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source: branches/f4grobner/mx-grobner.lisp@ 1696

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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 maxima->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 "Convert a Maxima representation of a list of polynomials to the internal form."
228 (case (caar expr)
229 (mlist (mapcar #'(lambda (p)
230 (maxima->poly p vars
231 ring order
232 primary-elimination-order
233 secondary-elimination-order))
234 (cdr expr)))
235 (otherwise (merror "Expression ~M is not a list of polynomials in variables ~M."
236 expr vars))))
237
238(defun maxima->poly-list-list (poly-list-list vars
239 &optional
240 (ring (find-ring-by-name $poly_coefficient_ring))
241 (order (find-order-by-name $poly_monomial_order))
242 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
243 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order)))
244 "Parse a Maxima representation of a list of lists of polynomials."
245 (mapcar #'(lambda (g) (parse-poly-list g vars ring-order primary-elimination-order secondary-elimination-order))
246 (coerce-maxima-list poly-list-list)))
247
248
249
250
251;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
252;;
253;; Conversion from internal form to Maxima general form
254;;
255;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
256
257(defun maxima-head ()
258 (if $poly_return_term_list
259 '(mlist)
260 '(mplus)))
261
262(defun coerce-to-maxima (poly-type object vars)
263 (case poly-type
264 (:polynomial
265 `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
266 (:poly-list
267 `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
268 (:term
269 `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
270 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
271 vars (coerce (term-monom object) 'list))))
272 ;; Assumes that Lisp and Maxima logicals coincide
273 (:logical object)
274 (otherwise
275 object)))
276
277
278;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
279;;
280;; Unary and binary operation definition facility
281;;
282;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
283
284(defmacro define-unop (maxima-name fun-name
285 &optional (documentation nil documentation-supplied-p))
286 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
287 `(defun ,maxima-name (p vars
288 &aux
289 (vars (coerce-maxima-list vars))
290 (p (parse-poly p vars)))
291 ,@(when documentation-supplied-p (list documentation))
292 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
293
294(defmacro define-binop (maxima-name fun-name
295 &optional (documentation nil documentation-supplied-p))
296 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
297 `(defmfun ,maxima-name (p q vars
298 &aux
299 (vars (coerce-maxima-list vars))
300 (p (parse-poly p vars))
301 (q (parse-poly q vars)))
302 ,@(when documentation-supplied-p (list documentation))
303 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
304
305
306;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
307;;
308;; Facilities for evaluating Grobner package expressions
309;; within a prepared environment
310;;
311;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
312
313(defmacro with-monomial-order ((order) &body body)
314 "Evaluate BODY with monomial order set to ORDER."
315 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
316 . ,body))
317
318(defmacro with-coefficient-ring ((ring) &body body)
319 "Evaluate BODY with coefficient ring set to RING."
320 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
321 . ,body))
322
323(defmacro with-ring-and-order ((ring order) &body body)
324 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
325 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
326 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
327 . ,body))
328
329(defmacro with-elimination-orders ((primary secondary elimination-order)
330 &body body)
331 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
332 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
333 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
334 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
335 . ,body))
336
337
338;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
339;;
340;; Maxima-level interface functions
341;;
342;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
343
344;; Auxillary function for removing zero polynomial
345(defun remzero (plist) (remove #'poly-zerop plist))
346
347;;Simple operators
348
349(define-binop $poly_add poly-add
350 "Adds two polynomials P and Q")
351
352(define-binop $poly_subtract poly-sub
353 "Subtracts a polynomial Q from P.")
354
355(define-binop $poly_multiply poly-mul
356 "Returns the product of polynomials P and Q.")
357
358(define-binop $poly_s_polynomial spoly
359 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
360
361(define-unop $poly_primitive_part poly-primitive-part
362 "Returns the polynomial P divided by GCD of its coefficients.")
363
364(define-unop $poly_normalize poly-normalize
365 "Returns the polynomial P divided by the leading coefficient.")
366
367;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
368;;
369;; Macro facility for writing Maxima-level wrappers for
370;; functions operating on internal representation
371;;
372;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
373
374(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
375 &key (polynomials nil)
376 (poly-lists nil)
377 (poly-list-lists nil)
378 (value-type nil))
379 &body body
380 &aux (vars (gensym))
381 (new-vars (gensym)))
382 `(let ((,vars (coerce-maxima-list ,maxima-vars))
383 ,@(when new-vars-supplied-p
384 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
385 (coerce-to-maxima
386 ,value-type
387 (with-coefficient-ring ($poly_coefficient_ring)
388 (with-monomial-order ($poly_monomial_order)
389 (with-elimination-orders ($poly_primary_elimination_order
390 $poly_secondary_elimination_order
391 $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(defmfun $poly_expt (p n vars)
416 (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
417 (poly-expt +maxima-ring+ p n)))
418
419(defmfun $poly_content (p vars)
420 (with-parsed-polynomials ((vars) :polynomials (p))
421 (poly-content +maxima-ring+ p)))
422
423(defmfun $poly_pseudo_divide (f fl vars
424 &aux (vars (coerce-maxima-list vars))
425 (f (parse-poly f vars))
426 (fl (parse-poly-list fl vars)))
427 (multiple-value-bind (quot rem c division-count)
428 (poly-pseudo-divide +maxima-ring+ f fl)
429 `((mlist)
430 ,(coerce-to-maxima :poly-list quot vars)
431 ,(coerce-to-maxima :polynomial rem vars)
432 ,c
433 ,division-count)))
434
435(defmfun $poly_exact_divide (f g vars)
436 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
437 (poly-exact-divide +maxima-ring+ f g)))
438
439(defmfun $poly_normal_form (f fl vars)
440 (with-parsed-polynomials ((vars) :polynomials (f)
441 :poly-lists (fl)
442 :value-type :polynomial)
443 (normal-form +maxima-ring+ f (remzero fl) nil)))
444
445(defmfun $poly_buchberger_criterion (g vars)
446 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
447 (buchberger-criterion +maxima-ring+ g)))
448
449(defmfun $poly_buchberger (fl vars)
450 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
451 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
452
453(defmfun $poly_reduction (plist vars)
454 (with-parsed-polynomials ((vars) :poly-lists (plist)
455 :value-type :poly-list)
456 (reduction +maxima-ring+ plist)))
457
458(defmfun $poly_minimization (plist vars)
459 (with-parsed-polynomials ((vars) :poly-lists (plist)
460 :value-type :poly-list)
461 (minimization plist)))
462
463(defmfun $poly_normalize_list (plist vars)
464 (with-parsed-polynomials ((vars) :poly-lists (plist)
465 :value-type :poly-list)
466 (poly-normalize-list +maxima-ring+ plist)))
467
468(defmfun $poly_grobner (f vars)
469 (with-parsed-polynomials ((vars) :poly-lists (f)
470 :value-type :poly-list)
471 (grobner +maxima-ring+ (remzero f))))
472
473(defmfun $poly_reduced_grobner (f vars)
474 (with-parsed-polynomials ((vars) :poly-lists (f)
475 :value-type :poly-list)
476 (reduced-grobner +maxima-ring+ (remzero f))))
477
478(defmfun $poly_depends_p (p var mvars
479 &aux (vars (coerce-maxima-list mvars))
480 (pos (position var vars)))
481 (if (null pos)
482 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
483 (poly-depends-p (parse-poly p vars) pos)))
484
485(defmfun $poly_elimination_ideal (flist k vars)
486 (with-parsed-polynomials ((vars) :poly-lists (flist)
487 :value-type :poly-list)
488 (elimination-ideal +maxima-ring+ flist k nil 0)))
489
490(defmfun $poly_colon_ideal (f g vars)
491 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
492 (colon-ideal +maxima-ring+ f g nil)))
493
494(defmfun $poly_ideal_intersection (f g vars)
495 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
496 (ideal-intersection +maxima-ring+ f g nil)))
497
498(defmfun $poly_lcm (f g vars)
499 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
500 (poly-lcm +maxima-ring+ f g)))
501
502(defmfun $poly_gcd (f g vars)
503 ($first ($divide (m* f g) ($poly_lcm f g vars))))
504
505(defmfun $poly_grobner_equal (g1 g2 vars)
506 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
507 (grobner-equal +maxima-ring+ g1 g2)))
508
509(defmfun $poly_grobner_subsetp (g1 g2 vars)
510 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
511 (grobner-subsetp +maxima-ring+ g1 g2)))
512
513(defmfun $poly_grobner_member (p g vars)
514 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
515 (grobner-member +maxima-ring+ p g)))
516
517(defmfun $poly_ideal_saturation1 (f p vars)
518 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
519 :value-type :poly-list)
520 (ideal-saturation-1 +maxima-ring+ f p 0)))
521
522(defmfun $poly_saturation_extension (f plist vars new-vars)
523 (with-parsed-polynomials ((vars new-vars)
524 :poly-lists (f plist)
525 :value-type :poly-list)
526 (saturation-extension +maxima-ring+ f plist)))
527
528(defmfun $poly_polysaturation_extension (f plist vars new-vars)
529 (with-parsed-polynomials ((vars new-vars)
530 :poly-lists (f plist)
531 :value-type :poly-list)
532 (polysaturation-extension +maxima-ring+ f plist)))
533
534(defmfun $poly_ideal_polysaturation1 (f plist vars)
535 (with-parsed-polynomials ((vars) :poly-lists (f plist)
536 :value-type :poly-list)
537 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
538
539(defmfun $poly_ideal_saturation (f g vars)
540 (with-parsed-polynomials ((vars) :poly-lists (f g)
541 :value-type :poly-list)
542 (ideal-saturation +maxima-ring+ f g 0 nil)))
543
544(defmfun $poly_ideal_polysaturation (f ideal-list vars)
545 (with-parsed-polynomials ((vars) :poly-lists (f)
546 :poly-list-lists (ideal-list)
547 :value-type :poly-list)
548 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
549
550(defmfun $poly_lt (f vars)
551 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
552 (make-poly-from-termlist (list (poly-lt f)))))
553
554(defmfun $poly_lm (f vars)
555 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
556 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
557
558|#
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