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source: branches/f4grobner/mx-grobner.lisp@ 1683

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