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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 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
166 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order))
167 &aux
168 (ring-and-order (make-ring-and-order
169 :ring ring
170 :order order
171 :primary-elimination-order primary-elimination-order
172 :secondary-elimination-order secondary-elimination-order)))
173 "Build RING-AND-ORDER structure. The defaults are determined by various Maxima-level switches,
174which are names of ring and orders."
175 ring-and-order)
176
177(defun maxima->poly (expr vars
178 &optional
179 (ring-and-order (find-ring-and-order-by-name))
180 &aux
181 (vars (coerce-maxima-list vars))
182 (ring (ro-ring ring-and-order)))
183 "Convert a maxima polynomial expression EXPR in variables VARS to
184internal form. This works by first converting the expression to Lisp,
185and then evaluating the expression using polynomial arithmetic
186implemented by the POLYNOMIAL package."
187 (labels ((parse (arg) (maxima->poly arg vars ring-and-order))
188 (parse-list (args) (mapcar #'parse args)))
189 (cond
190 ((eql expr 0) (make-poly-zero))
191 ((member expr vars :test #'equal-test-p)
192 (let ((pos (position expr vars :test #'equal-test-p)))
193 (make-poly-variable ring (length vars) pos)))
194 ((free-of-vars expr vars)
195 ;;This means that variable-free CRE and Poisson forms will be converted
196 ;;to coefficients intact
197 (coerce-coeff ring expr vars))
198 (t
199 (case (caar expr)
200 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
201 (mminus (poly-uminus ring (parse (cadr expr))))
202 (mtimes
203 (if (endp (cddr expr)) ;unary
204 (parse (cdr expr))
205 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
206 (mexpt
207 (cond
208 ((member (cadr expr) vars :test #'equal-test-p)
209 ;;Special handling of (expt var pow)
210 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
211 (make-poly-variable ring (length vars) pos (caddr expr))))
212 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
213 ;; Negative power means division in coefficient ring
214 ;; Non-integer power means non-polynomial coefficient
215 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
216 expr)
217 (coerce-coeff ring expr vars))
218 (t (poly-expt ring (parse (cadr expr)) (caddr expr)))))
219 (mrat (parse ($ratdisrep expr)))
220 (mpois (parse ($outofpois expr)))
221 (otherwise
222 (coerce-coeff ring expr vars)))))))
223
224(defun maxima->poly-list (expr vars
225 &optional
226 (ring-and-order (find-ring-and-order-by-name)))
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 ring-and-order))
231 (cdr expr)))
232 (otherwise (merror "Expression ~M is not a list of polynomials in variables ~M."
233 expr vars))))
234
235(defun maxima->poly-list-of-lists (poly-list-of-lists vars
236 &optional
237 (ring-and-order (find-ring-and-order-by-name)))
238 "Parse a Maxima representation of a list of lists of polynomials."
239 (mapcar #'(lambda (g) (maxima->poly-list g vars ring-and-order))
240 (coerce-maxima-list poly-list-of-lists)))
241
242
243
244;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
245;;
246;; Conversion from internal form to Maxima general form
247;;
248;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
249
250(defun maxima-head ()
251 (if $poly_return_term_list
252 '(mlist)
253 '(mplus)))
254
255(defun poly->maxima (poly-type object vars)
256 (case poly-type
257 (:custom object) ;Bypass processing
258 (:polynomial
259 `(,(maxima-head) ,@(mapcar #'(lambda (term) (poly->maxima :term term vars)) (poly-termlist object))))
260 (:poly-list
261 `((mlist) ,@(mapcar #'(lambda (p) ($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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
301;;
302;; Facilities for evaluating Grobner package expressions
303;; within a prepared environment
304;;
305;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
306
307#|
308(defmacro with-monomial-order ((order) &body body)
309 "Evaluate BODY with monomial order set to ORDER."
310 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
311 . ,body))
312
313(defmacro with-coefficient-ring ((ring) &body body)
314 "Evaluate BODY with coefficient ring set to RING."
315 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
316 . ,body))
317
318(defmacro with-ring-and-order ((ring order) &body body)
319 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
320 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
321 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
322 . ,body))
323
324(defmacro with-elimination-orders ((primary secondary elimination-order)
325 &body body)
326 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
327 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
328 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
329 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
330 . ,body))
331
332|#
333
334
335;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
336;;
337;; Maxima-level interface functions
338;;
339;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
340
341;; Auxillary function for removing zero polynomial
342(defun remzero (plist) (remove #'poly-zerop plist))
343
344;;Simple operators
345
346#|
347(define-binop $poly_add poly-add
348 "Adds two polynomials P and Q")
349
350(define-binop $poly_subtract poly-sub
351 "Subtracts a polynomial Q from P.")
352
353(define-binop $poly_multiply poly-mul
354 "Returns the product of polynomials P and Q.")
355
356(define-binop $poly_s_polynomial spoly
357 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
358
359(define-unop $poly_primitive_part poly-primitive-part
360 "Returns the polynomial P divided by GCD of its coefficients.")
361
362(define-unop $poly_normalize poly-normalize
363 "Returns the polynomial P divided by the leading coefficient.")
364|#
365
366;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
367;;
368;; Macro facility for writing Maxima-level wrappers for
369;; functions operating on internal representation
370;;
371;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
372
373(defmacro with-ring-and-order (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
374 &key
375 (polynomials nil)
376 (poly-lists nil)
377 (poly-list-lists nil)
378 (value-type nil)
379 (ring-and-order-var 'ring-and-order))
380 &body
381 body
382 &aux
383 (vars (gensym))
384 (new-vars (gensym)))
385 "Evaluate a polynomial expression BODY in an environment
386constructred from Maxima switches. The supplied arguments
387POLYNOMIALS, POLY-LISTS and POLY-LIST-LISTS should be polynomials,
388polynomial lists an lists of lists of polynomials, in Maxima general
389form. These are translated to NGROBNER package internal form and
390evaluated using operations in the NGROBNER package. The BODY should be
391defined in terms of those operations. MAXIMA-VARS is set to the list
392of variable names used at the Maxima level. The evaluation is
393performed by the NGROBNER package which ignores variable names, thus
394MAXIMA-VARS is used only to translate the polynomial expression to
395NGROBNER internal form. After evaluation, the value of BODY is
396translated back to the Maxima general form. When MAXIMA-NEW-VARS is
397present, it is appended to MAXIMA-VARS upon translation from the
398internal form back to Maxima general form, thus allowing extra
399variables which may have been created by the evaluation process. The
400value type can be either :POLYNOMIAL, :POLY-LIST or :TERM, depending
401on the form of the result returned by the top NGROBNER operation."
402 `(let ((,vars (coerce-maxima-list ,maxima-vars))
403 ,@(when new-vars-supplied-p
404 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
405 (poly->maxima
406 ,value-type
407 (let ((,ring-and-order-var ,(find-ring-and-order-by-name)))
408 (let ,(let ((args nil))
409 (dolist (p polynomials args)
410 (setf args (cons `(,p (maxima->poly ,p ,vars ,ring-and-order-var)) args)))
411 (dolist (p poly-lists args)
412 (setf args (cons `(,p (maxima->poly-list ,p ,vars ,ring-and-order-var)) args)))
413 (dolist (p poly-list-lists args)
414 (setf args (cons `(,p (maxima->poly-list-list ,p ,vars ,ring-and-order-var)) args))))
415 . ,body))
416 ,(if new-vars-supplied-p
417 `(append ,vars ,new-vars)
418 vars))))
419
420
421;;Functions
422
423(defmfun $poly_expand (p vars)
424 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
425If the representation is not compatible with a polynomial in variables VARS,
426the result is an error."
427 (with-ring-and-order ((vars) :polynomials (p) :value-type :polynomial) p))
428
429
430(defmfun $poly_expt (p n vars)
431 (with-ring-and-order ((vars) :polynomials (p) :value-type :polynomial)
432 (poly-expt ring-and-order p n)))
433
434(defmfun $poly_content (p vars)
435 (with-ring-and-order ((vars) :polynomials (p))
436 (poly-content ring-and-order p)))
437
438#|
439(defmfun $poly_pseudo_divide (f fl vars)
440 (with-ring-and-order ((vars)
441 :polynomials (f)
442 :poly-lists (fl)
443 :value-type :custom)
444 (multiple-value-bind (quot rem c division-count)
445 (poly-pseudo-divide ring-and-order f fl)
446 `((mlist)
447 ,(poly->maxima :poly-list quot vars)
448 ,(poly->maxima :polynomial rem vars)
449 ,c
450 ,division-count))))
451|#
452
453
454(defmfun $poly_exact_divide (f g vars)
455 (with-ring-and-order ((vars) :polynomials (f g) :value-type :polynomial)
456 (poly-exact-divide ring-and-order f g)))
457
458(defmfun $poly_normal_form (f fl vars)
459 (with-ring-and-order ((vars) :polynomials (f)
460 :poly-lists (fl)
461 :value-type :polynomial)
462 (normal-form ring-and-order f (remzero fl) nil)))
463
464(defmfun $poly_buchberger_criterion (g vars)
465 (with-ring-and-order ((vars) :poly-lists (g) :value-type :logical)
466 (buchberger-criterion ring-and-order g)))
467
468(defmfun $poly_buchberger (fl vars)
469 (with-ring-and-order ((vars) :poly-lists (fl) :value-type :poly-list)
470 (buchberger ring-and-order (remzero fl) 0 nil)))
471
472(defmfun $poly_reduction (plist vars)
473 (with-ring-and-order ((vars) :poly-lists (plist)
474 :value-type :poly-list)
475 (reduction ring-and-order plist)))
476
477(defmfun $poly_minimization (plist vars)
478 (with-ring-and-order ((vars) :poly-lists (plist)
479 :value-type :poly-list)
480 (minimization plist)))
481
482(defmfun $poly_normalize_list (plist vars)
483 (with-ring-and-order ((vars) :poly-lists (plist)
484 :value-type :poly-list)
485 (poly-normalize-list ring-and-order plist)))
486
487(defmfun $poly_grobner (f vars)
488 (with-ring-and-order ((vars) :poly-lists (f)
489 :value-type :poly-list)
490 (grobner ring-and-order (remzero f))))
491
492(defmfun $poly_reduced_grobner (f vars)
493 (with-ring-and-order ((vars) :poly-lists (f)
494 :value-type :poly-list)
495 (reduced-grobner ring-and-order (remzero f))))
496
497(defmfun $poly_depends_p (p var mvars
498 &aux (vars (coerce-maxima-list mvars))
499 (pos (position var vars)))
500 (if (null pos)
501 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
502 (poly-depends-p (parse-poly p vars) pos)))
503
504(defmfun $poly_elimination_ideal (flist k vars)
505 (with-ring-and-order ((vars) :poly-lists (flist)
506 :value-type :poly-list)
507 (elimination-ideal ring-and-order flist k nil 0)))
508
509(defmfun $poly_colon_ideal (f g vars)
510 (with-ring-and-order ((vars) :poly-lists (f g) :value-type :poly-list)
511 (colon-ideal ring-and-order f g nil)))
512
513(defmfun $poly_ideal_intersection (f g vars)
514 (with-ring-and-order ((vars) :poly-lists (f g) :value-type :poly-list)
515 (ideal-intersection ring-and-order f g nil)))
516
517(defmfun $poly_lcm (f g vars)
518 (with-ring-and-order ((vars) :polynomials (f g) :value-type :polynomial)
519 (poly-lcm ring-and-order f g)))
520
521(defmfun $poly_gcd (f g vars)
522 ($first ($divide (m* f g) ($poly_lcm f g vars))))
523
524(defmfun $poly_grobner_equal (g1 g2 vars)
525 (with-ring-and-order ((vars) :poly-lists (g1 g2))
526 (grobner-equal ring-and-order g1 g2)))
527
528(defmfun $poly_grobner_subsetp (g1 g2 vars)
529 (with-ring-and-order ((vars) :poly-lists (g1 g2))
530 (grobner-subsetp ring-and-order g1 g2)))
531
532(defmfun $poly_grobner_member (p g vars)
533 (with-ring-and-order ((vars) :polynomials (p) :poly-lists (g))
534 (grobner-member ring-and-order p g)))
535
536(defmfun $poly_ideal_saturation1 (f p vars)
537 (with-ring-and-order ((vars) :poly-lists (f) :polynomials (p)
538 :value-type :poly-list)
539 (ideal-saturation-1 ring-and-order f p 0)))
540
541(defmfun $poly_saturation_extension (f plist vars new-vars)
542 (with-ring-and-order ((vars new-vars)
543 :poly-lists (f plist)
544 :value-type :poly-list)
545 (saturation-extension ring-and-order f plist)))
546
547(defmfun $poly_polysaturation_extension (f plist vars new-vars)
548 (with-ring-and-order ((vars new-vars)
549 :poly-lists (f plist)
550 :value-type :poly-list)
551 (polysaturation-extension ring-and-order f plist)))
552
553(defmfun $poly_ideal_polysaturation1 (f plist vars)
554 (with-ring-and-order ((vars) :poly-lists (f plist)
555 :value-type :poly-list)
556 (ideal-polysaturation-1 ring-and-order f plist 0 nil)))
557
558(defmfun $poly_ideal_saturation (f g vars)
559 (with-ring-and-order ((vars) :poly-lists (f g)
560 :value-type :poly-list)
561 (ideal-saturation ring-and-order f g 0 nil)))
562
563(defmfun $poly_ideal_polysaturation (f ideal-list vars)
564 (with-ring-and-order ((vars) :poly-lists (f)
565 :poly-list-lists (ideal-list)
566 :value-type :poly-list)
567 (ideal-polysaturation ring-and-order f ideal-list 0 nil)))
568
569(defmfun $poly_lt (f vars)
570 (with-ring-and-order ((vars) :polynomials (f) :value-type :polynomial)
571 (make-poly-from-termlist (list (poly-lt f)))))
572
573(defmfun $poly_lm (f vars)
574 (with-ring-and-order ((vars) :polynomials (f) :value-type :polynomial)
575 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit ring-and-order)))))))
576
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