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source: branches/f4grobner/mx-grobner.lisp@ 998

Last change on this file since 998 was 998, checked in by Marek Rychlik, 10 years ago

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1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
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) ($gcd x y))))
97
98;; Rebind some global variables for Maxima environment
99(setf *expression-ring* *maxima-ring* ; Coefficient arithmetic done by Maxima
100 *ratdisrep-fun* '$ratdisrep ; Coefficients are converted to general form
101 )
102
103;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
104;;
105;; Maxima expression parsing
106;;
107;;
108;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
109;;
110;; Functions and macros dealing with internal representation
111;; structure.
112;;
113;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
114
115(defun equal-test-p (expr1 expr2)
116 (alike1 expr1 expr2))
117
118(defun coerce-maxima-list (expr)
119 "Convert a Maxima list to Lisp list."
120 (cond
121 ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
122 (t expr)))
123
124(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
125
126(defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
127 "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
128 (labels ((parse (arg) (parse-poly arg vars))
129 (parse-list (args) (mapcar #'parse args)))
130 (cond
131 ((eql expr 0) (make-poly-zero))
132 ((member expr vars :test #'equal-test-p)
133 (let ((pos (position expr vars :test #'equal-test-p)))
134 (make-variable *expression-ring* (length vars) pos)))
135 ((free-of-vars expr vars)
136 ;;This means that variable-free CRE and Poisson forms will be converted
137 ;;to coefficients intact
138 (coerce-coeff *expression-ring* expr vars))
139 (t
140 (case (caar expr)
141 (mplus (reduce #'(lambda (x y) (poly-add *expression-ring* x y)) (parse-list (cdr expr))))
142 (mminus (poly-uminus *expression-ring* (parse (cadr expr))))
143 (mtimes
144 (if (endp (cddr expr)) ;unary
145 (parse (cdr expr))
146 (reduce #'(lambda (p q) (poly-mul *expression-ring* p q)) (parse-list (cdr expr)))))
147 (mexpt
148 (cond
149 ((member (cadr expr) vars :test #'equal-test-p)
150 ;;Special handling of (expt var pow)
151 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
152 (make-variable *expression-ring* (length vars) pos (caddr expr))))
153 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
154 ;; Negative power means division in coefficient ring
155 ;; Non-integer power means non-polynomial coefficient
156 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
157 expr)
158 (coerce-coeff *expression-ring* expr vars))
159 (t (poly-expt *expression-ring* (parse (cadr expr)) (caddr expr)))))
160 (mrat (parse ($ratdisrep expr)))
161 (mpois (parse ($outofpois expr)))
162 (otherwise
163 (coerce-coeff *expression-ring* expr vars)))))))
164
165(defun parse-poly-list (expr vars)
166 "Parse a Maxima representation of a list of polynomials."
167 (case (caar expr)
168 (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
169 (t (merror "Expression ~M is not a list of polynomials in variables ~M."
170 expr vars))))
171
172(defun parse-poly-list-list (poly-list-list vars)
173 "Parse a Maxima representation of a list of lists of polynomials."
174 (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
175
176
177;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
178;;
179;; Conversion from internal form to Maxima general form
180;;
181;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
182
183(defun maxima-head ()
184 (if $poly_return_term_list
185 '(mlist)
186 '(mplus)))
187
188(defun coerce-to-maxima (poly-type object vars)
189 (case poly-type
190 (:polynomial
191 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
192 (:poly-list
193 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
194 (:term
195 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
196 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
197 vars (coerce (term-monom object) 'list))))
198 ;; Assumes that Lisp and Maxima logicals coincide
199 (:logical object)
200 (otherwise
201 object)))
202
203
204;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
205;;
206;; Unary and binary operation definition facility
207;;
208;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
209
210(defmacro define-unop (maxima-name fun-name
211 &optional (documentation nil documentation-supplied-p))
212 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
213 `(defun ,maxima-name (p vars
214 &aux
215 (vars (coerce-maxima-list vars))
216 (p (parse-poly p vars)))
217 ,@(when documentation-supplied-p (list documentation))
218 (coerce-to-maxima :polynomial (,fun-name *expression-ring* p) vars)))
219
220(defmacro define-binop (maxima-name fun-name
221 &optional (documentation nil documentation-supplied-p))
222 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
223 `(defmfun ,maxima-name (p q vars
224 &aux
225 (vars (coerce-maxima-list vars))
226 (p (parse-poly p vars))
227 (q (parse-poly q vars)))
228 ,@(when documentation-supplied-p (list documentation))
229 (coerce-to-maxima :polynomial (,fun-name *expression-ring* p q) vars)))
230
231
232;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
233;;
234;; Order utilities
235;;
236;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
237
238(defun find-order (order)
239 "This function returns the order function bases on its name."
240 (cond
241 ((null order) nil)
242 ((symbolp order)
243 (case order
244 ((lex :lex $lex) #'lex>)
245 ((grlex :grlex $grlex) #'grlex>)
246 ((grevlex :grevlex $grevlex) #'grevlex>)
247 ((invlex :invlex $invlex) #'invlex>)
248 ((elimination-order-1 :elimination-order-1 elimination_order_1) #'elimination-order-1)
249 (otherwise
250 (mtell "~%Warning: Order ~M not found. Using default.~%" order))))
251 (t
252 (mtell "~%Order specification ~M is not recognized. Using default.~%" order)
253 nil)))
254
255;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
256;;
257;; Ring utilities
258;;
259;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
260
261(defun find-ring (ring)
262 "This function returns the ring structure bases on input symbol."
263 (cond
264 ((null ring) nil)
265 ((symbolp ring)
266 (case ring
267 ((expression-ring :expression-ring $expression_ring) *expression-ring*)
268 ((ring-of-integers :ring-of-integers $ring_of_integers) *ring-of-integers*)
269 (otherwise
270 (mtell "~%Warning: Ring ~M not found. Using default.~%" ring))))
271 (t
272 (mtell "~%Ring specification ~A is not recognized. Using default.~%" ring)
273 nil)))
274
275
276;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
277;;
278;; Facilities for evaluating Grobner package expressions
279;; within a prepared environment
280;;
281;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
282
283(defmacro with-monomial-order ((order) &body body)
284 "Evaluate BODY with monomial order set to ORDER."
285 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
286 . ,body))
287
288(defmacro with-coefficient-ring ((ring) &body body)
289 "Evaluate BODY with coefficient ring set to RING."
290 `(let ((*expression-ring* (or (find-ring ,ring) *expression-ring*)))
291 . ,body))
292
293(defmacro with-ring-and-order ((ring order) &body body)
294 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
295 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
296 (*expression-ring* (or (find-ring ,ring) *expression-ring*)))
297 . ,body))
298
299(defmacro with-elimination-orders ((primary secondary elimination-order)
300 &body body)
301 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
302 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
303 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
304 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
305 . ,body))
306
307
308;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
309;;
310;; Maxima-level interface functions
311;;
312;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
313
314;; Auxillary function for removing zero polynomial
315(defun remzero (plist) (remove #'poly-zerop plist))
316
317;;Simple operators
318
319(define-binop $poly_add poly-add
320 "Adds two polynomials P and Q")
321
322(define-binop $poly_subtract poly-sub
323 "Subtracts a polynomial Q from P.")
324
325(define-binop $poly_multiply poly-mul
326 "Returns the product of polynomials P and Q.")
327
328(define-binop $poly_s_polynomial spoly
329 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
330
331(define-unop $poly_primitive_part poly-primitive-part
332 "Returns the polynomial P divided by GCD of its coefficients.")
333
334(define-unop $poly_normalize poly-normalize
335 "Returns the polynomial P divided by the leading coefficient.")
336
337;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
338;;
339;; Macro facility for writing Maxima-level wrappers for
340;; functions operating on internal representation
341;;
342;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
343
344(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
345 &key (polynomials nil)
346 (poly-lists nil)
347 (poly-list-lists nil)
348 (value-type nil))
349 &body body
350 &aux (vars (gensym))
351 (new-vars (gensym)))
352 `(let ((,vars (coerce-maxima-list ,maxima-vars))
353 ,@(when new-vars-supplied-p
354 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
355 (coerce-to-maxima
356 ,value-type
357 (with-coefficient-ring ($poly_coefficient_ring)
358 (with-monomial-order ($poly_monomial_order)
359 (with-elimination-orders ($poly_primary_elimination_order
360 $poly_secondary_elimination_order
361 $poly_elimination_order)
362 (let ,(let ((args nil))
363 (dolist (p polynomials args)
364 (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
365 (dolist (p poly-lists args)
366 (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
367 (dolist (p poly-list-lists args)
368 (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
369 . ,body))))
370 ,(if new-vars-supplied-p
371 `(append ,vars ,new-vars)
372 vars))))
373
374
375;;Functions
376
377(defmfun $poly_expand (p vars)
378 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
379If the representation is not compatible with a polynomial in variables VARS,
380the result is an error."
381 (with-parsed-polynomials ((vars) :polynomials (p)
382 :value-type :polynomial)
383 p))
384
385(defmfun $poly_expt (p n vars)
386 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
387 (poly-expt *expression-ring* p n)))
388
389(defmfun $poly_content (p vars)
390 (with-parsed-polynomials ((vars) :polynomials (p))
391 (poly-content *expression-ring* p)))
392
393(defmfun $poly_pseudo_divide (f fl vars
394 &aux (vars (coerce-maxima-list vars))
395 (f (parse-poly f vars))
396 (fl (parse-poly-list fl vars)))
397 (multiple-value-bind (quot rem c division-count)
398 (poly-pseudo-divide *expression-ring* f fl)
399 `((mlist)
400 ,(coerce-to-maxima :poly-list quot vars)
401 ,(coerce-to-maxima :polynomial rem vars)
402 ,c
403 ,division-count)))
404
405(defmfun $poly_exact_divide (f g vars)
406 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
407 (poly-exact-divide *expression-ring* f g)))
408
409(defmfun $poly_normal_form (f fl vars)
410 (with-parsed-polynomials ((vars) :polynomials (f)
411 :poly-lists (fl)
412 :value-type :polynomial)
413 (normal-form *expression-ring* f (remzero fl) nil)))
414
415(defmfun $poly_buchberger_criterion (g vars)
416 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
417 (buchberger-criterion *expression-ring* g)))
418
419(defmfun $poly_buchberger (fl vars)
420 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
421 (buchberger *expression-ring* (remzero fl) 0 nil)))
422
423(defmfun $poly_reduction (plist vars)
424 (with-parsed-polynomials ((vars) :poly-lists (plist)
425 :value-type :poly-list)
426 (reduction *expression-ring* plist)))
427
428(defmfun $poly_minimization (plist vars)
429 (with-parsed-polynomials ((vars) :poly-lists (plist)
430 :value-type :poly-list)
431 (minimization plist)))
432
433(defmfun $poly_normalize_list (plist vars)
434 (with-parsed-polynomials ((vars) :poly-lists (plist)
435 :value-type :poly-list)
436 (poly-normalize-list *expression-ring* plist)))
437
438(defmfun $poly_grobner (f vars)
439 (with-parsed-polynomials ((vars) :poly-lists (f)
440 :value-type :poly-list)
441 (grobner *expression-ring* (remzero f))))
442
443(defmfun $poly_reduced_grobner (f vars)
444 (with-parsed-polynomials ((vars) :poly-lists (f)
445 :value-type :poly-list)
446 (reduced-grobner *expression-ring* (remzero f))))
447
448(defmfun $poly_depends_p (p var mvars
449 &aux (vars (coerce-maxima-list mvars))
450 (pos (position var vars)))
451 (if (null pos)
452 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
453 (poly-depends-p (parse-poly p vars) pos)))
454
455(defmfun $poly_elimination_ideal (flist k vars)
456 (with-parsed-polynomials ((vars) :poly-lists (flist)
457 :value-type :poly-list)
458 (elimination-ideal *expression-ring* flist k nil 0)))
459
460(defmfun $poly_colon_ideal (f g vars)
461 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
462 (colon-ideal *expression-ring* f g nil)))
463
464(defmfun $poly_ideal_intersection (f g vars)
465 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
466 (ideal-intersection *expression-ring* f g nil)))
467
468(defmfun $poly_lcm (f g vars)
469 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
470 (poly-lcm *expression-ring* f g)))
471
472(defmfun $poly_gcd (f g vars)
473 ($first ($divide (m* f g) ($poly_lcm f g vars))))
474
475(defmfun $poly_grobner_equal (g1 g2 vars)
476 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
477 (grobner-equal *expression-ring* g1 g2)))
478
479(defmfun $poly_grobner_subsetp (g1 g2 vars)
480 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
481 (grobner-subsetp *expression-ring* g1 g2)))
482
483(defmfun $poly_grobner_member (p g vars)
484 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
485 (grobner-member *expression-ring* p g)))
486
487(defmfun $poly_ideal_saturation1 (f p vars)
488 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
489 :value-type :poly-list)
490 (ideal-saturation-1 *expression-ring* f p 0)))
491
492(defmfun $poly_saturation_extension (f plist vars new-vars)
493 (with-parsed-polynomials ((vars new-vars)
494 :poly-lists (f plist)
495 :value-type :poly-list)
496 (saturation-extension *expression-ring* f plist)))
497
498(defmfun $poly_polysaturation_extension (f plist vars new-vars)
499 (with-parsed-polynomials ((vars new-vars)
500 :poly-lists (f plist)
501 :value-type :poly-list)
502 (polysaturation-extension *expression-ring* f plist)))
503
504(defmfun $poly_ideal_polysaturation1 (f plist vars)
505 (with-parsed-polynomials ((vars) :poly-lists (f plist)
506 :value-type :poly-list)
507 (ideal-polysaturation-1 *expression-ring* f plist 0 nil)))
508
509(defmfun $poly_ideal_saturation (f g vars)
510 (with-parsed-polynomials ((vars) :poly-lists (f g)
511 :value-type :poly-list)
512 (ideal-saturation *expression-ring* f g 0 nil)))
513
514(defmfun $poly_ideal_polysaturation (f ideal-list vars)
515 (with-parsed-polynomials ((vars) :poly-lists (f)
516 :poly-list-lists (ideal-list)
517 :value-type :poly-list)
518 (ideal-polysaturation *expression-ring* f ideal-list 0 nil)))
519
520(defmfun $poly_lt (f vars)
521 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
522 (make-poly-from-termlist (list (poly-lt f)))))
523
524(defmfun $poly_lm (f vars)
525 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
526 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *expression-ring*)))))))
527
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