_equal (g1 g2 vars)
486 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
487 (grobner-equal +maxima-ring+ g1 g2)))
488
489(defmfun $poly_grobner_subsetp (g1 g2 vars)
490 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
491 (grobner-subsetp +maxima-ring+ g1 g2)))
492
493(defmfun $poly_grobner_member (p g vars)
494 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
495 (grobner-member +maxima-ring+ p g)))
496
497(defmfun $poly_ideal_saturation1 (f p vars)
498 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
499 :value-type :poly-list)
500 (ideal-saturation-1 +maxima-ring+ f p 0)))
501
502(defmfun $poly_saturation_extension (f plist vars new-vars)
503 (with-parsed-polynomials ((vars new-vars)
504 :poly-lists (f plist)
505 :value-type :poly-list)
506 (saturation-extension +maxima-ring+ f plist)))
507
508(defmfun $poly_polysaturation_extension (f plist vars new-vars)
509 (with-parsed-polynomials ((vars new-vars)
510 :poly-lists (f plist)
511 :value-type :poly-list)
512 (polysaturation-extension +maxima-ring+ f plist)))
513
514(defmfun $poly_ideal_polysaturation1 (f plist vars)
515 (with-parsed-polynomials ((vars) :poly-lists (f plist)
516 :value-type :poly-list)
517 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
518
519(defmfun $poly_ideal_saturation (f g vars)
520 (with-parsed-polynomials ((vars) :poly-lists (f g)
521 :value-type :poly-list)
522 (ideal-saturation +maxima-ring+ f g 0 nil)))
523
524(defmfun $poly_ideal_polysaturation (f ideal-list vars)
525 (with-parsed-polynomials ((vars) :poly-lists (f)
526 :poly-list-lists (ideal-list)
527 :value-type :poly-list)
528 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
529
530(defmfun $poly_lt (f vars)
531 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
532 (make-poly-from-termlist (list (poly-lt f)))))
533
534(defmfun $poly_lm (f vars)
535 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
536 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
537
538|#
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