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source: branches/f4grobner/mx-grobner.lisp@ 438

Last change on this file since 438 was 391, checked in by Marek Rychlik, 9 years ago
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Rev	Line
[98]	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
[133]	22	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	23	;;
[268]	24	;; Load this file into Maxima to bootstrap the Grobner package.
[390]	25	;; NOTE: This file does use symbols defined by Maxima, so it
	26	;; will not work when loaded in Common Lisp.
[133]	27	;;
[268]	28	;; DETAILS: This file implements an interface between the Grobner
[374]	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.
[268]	34	;;
[270]	35	;; Also, since the NGROBNER package consists of many Lisp files, it is
[375]	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.
[270]	39	;;
[133]	40	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	41
[98]	42	(in-package :maxima)
	43
	44	(macsyma-module cgb-maxima)
	45
	46	(eval-when
	47	#+gcl (load eval)
	48	#-gcl (:load-toplevel :execute)
	49	(format t "~&Loading maxima-grobner ~a ~a~%"
	50	"$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
	51
	52	;;FUNCTS is loaded because it contains the definition of LCM
	53	($load "functs")
[152]	54
[275]	55	#+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
[274]	56
[229]	57	(use-package :ngrobner)
	58
[98]	59	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	60	;;
	61	;; Maxima expression ring
	62	;;
	63	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	64
[230]	65	(defparameter maxima-ring
	66	(make-ring
[98]	67	;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
	68	:parse #'(lambda (expr)
	69	(when modulus (setf expr ($rat expr)))
	70	expr)
	71	:unit #'(lambda () (if modulus ($rat 1) 1))
	72	:zerop #'(lambda (expr)
	73	;;When is exactly a maxima expression equal to 0?
	74	(cond ((numberp expr)
	75	(= expr 0))
	76	((atom expr) nil)
	77	(t
	78	(case (caar expr)
	79	(mrat (eql ($ratdisrep expr) 0))
	80	(otherwise (eql ($totaldisrep expr) 0))))))
	81	:add #'(lambda (x y) (m+ x y))
	82	:sub #'(lambda (x y) (m- x y))
	83	:uminus #'(lambda (x) (m- x))
	84	:mul #'(lambda (x y) (m* x y))
	85	;;(defun coeff-div (x y) (cadr ($divide x y)))
	86	:div #'(lambda (x y) (m// x y))
	87	:lcm #'(lambda (x y) (meval1 `((\|$LCM\|) ,x ,y)))
	88	:ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
	89	;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
	90	:gcd #'(lambda (x y) ($gcd x y))))
	91
[369]	92	;; Rebind some global variables for Maxima environment
[371]	93	(setf expression-ring maxima-ring ; Coefficient arithmetic done by Maxima
	94	ratdisrep-fun '$ratdisrep ; Coefficients are converted to general form
[370]	95	)
[237]	96
[114]	97	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	98	;;
	99	;; Maxima expression parsing
	100	;;
	101	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	102
	103	(defun equal-test-p (expr1 expr2)
	104	(alike1 expr1 expr2))
	105
	106	(defun coerce-maxima-list (expr)
[391]	107	"Convert a Maxima list to Lisp list."
[114]	108	(cond
	109	((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
	110	(t expr)))
	111
	112	(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
	113
	114	(defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
	115	"Convert a maxima polynomial expression EXPR in variables VARS to internal form."
	116	(labels ((parse (arg) (parse-poly arg vars))
	117	(parse-list (args) (mapcar #'parse args)))
	118	(cond
	119	((eql expr 0) (make-poly-zero))
	120	((member expr vars :test #'equal-test-p)
	121	(let ((pos (position expr vars :test #'equal-test-p)))
[233]	122	(make-variable expression-ring (length vars) pos)))
[114]	123	((free-of-vars expr vars)
	124	;;This means that variable-free CRE and Poisson forms will be converted
	125	;;to coefficients intact
[233]	126	(coerce-coeff expression-ring expr vars))
[114]	127	(t
	128	(case (caar expr)
[233]	129	(mplus (reduce #'(lambda (x y) (poly-add expression-ring x y)) (parse-list (cdr expr))))
	130	(mminus (poly-uminus expression-ring (parse (cadr expr))))
[114]	131	(mtimes
	132	(if (endp (cddr expr)) ;unary
	133	(parse (cdr expr))
[233]	134	(reduce #'(lambda (p q) (poly-mul expression-ring p q)) (parse-list (cdr expr)))))
[114]	135	(mexpt
	136	(cond
	137	((member (cadr expr) vars :test #'equal-test-p)
	138	;;Special handling of (expt var pow)
	139	(let ((pos (position (cadr expr) vars :test #'equal-test-p)))
[233]	140	(make-variable expression-ring (length vars) pos (caddr expr))))
[114]	141	((not (and (integerp (caddr expr)) (plusp (caddr expr))))
	142	;; Negative power means division in coefficient ring
	143	;; Non-integer power means non-polynomial coefficient
	144	(mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
	145	expr)
[233]	146	(coerce-coeff expression-ring expr vars))
	147	(t (poly-expt expression-ring (parse (cadr expr)) (caddr expr)))))
[114]	148	(mrat (parse ($ratdisrep expr)))
	149	(mpois (parse ($outofpois expr)))
	150	(otherwise
[233]	151	(coerce-coeff expression-ring expr vars)))))))
[114]	152
	153	(defun parse-poly-list (expr vars)
	154	(case (caar expr)
	155	(mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
	156	(t (merror "Expression ~M is not a list of polynomials in variables ~M."
	157	expr vars))))
	158	(defun parse-poly-list-list (poly-list-list vars)
	159	(mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
	160
	161
[111]	162	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	163	;;
[241]	164	;; Conversion from internal form to Maxima general form
	165	;;
	166	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	167
	168	(defun maxima-head ()
	169	(if $poly_return_term_list
	170	'(mlist)
	171	'(mplus)))
	172
	173	(defun coerce-to-maxima (poly-type object vars)
	174	(case poly-type
	175	(:polynomial
	176	`(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
	177	(:poly-list
	178	`((mlist) ,@(mapcar #'(lambda (p) (funcall ratdisrep-fun (coerce-to-maxima :polynomial p vars))) object)))
	179	(:term
	180	`((mtimes) ,(funcall ratdisrep-fun (term-coeff object))
	181	,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
	182	vars (monom-exponents (term-monom object)))))
	183	;; Assumes that Lisp and Maxima logicals coincide
	184	(:logical object)
	185	(otherwise
	186	object)))
	187
	188
	189	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	190	;;
[111]	191	;; Unary and binary operation definition facility
	192	;;
	193	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
[98]	194
[111]	195	(defmacro define-unop (maxima-name fun-name
	196	&optional (documentation nil documentation-supplied-p))
	197	"Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
	198	`(defun ,maxima-name (p vars
	199	&aux
	200	(vars (coerce-maxima-list vars))
	201	(p (parse-poly p vars)))
	202	,@(when documentation-supplied-p (list documentation))
[233]	203	(coerce-to-maxima :polynomial (,fun-name expression-ring p) vars)))
[111]	204
	205	(defmacro define-binop (maxima-name fun-name
	206	&optional (documentation nil documentation-supplied-p))
	207	"Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
	208	`(defmfun ,maxima-name (p q vars
	209	&aux
	210	(vars (coerce-maxima-list vars))
	211	(p (parse-poly p vars))
	212	(q (parse-poly q vars)))
	213	,@(when documentation-supplied-p (list documentation))
[233]	214	(coerce-to-maxima :polynomial (,fun-name expression-ring p q) vars)))
[111]	215
	216
[219]	217	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	218	;;
	219	;; Facilities for evaluating Grobner package expressions
	220	;; within a prepared environment
	221	;;
	222	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	223
	224	(defmacro with-monomial-order ((order) &body body)
	225	"Evaluate BODY with monomial order set to ORDER."
	226	`(let ((monomial-order (or (find-order ,order) monomial-order)))
	227	. ,body))
	228
	229	(defmacro with-coefficient-ring ((ring) &body body)
	230	"Evaluate BODY with coefficient ring set to RING."
[233]	231	`(let ((expression-ring (or (find-ring ,ring) expression-ring)))
[219]	232	. ,body))
	233
	234	(defmacro with-elimination-orders ((primary secondary elimination-order)
	235	&body body)
	236	"Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
	237	`(let ((primary-elimination-order (or (find-order ,primary) primary-elimination-order))
	238	(secondary-elimination-order (or (find-order ,secondary) secondary-elimination-order))
	239	(elimination-order (or (find-order ,elimination-order) elimination-order)))
	240	. ,body))
	241
	242
[98]	243	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	244	;;
	245	;; Maxima-level interface functions
	246	;;
	247	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	248
	249	;; Auxillary function for removing zero polynomial
	250	(defun remzero (plist) (remove #'poly-zerop plist))
	251
	252	;;Simple operators
	253
	254	(define-binop $poly_add poly-add
	255	"Adds two polynomials P and Q")
	256
	257	(define-binop $poly_subtract poly-sub
	258	"Subtracts a polynomial Q from P.")
	259
	260	(define-binop $poly_multiply poly-mul
	261	"Returns the product of polynomials P and Q.")
	262
	263	(define-binop $poly_s_polynomial spoly
	264	"Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
	265
	266	(define-unop $poly_primitive_part poly-primitive-part
	267	"Returns the polynomial P divided by GCD of its coefficients.")
	268
	269	(define-unop $poly_normalize poly-normalize
	270	"Returns the polynomial P divided by the leading coefficient.")
	271
[222]	272	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	273	;;
	274	;; Macro facility for writing Maxima-level wrappers for
	275	;; functions operating on internal representation
	276	;;
	277	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	278
	279	(defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
	280	&key (polynomials nil)
	281	(poly-lists nil)
	282	(poly-list-lists nil)
	283	(value-type nil))
	284	&body body
	285	&aux (vars (gensym))
	286	(new-vars (gensym)))
	287	`(let ((,vars (coerce-maxima-list ,maxima-vars))
	288	,@(when new-vars-supplied-p
	289	(list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
	290	(coerce-to-maxima
	291	,value-type
	292	(with-coefficient-ring ($poly_coefficient_ring)
	293	(with-monomial-order ($poly_monomial_order)
	294	(with-elimination-orders ($poly_primary_elimination_order
	295	$poly_secondary_elimination_order
	296	$poly_elimination_order)
	297	(let ,(let ((args nil))
	298	(dolist (p polynomials args)
	299	(setf args (cons `(,p (parse-poly ,p ,vars)) args)))
	300	(dolist (p poly-lists args)
	301	(setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
	302	(dolist (p poly-list-lists args)
	303	(setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
	304	. ,body))))
	305	,(if new-vars-supplied-p
	306	`(append ,vars ,new-vars)
	307	vars))))
	308
	309
[98]	310	;;Functions
	311
	312	(defmfun $poly_expand (p vars)
	313	"This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
	314	If the representation is not compatible with a polynomial in variables VARS,
	315	the result is an error."
	316	(with-parsed-polynomials ((vars) :polynomials (p)
	317	:value-type :polynomial)
	318	p))
	319
	320	(defmfun $poly_expt (p n vars)
	321	(with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
[233]	322	(poly-expt expression-ring p n)))
[98]	323
	324	(defmfun $poly_content (p vars)
	325	(with-parsed-polynomials ((vars) :polynomials (p))
[233]	326	(poly-content expression-ring p)))
[98]	327
	328	(defmfun $poly_pseudo_divide (f fl vars
	329	&aux (vars (coerce-maxima-list vars))
	330	(f (parse-poly f vars))
	331	(fl (parse-poly-list fl vars)))
	332	(multiple-value-bind (quot rem c division-count)
[233]	333	(poly-pseudo-divide expression-ring f fl)
[98]	334	`((mlist)
	335	,(coerce-to-maxima :poly-list quot vars)
	336	,(coerce-to-maxima :polynomial rem vars)
	337	,c
	338	,division-count)))
	339
	340	(defmfun $poly_exact_divide (f g vars)
	341	(with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
[233]	342	(poly-exact-divide expression-ring f g)))
[98]	343
	344	(defmfun $poly_normal_form (f fl vars)
	345	(with-parsed-polynomials ((vars) :polynomials (f)
	346	:poly-lists (fl)
	347	:value-type :polynomial)
[233]	348	(normal-form expression-ring f (remzero fl) nil)))
[98]	349
	350	(defmfun $poly_buchberger_criterion (g vars)
	351	(with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
[233]	352	(buchberger-criterion expression-ring g)))
[98]	353
	354	(defmfun $poly_buchberger (fl vars)
	355	(with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
[233]	356	(buchberger expression-ring (remzero fl) 0 nil)))
[98]	357
	358	(defmfun $poly_reduction (plist vars)
	359	(with-parsed-polynomials ((vars) :poly-lists (plist)
	360	:value-type :poly-list)
[233]	361	(reduction expression-ring plist)))
[98]	362
	363	(defmfun $poly_minimization (plist vars)
	364	(with-parsed-polynomials ((vars) :poly-lists (plist)
	365	:value-type :poly-list)
	366	(minimization plist)))
	367
	368	(defmfun $poly_normalize_list (plist vars)
	369	(with-parsed-polynomials ((vars) :poly-lists (plist)
	370	:value-type :poly-list)
[233]	371	(poly-normalize-list expression-ring plist)))
[98]	372
	373	(defmfun $poly_grobner (f vars)
	374	(with-parsed-polynomials ((vars) :poly-lists (f)
	375	:value-type :poly-list)
[233]	376	(grobner expression-ring (remzero f))))
[98]	377
	378	(defmfun $poly_reduced_grobner (f vars)
	379	(with-parsed-polynomials ((vars) :poly-lists (f)
	380	:value-type :poly-list)
[233]	381	(reduced-grobner expression-ring (remzero f))))
[98]	382
	383	(defmfun $poly_depends_p (p var mvars
	384	&aux (vars (coerce-maxima-list mvars))
	385	(pos (position var vars)))
	386	(if (null pos)
	387	(merror "~%Variable ~M not in the list of variables ~M." var mvars)
	388	(poly-depends-p (parse-poly p vars) pos)))
	389
	390	(defmfun $poly_elimination_ideal (flist k vars)
	391	(with-parsed-polynomials ((vars) :poly-lists (flist)
	392	:value-type :poly-list)
[233]	393	(elimination-ideal expression-ring flist k nil 0)))
[98]	394
	395	(defmfun $poly_colon_ideal (f g vars)
	396	(with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
[233]	397	(colon-ideal expression-ring f g nil)))
[98]	398
	399	(defmfun $poly_ideal_intersection (f g vars)
	400	(with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
[233]	401	(ideal-intersection expression-ring f g nil)))
[98]	402
	403	(defmfun $poly_lcm (f g vars)
	404	(with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
[233]	405	(poly-lcm expression-ring f g)))
[98]	406
	407	(defmfun $poly_gcd (f g vars)
	408	($first ($divide (m* f g) ($poly_lcm f g vars))))
	409
	410	(defmfun $poly_grobner_equal (g1 g2 vars)
	411	(with-parsed-polynomials ((vars) :poly-lists (g1 g2))
[233]	412	(grobner-equal expression-ring g1 g2)))
[98]	413
	414	(defmfun $poly_grobner_subsetp (g1 g2 vars)
	415	(with-parsed-polynomials ((vars) :poly-lists (g1 g2))
[233]	416	(grobner-subsetp expression-ring g1 g2)))
[98]	417
	418	(defmfun $poly_grobner_member (p g vars)
	419	(with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
[233]	420	(grobner-member expression-ring p g)))
[98]	421
	422	(defmfun $poly_ideal_saturation1 (f p vars)
	423	(with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
	424	:value-type :poly-list)
[233]	425	(ideal-saturation-1 expression-ring f p 0)))
[98]	426
	427	(defmfun $poly_saturation_extension (f plist vars new-vars)
	428	(with-parsed-polynomials ((vars new-vars)
	429	:poly-lists (f plist)
	430	:value-type :poly-list)
[233]	431	(saturation-extension expression-ring f plist)))
[98]	432
	433	(defmfun $poly_polysaturation_extension (f plist vars new-vars)
	434	(with-parsed-polynomials ((vars new-vars)
	435	:poly-lists (f plist)
	436	:value-type :poly-list)
[233]	437	(polysaturation-extension expression-ring f plist)))
[98]	438
	439	(defmfun $poly_ideal_polysaturation1 (f plist vars)
	440	(with-parsed-polynomials ((vars) :poly-lists (f plist)
	441	:value-type :poly-list)
[233]	442	(ideal-polysaturation-1 expression-ring f plist 0 nil)))
[98]	443
	444	(defmfun $poly_ideal_saturation (f g vars)
	445	(with-parsed-polynomials ((vars) :poly-lists (f g)
	446	:value-type :poly-list)
[233]	447	(ideal-saturation expression-ring f g 0 nil)))
[98]	448
	449	(defmfun $poly_ideal_polysaturation (f ideal-list vars)
	450	(with-parsed-polynomials ((vars) :poly-lists (f)
	451	:poly-list-lists (ideal-list)
	452	:value-type :poly-list)
[233]	453	(ideal-polysaturation expression-ring f ideal-list 0 nil)))
[98]	454
	455	(defmfun $poly_lt (f vars)
	456	(with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
	457	(make-poly-from-termlist (list (poly-lt f)))))
	458
	459	(defmfun $poly_lm (f vars)
	460	(with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
[233]	461	(make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit expression-ring)))))))
[98]	462

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