Annotation of OpenXM/src/kan96xx/Doc/oxasir.sm1, Revision 1.12
1.12 ! takayama 1: % $OpenXM: OpenXM/src/kan96xx/Doc/oxasir.sm1,v 1.11 2002/11/09 01:24:08 takayama Exp $
1.1 maekawa 2: %% kxx/oxasir.sm1 1998, 2/12 (this version is at Old/oxasir.sm1.19980212
3: %% 3/1, 1995, 11/5, 11/21
4: %% This file is error clean.
5: %%%%%%% How to install.
6: %%% Set ASIR_LIBDIR if necessary. Ex. /u/nobuki/lib/asir
1.7 takayama 7: %%% write ~/.asirrc : load("gr")$ load("primdec")$ load("bfct")$ end$
8: %%% or it is written in OpenXM/rc/asirrc in OpenXM env, it's fine.
1.1 maekawa 9: %%% oxasir.asir must be in
10: %%% LOAD_SM1_PATH or oxasirpath.asirlib
11: %%% Edit below
12: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13: %%% /usr/local/lib/sm1, SM1_LOAD_PATH, /usr/local/lib/asir, ASIR_LOAD_PATH
14: /oxasirpath.oxasir (ox_asir) def %% loadmethod is 1
15: /oxasirpath.asirlib (oxasir.asir) def
16:
17: /ox_asirConnectMethod { asirconnectr /oxasir.ccc set } def
18: %/ox_asirConnectMethod { asirconnect2 } def
19:
20: %% Old path
21: %/oxasirpath.oxasir (/home/nobuki/kxx/ox_asir) def %% loadmethod is 1
22: %/oxasirpath.asirlib (/home/nobuki/kxx/oxasir.asir) def
23: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
24: /oxasir.loadmethod 1 def %% "..." oxsendcmo (load) ox...
25: %/oxasir.loadmethod 0 def %% load("..."); %% at MSRI
26: %%%%%%%%%%%%%%%% end of configuration.
27: /initializePathNamesForOxAsir {
28: [oxasirpath.oxasir] getPathNameAsir /oxasirpath.oxasir set
29: [oxasirpath.asirlib] getPathNameSm1 /oxasirpath.asirlib set
30: } def
31:
32:
33: /oxasir.verbose 0 def
34: /oxasir.version (2.981105) def
35: oxasir.version [(Version)] system_variable gt
36: { [(This package requires the latest version of kan/sm1) nl
37: (Please get it from http://www.math.kobe-u.ac.jp/KAN) ] cat
38: error
39: } { } ifelse
40: (oxasir.sm1, --- open asir protocol module 3/1 1998, 6/5 1999) message-quiet
41: ( asirconnect, asir, fctr, primadec, (C) M.Noro, N.Takayama ) message-quiet
42:
43: /oxasir.ccc load isArray
44: { }
45: { /oxasir.ccc [ ] def } ifelse
46:
47: [(parse) (ox.sm1) pushfile] extension pop
48: oxasir.verbose {
49: (type in asirconnect to connect, asir is used to execute asir command. )
50: message
51: (type in asirconnect2 to open a new window for ox_asir, connect, asir is used to execute asir command [you need to edit asirconnect2 to tell the path to load ox_asir] )
52: message
53: } { } ifelse
54:
55: /loadAsirFile {
56: /arg1 set
57: [/in-loadAsirFile /peer /fname] pushVariables
58: [
59: /peer arg1 0 get def
60: /fname arg1 1 get def
61: oxasir.loadmethod {
62: peer fname oxsendcmo peer 1 oxsendcmo
63: peer (load) oxexec
64: }{
65: peer [$load("$ fname $");$] cat oxsubmit
66: }ifelse
67: ] pop
68: popVariables
69: } def
70: [(loadAsirFile)
71: [$[client fname] loadAsirFile (ox_asir function)$
72: $Load a file into the client$
73: ]] putUsages
74:
75: /asirinit {
76: %% gr and primdec are loaded by .asirrc
77: /asirinit.peer set
1.4 takayama 78: [(ostype)] extension 0 get (windows) eq {
1.6 takayama 79: [(getenv) (OSTYPE)] extension tag 0 eq {
80: [asirinit.peer (oxasir-win.rr)] oxasirParseFile
81: }{
1.5 takayama 82: [(getenv) (OSTYPE)] extension (cygwin) eq {
83: [asirinit.peer oxasirpath.asirlib] loadAsirFile
84: }{
85: [asirinit.peer (oxasir-win.rr)] oxasirParseFile
86: } ifelse
1.6 takayama 87: } ifelse
1.4 takayama 88: }{
89: [asirinit.peer oxasirpath.asirlib] loadAsirFile
1.11 takayama 90: } ifelse
91: asirinit.peer oxmathcap
92: asirinit.peer oxsetmathcap
1.12 ! takayama 93: (Ox103_loaded) boundp
! 94: {
! 95: asirinit.peer ox103_asir_init
! 96: }{ } ifelse
1.1 maekawa 97: } def
98: /asirconnect {
99: [(localhost) 1300 1200] oxconnect /oxasir.ccc set
100: /ccc oxasir.ccc def %% for compatibility.
101: oxasir.ccc asirinit
102: } def
103: /asirconnect2 {
104: [oxpath.oxlog.xterm oxpath.ox ( -ox ) oxasirpath.oxasir
105: oxpath.null
1.2 takayama 106: ( & )] cat system-csh
107: % (xterm -e /home/nobuki/kxx/ox -ox /home/nobuki/kxx/ox_asir &) system-csh
108: % (kterm -iconic -e /home/nobuki/kxx/ox -ox /home/nobuki/kxx/ox_asir &) system-csh
1.1 maekawa 109: % For MSRI
110: % Eterm is also nice (including kanji). rxvt is also nice.
1.2 takayama 111: %(xterm -icon -e /u/nobuki/tmp/kxx/ox -ox /u/nobuki/tmp/Ox/ox_asir2 &) system-csh
112: %(kterm2 -e /u/nobuki/tmp/kxx/ox -ox /u/nobuki/tmp/Ox/ox_asir2 &) system-csh
1.1 maekawa 113: % (If you start the server automatically, you may have a trouble to) message
114: % (oxreset. In order to avoid this trouble, start the server by hand.) message
1.2 takayama 115: (sleep 5) system-csh
1.1 maekawa 116: [(localhost) 1300 1200] oxconnect /oxasir.ccc set
117: /ccc oxasir.ccc def %% for compatibility.
118: oxasir.ccc asirinit
119: } def
120:
121: [(asirconnect2)
122: [(asirconnect2 starts ox_asir server. (ox_asir function))
123: (Open xxx protocol is used for the communication between sm1 and ox_asir.)
124: (cf. oxhelp, asir.)
125: (You need to install ox_asir server to use this function. cf. oxasir)
126: ]] putUsages
127:
128: /asirconnect3 {
129: [oxpath.oxlog.xterm oxpath.ox ( -ox ) oxasirpath.oxasir
130: ( -data 2300 -control 2200) oxpath.null
1.2 takayama 131: ( & )] cat system-csh
1.1 maekawa 132: % (If you start the server automatically, you may have a trouble to) message
133: % (oxreset. In order to avoid this trouble, start the server by hand.) message
1.2 takayama 134: (sleep 5) system-csh
1.1 maekawa 135: [(localhost) 2300 2200] oxconnect /oxasir.ccc2 set
136: /ccc2 oxasir.ccc2 def %% for compatibility.
137: oxasir.ccc2 asirinit
138: (The client is stored in oxasir.ccc2.) message
139: } def
140:
141: [(asir)
142: [(pid [asir-command, asir-arg1, asir-arg2, ...] asir result (ox_asir function))
143: (Call open asir server. You need to install ox_asir on your system)
144: (to use this function. cf. primadec, fctr, asirconnect2, asirconnectr.)
145: (If you interrupted the computation by typing ctrl-C, type in )
146: ( oxasir.ccc oxreset ; )
147: (to interrupt the ox_asir server.)
148: (Example: oxasir.ccc [(fctr) (x^10-1).] asir )
149: ( )
150: (This function requires plugins cmo, socket and ox_asir server. cf. oxasir)
151: (See, ftp://endeavor.fujitsu.co.jp/pub/isis/asir on asir)
152: ]
153: ] putUsages
154:
155: /asir {
156: /arg2 set
157: /arg1 set
158: [/pid /asir-comm /comm /n /i /rr] pushVariables
159: [(CurrentRingp)] pushEnv
160: [
161: /pid arg1 def
162: /asir-comm arg2 def
163: pid tag 6 eq { } { (Invalid pid. See asir.) error } ifelse
164: pid 0 get (client) eq { } { (Invalid pid. See asir.) error } ifelse
165: asir-comm tag 6 eq { } { (Invalid argument asir-comm. See asir) error } ifelse
166:
167: [ %% Change the current ring if necessary to send a correct OxVlist.
168: asir-comm oxasir.changeRing
169: ] pop
170: %%% Setting OxVlist to tell asir a way to change dist-poly <==> poly.
171: (OxVlist=) getVlist2 toString (;) 3 cat_n /comm set
172: %% comm message
173: pid comm oxsubmit
174: pid (print(OxVlist);) oxsubmit
175:
176:
177: /n asir-comm length def
178: n 1 sub -1 1 {
179: /i set
180: pid asir-comm i get oxsendcmo
181: pid 1 oxsendcmo pid (ox_dtop) oxexec
182: } for
183: pid n 1 sub oxsendcmo
184: pid asir-comm 0 get oxexec
185:
186: pid 1 oxsendcmo pid (ox_ptod) oxexec
187: pid oxpopcmo /arg1 set
188:
189:
190: ] pop
191: popEnv
192: popVariables
193: arg1
194: } def
195:
196: /oxasir.changeRing {
197: /arg1 set
198: [/in-oxasir.changeRing /f /rr] pushVariables
199: [
200: /f arg1 def
201: f isArray {
202: f {oxasir.changeRing} map
203: }{
204: f isPolynomial {
205: f (0). eq { }
206: { f (ring) dc /rr set [(CurrentRingp) rr] system_variable } ifelse
207: } { } ifelse
208: } ifelse
209: ] pop
210: popVariables
211: } def
212:
213: /fctr {
214: /arg1 set
215: [/f /comm /vv] pushVariables
216: [(CurrentRingp)] pushEnv
217: [
218: /f arg1 def
219: oxasir.ccc [ ] eq {
220: (Starting ox_asir server.) message
221: ox_asirConnectMethod
222: } { } ifelse
223:
224: f isPolynomial not {
225: /vv f 1 get def
226: vv isArray { /vv vv from_records def } { } ifelse
227: /f f 0 get def
228: [vv ring_of_polynomials 0] define_ring
229: f . /f set
230: }{ } ifelse
231: oxasir.ccc [(fctr) f] asir /arg1 set
232: ] pop
233: popEnv
234: popVariables
235: arg1
236: } def
237:
238: [(fctr)
239: [(You need to install ox_asir server to use this function. (ox_asir function))
240: (f fctr g)
241: (poly f; array g;)
242: ([f v] fctr g ; string f, string or array of string v)
243: (This function factors the polynomial f over Q.)
244: ( )
245: (Example 1: [(x^10-y^10) (x,y)] fctr ::)
246: (Example 2: (x^10-1). fctr ::)
247: ( )
248: (If you interrupted the computation by typing ctrl-C, type in )
249: ( oxasir.ccc oxreset ; )
250: (to interrupt the ox_asir server.)
251: ( )
252: (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)
253: ]] putUsages
254:
255:
256: [(primadec)
257: [(You need to install ox_asir server to use this function. (ox_asir function))
258: ([ ii ] primadec [[q1 p1] [q2 p2] ... ] )
259: ( array of poly ii; array of poly q1, p1, q2, p2 ...;)
260: ( q1, q2, ... are primary components of the primary ideal decomposition)
261: ( of the ideal generated by << ii >>.)
262: ( )
263: ([ ii v ] primadec [[q1 p1] [q2 p2] ... ] )
264: ( array of poly or string ii; array of string v; array of poly q1, p1, q2, p2 ...;)
265: (<< v >> is an array of independent variables.)
266: ( )
267: ([ ii v ] primadec [[q1 p1] [q2 p2] ... ] )
268: ( array of poly or string ii; array of string v; array of poly q1, p1, q2, p2 ...;)
269: ( v is a string of variables separated by , )
270: ( )
271: (Example: [(x,y) ring_of_polynomials 0] define_ring)
272: ( [ [(x^2-1). (x y).] ] primadec pmat ;)
273: ( )
274: (Example: [ [(x^2-1) (x y)] [(x) (y)]] primadec pmat ;)
275: ( )
276: (If you interrupted the computation by typing ctrl-C, type in )
277: ( oxasir.ccc oxreset ; )
278: (to interrupt the ox_asir server.)
279: ( )
280: (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)
281: ]] putUsages
282:
283: /primadec {
284: /arg1 set
285: [/in-primadec /aa /f /comm /vvv /r /setarg] pushVariables
286: [(CurrentRingp)] pushEnv
287: [
288: /aa arg1 def
289: aa isArray { } { (<<array>> primadec) error } ifelse
290: /setarg 0 def
291: oxasir.ccc [ ] eq {
292: (Starting ox_asir server.) message
293: ox_asirConnectMethod
294: } { } ifelse
295: aa { tag } map /typev set
296: typev [ ArrayP ] eq
297: { /f aa 0 get def
298: f 0 get (ring) dc /r set
299: [(CurrentRingp) r] system_variable
300: /vvv getVariableNames def
301: /setarg 1 def
302: } { } ifelse
303: typev [ArrayP StringP] eq
304: { /f aa 0 get def
305: /vvv [ aa 1 get to_records pop ] def
306: /setarg 1 def
307: } { } ifelse
308: typev [ArrayP ArrayP] eq
309: { /f aa 0 get def
310: /vvv aa 1 get {toString} map def
311: /setarg 1 def
312: } { } ifelse
313: setarg { } { (primadec : Argument mismatch) error } ifelse
314:
315: f 0 get isPolynomial {
316: /r f 0 get (ring) dc def
317: /vvv vvv { r ,, } map def
318: }
319: {
320: [vvv from_records ring_of_polynomials 0] define_ring
321: f { toString . } map /f set
322: vvv { . } map /vvv set
323: } ifelse
324: oxasir.ccc [(primadec) f vvv] asir /arg1 set
325: ] pop
326: popEnv
327: popVariables
328: arg1
329: } def
330:
331:
332: /getVlist2 {
333: [/n /i ] pushVariables
334: [
335: /n [(N)] system_variable def
336: [
337: 0 1 n 1 sub { /i set (x) i (dollar) dc 2 cat_n } for
338: 0 1 n 1 sub { /i set (d) i (dollar) dc 2 cat_n } for
339: ] /arg1 set
340: ] pop
341: popVariables
342: arg1
343: } def
344:
345: %%%%%%%%%%%%%%%%%%%
346: /getVlist {
347: [/n /i ] pushVariables
348: [
349: /n [(N)] system_variable def
350: [
351: 0 1 n 1 sub { /i set [(x) (var) i] system_variable } for
352: 0 1 n 1 sub { /i set [(D) (var) i] system_variable } for
353: ] /arg1 set
354: ] pop
355: popVariables
356: arg1
357: } def
358:
359: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
360: [(chattr) 0 /findIntegralRoots] extension pop
361: oxasir.verbose {
362: (Overloaded on findIntegralRoots.) message
363: } { } ifelse
364: /findIntegralRoots {
365: /arg1 set
366: [/in-findIntegralRoots /pp ] pushVariables
367: [
368: /pp arg1 def
369: oxasir.ccc [ ] eq {
370: (Starting ox_asir server.) message
371: ox_asirConnectMethod
372: } { } ifelse
373: oxasir.ccc oxIsServerReady
374: { pp findIntegralRoots.oxasir /arg1 set}
375: { pp findIntegralRoots.slow /arg1 set} ifelse
376: ] pop
377: popVariables
378: arg1
379: } def
380:
381: /findIntegralRoots.oxasir {
382: /arg1 set
383: [/in-findIntegralRoots /f /r /g /aa /rlist] pushVariables
384: [(CurrentRingp) (KanGBmessage)] pushEnv
385: [
386: /f arg1 def
387: [(s) ring_of_polynomials 0] define_ring
388: f toString . /f set
389: f fctr rest /g set
390: g {
391: 0 get /aa set
392: aa (s). degree 1 eq {
393: aa (s). coeff 1 get /aa set
394: aa length 1 eq { 0 }
395: { aa 0 get (1). eq {
396: 0 << aa 1 get (integer) dc >> sub
397: } { } ifelse
398: } ifelse
399: }{ } ifelse
400: } map
401: /rlist set
402: %% rlist ::
403: [-1000000] rlist join shell rest /arg1 set
404: ] pop
405: popEnv
406: popVariables
407: arg1
408: } def
409:
410:
411: %%%%%%%%%%%%%%%%%%%%%%%%%%
412:
413: /asirconnectr {
414: [/in-asirconnectr /pass /peer /data /control /oxasir] pushVariables
415: [
416: /pass [(oxGenPass)] extension def
417: /peer [(oxGetPort) (localhost)] extension def
418: /data peer 1 get toString def
419: /control peer 3 get toString def
420: peer message
421: [oxpath.oxlog.xterm oxpath.ox ( -reverse -ox ) oxasirpath.oxasir
422: ( -data ) data ( -control ) control ( -pass ) pass
423: oxpath.null
1.2 takayama 424: ( &)] cat system-csh
1.1 maekawa 425: [(oxCreateClient2) peer 0 pass] extension /oxasir set
426: %% 0 means connect from only localhost.
427: oxasir asirinit
428: /arg1 oxasir def
429: ] pop
430: popVariables
431: arg1
432: } def
433: [(asirconnectr)
434: [(asirconnectr server (ox_asir function))
435: (array server;)
436: (Example: asirconnectr /oxasir.ccc set)
437: ]] putUsages
438:
439:
440: %%%%%%%%%%%%% From gbhg3/Int/intw.sm1
441: %% This function needs solv1.asir and ox_asir.
442: %% See solv1.asir for the usage of this function.
443: /rationalRoots2 {
444: /arg1 set
445: [/in-rationalRoots2 /aa /f /comm /vvv /r /setarg
446: /w /ans
447: ] pushVariables
448: [(CurrentRingp) (KanGBmessage)] pushEnv
449: [
450: /aa arg1 def
451: aa isArray { } { (<<array>> rationalRoots2) error } ifelse
452: /setarg 0 def
453: oxasir.ccc [ ] eq {
454: (Starting ox_asir server.) message
455: ox_asirConnectMethod
456: } { } ifelse
457: aa { tag } map /typev set
458: typev [ArrayP StringP ArrayP] eq
459: { /f aa 0 get def
460: /vvv [ aa 1 get to_records pop ] def
461: /w aa 2 get def
462: /setarg 1 def
463: } { } ifelse
464: typev [ArrayP ArrayP ArrayP] eq
465: { /f aa 0 get def
466: /vvv aa 1 get {toString} map def
467: /setarg 1 def
468: /w aa 2 get def
469: } { } ifelse
470: setarg { } { (rationalRoots2 : Argument mismatch) error } ifelse
471:
472:
473: [vvv from_records ring_of_polynomials 0] define_ring
474: f { toString . } map /f set
475: vvv { . } map /vvv set
476: w { toString . } map /w set
477:
478: (rationalRoots2 -- f = ) messagen f messagen
479: ( , vvv= ) messagen vvv messagen ( , w = ) messagen w message
480:
481: vvv length 1 eq w 0 get (1). eq and
482: {
483: [(KanGBmessage) 0] system_variable
484: [f] groebner_sugar 0 get /f set
485: vvv 0 get toString (s) eq {
486: }{ [[vvv 0 get toString (s)] from_records ring_of_polynomials 0] define_ring}
487: ifelse
488: f 0 get toString . [[vvv 0 get toString . (s).]] replace
489: findIntegralRoots /ans set
490: }
491: {
492: oxasir.ccc [(sm1_rationalRoots2) f vvv w] asir
493: {(integer) dc} map
494: /ans set
495: } ifelse
496:
497: /arg1 ans def
498: ] pop
499: popEnv
500: popVariables
501: arg1
502: } def
503: [(rationalRoots2)
504: [(rationalRoots2 (ox_asir function) called from intw.sm1 to analyze integral)
505: (roots.)
506: ]] putUsages
507:
508: /ptozp_subst {
509: /arg1 set
510: [/in-ptozp_subst /aaa /fff /xxx /vvv /vlist] pushVariables
511: [(CurrentRingp)] pushEnv
512: [
513: /aaa arg1 def
514: /fff aaa 0 get def
515: /xxx aaa 1 get toString def
516: /vvv aaa 2 get {toString ..} map def
517: aaa length 4 eq {
518: /vlist aaa 3 get def
519: } {
520: /vlist 0 def
521: } ifelse
522: oxasir.ccc [ ] eq {
523: (Starting ox_asir server.) message
524: ox_asirConnectMethod
525: } { } ifelse
526: fff isPolynomial {
527: fff (ring) dc ring_def
528: fff toString /fff set
529: }
530: { vlist isInteger { (ptozp_subst: need variable names.) error } { } ifelse
531: [vlist ring_of_differential_operators 0] define_ring
532: } ifelse
533: oxasir.ccc [(sm1_ptozp_subst) fff . xxx . vvv] asir
534: /arg1 set
535: ] pop
536: popEnv
537: popVariables
538: arg1
539: } def
540:
541: [(ptozp_subst)
542: [$[f s [p q] v] ptozp_subst g (ox_asir function)$
543: $It returns ptozp(subst(f,s,p/q))$
544: $Example 1: [ (x Dx - s) (s) [2 3] (x,s)] ptozp_subst $
545: $ ===> 3 x Dx - 2 $
546: ]] putUsages
547:
548: /reduceByAsir {
549: /arg1 set
550: [/in-reduceByAsir /aaa /fff /fff0 /fff1 /vlist] pushVariables
551: [(CurrentRingp)] pushEnv
552: [
553: /aaa arg1 def
554: /fff aaa 0 get def
555: aaa length 2 eq {
556: /vlist aaa 1 get def
557: } {
558: /vlist 0 def
559: } ifelse
560: oxasir.ccc [ ] eq {
561: (Starting ox_asir server.) message
562: ox_asirConnectMethod
563: } { } ifelse
564: fff isArray {
565: fff length 2 eq {
566: /fff0 fff 0 get def
567: /fff1 fff 1 get def
568: } {
569: ([ << [f g] >> vlist ] reduceByAsir ) error
570: } ifelse
571: } {
572: ([ << [f g] >> vlist ] reduceByAsir ) error
573: } ifelse
574: fff0 isPolynomial fff1 isPolynomial and {
575: fff0 (ring) dc ring_def
576: fff0 toString . /fff0 set
577: fff1 (ring) dc ring_def
578: fff1 toString . /fff1 set
579: }
580: { vlist isInteger { (reduceByAsir: need variable names.) error } { } ifelse
581: [vlist ring_of_differential_operators 0] define_ring
582: fff0 toString . /fff0 set
583: fff1 toString . /fff1 set
584: } ifelse
585: oxasir.ccc [(sm1_rat2plist2) [fff0 fff1]] asir
586: /arg1 set
587: ] pop
588: popEnv
589: popVariables
590: arg1
591: } def
592:
593: [(reduceByAsir)
594: [$ [[f g] v] reduceByAsir [ff gg] (ox_asir function)$
595: $ [[f g]] reduceByAsir [ff gg] $
596: $Example 1: [[(2 x -2) (4 x - 8)] (x)] reduceByAsir $
597: (Note that there may be a gcd that is more than 1 among the coefficients.)
598: ]] putUsages
1.4 takayama 599:
600: %% File should be preprocessed by OpenXM/misc/packages/Windows/oxpp
601: %% and ./oxapp --removeSharp
602: [(oxasirParseFile)
603: [$[peer filename] oxasirParseFile $
604: $File should be preprocessed by OpenXM/misc/packages/Windows/oxpp$
605: $and ./oxapp --removeSharp $
606: ]] putUsages
607:
608: /oxasirParseFile {
609: /arg1 set
610: [/in-oxasirParseFile /fname /sss] pushVariables
611: [
612: /fname arg1 1 get def
613: /peer arg1 0 get def
614: fname pushfile /sss set
615: peer
616: [$if (1) { ; $ sss (}$)] cat
617: oxsubmit
618: ] pop
619: popVariables
1.7 takayama 620: } def
621:
622: [(bfct)
1.8 takayama 623: [
1.7 takayama 624: ( f bfct b )
625: ( poly f; poly b)
626: ([f v] bfct b)
627: ( string f )
628: ( b is the global b-function of the polynomial f.)
1.10 takayama 629: (Example: [(x^3-y^2) (x,y)] bfct fctr :: )
1.9 takayama 630: (Algorithm: M.Noro, Mathematical Software, icms 2002, pp.147--157.)
1.7 takayama 631: ( )
632: (If you interrupted the computation by typing ctrl-C, type in )
633: ( oxasir.ccc oxreset ; )
634: (to interrupt the ox_asir server.)
635: ( )
636: (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)
1.8 takayama 637: (You need to install ox_asir server to use this function. (ox_asir function))
1.7 takayama 638: ]] putUsages
639:
640: /bfct {
641: /arg1 set
642: [/in-bfct /f /comm /vv] pushVariables
643: [(CurrentRingp)] pushEnv
644: [
645: /f arg1 def
646: oxasir.ccc [ ] eq {
647: (Starting ox_asir server.) message
648: ox_asirConnectMethod
649: } { } ifelse
650:
651: f isPolynomial not {
652: /vv f 1 get def
653: vv isArray { /vv vv from_records def } { } ifelse
654: /f f 0 get def
655: [vv ring_of_polynomials 0] define_ring
656: f . /f set
657: }{ } ifelse
658: oxasir.ccc [(oxasir_bfct) f] asir /f set
659: [(s) ring_of_polynomials 0] define_ring
660: f . /f set
661: [f f fctr] /arg1 set
662: ] pop
663: popEnv
664: popVariables
665: arg1
1.4 takayama 666: } def
667:
1.8 takayama 668: [(generic_bfct)
669: [
670: ( [ii weight] generic_bfct b )
671: ( list of poly ii; list weight)
672: ([ii weight variables] generic_bfct b)
673: ( list of string ii; list weight; list variables)
674: ( b is the general b-function of the ideal ii w.r.t the weight.)
675: (Example: [[(Dx^2) (Dy^2)] [(x) -1 (Dx) 1] [(x) (y)]] generic_bfct :: )
676: (Notion: Saito, Sturmfels, Takayama, Grobner deformations of hypergeometric differential equaitons)
1.9 takayama 677: (Algorithm: M.Noro, Mathematical Software, icms 2002, pp.147--157.)
1.8 takayama 678: ( )
679: (If you interrupted the computation by typing ctrl-C, type in )
680: ( oxasir.ccc oxreset ; )
681: (to interrupt the ox_asir server.)
682: ( )
683: (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)
684: (You need to install ox_asir server to use this function. (ox_asir function))
685: ]] putUsages
686:
687: /generic_bfct {
688: /arg1 set
689: [/in-generic_bfct /aa /f /comm /vvv0 /n /vvv /ddd /r /setarg
690: /bf /wt ] pushVariables
691: [(CurrentRingp)] pushEnv
692: [
693: /aa arg1 def
694: aa isArray { } { (<<array>> generic_bfct) error } ifelse
695: /setarg 0 def
696: aa { tag } map /typev set
697: typev [ ArrayP ArrayP] eq
698: { /f aa 0 get def
699: f 0 tag PolyP { } { (The first argument must be a list of differential operators. Give the third variable: a list of variables) error } ifelse
700: f 0 get (ring) dc /r set
701: [(CurrentRingp) r] system_variable
702: /wt aa 1 get def
703:
704: /vvv0 getVariableNames def
705: /n [(N)] system_variable def
706: /vvv vvv0 n carN rest reverse rest reverse def
707: /ddd vvv0 reverse n carN reverse
708: rest reverse rest reverse def
709:
710: /wt wt generic_bfct.aux1 def
711:
712: /setarg 1 def
713: } { } ifelse
714: typev [ArrayP ArrayP StringP] eq
715: { /f aa 0 get def
716: /vvv [ aa 2 get to_records pop ] def
717: /wt aa 1 get def
718:
719: /n vvv length def
720: /ddd vvv { (D) 2 1 roll 2 cat_n } map def
721:
722: /setarg 1 def
723: } { } ifelse
724: typev [ArrayP ArrayP ArrayP] eq
725: { /f aa 0 get def
726: /vvv aa 2 get {toString} map def
727: /wt aa 1 get def
728:
729: /n vvv length def
730: /ddd vvv { (D) 2 1 roll 2 cat_n } map def
731:
732: /setarg 1 def
733: } { } ifelse
734: setarg { } { (generic_bfct : Argument mismatch) error } ifelse
735:
736: f 0 get isPolynomial {
737:
738: }
739: {
740: [vvv from_records ring_of_differential_operators 0] define_ring
741: f { toString . } map /f set
742: vvv { . } map /vvv set
743: ddd { . } map /ddd set
744: /wt wt generic_bfct.aux1 def
745: } ifelse
746: [f vvv ddd wt] message
747:
748: oxasir.ccc [ ] eq {
749: (Starting ox_asir server.) message
750: ox_asirConnectMethod
751: } { } ifelse
752:
753: oxasir.ccc [(oxasir_generic_bfct) f vvv ddd wt] asir /bf set
754: [(s) ring_of_polynomials 0] define_ring
755: bf . /bf set
756: [bf bf fctr] /arg1 set
757: ] pop
758: popEnv
759: popVariables
760: arg1
761: } def
762:
763: /generic_bfct.aux1 {
764: /arg1 set
765: [/in-generic_bfct.aux1 /wt /wtx /wtd /n] pushVariables
766: [
767: arg1 /wt set
768: /n [(N)] system_variable def
769: wt { dup tag PolyP eq { toString } { } ifelse } map /wt set
770: wt weightv /wt set
771: /wtx wt n carN rest reverse rest reverse def
772: /wtd wt reverse n carN reverse
773: rest reverse rest reverse def
774: wtx wtd join /wt set
775: wt { dup tag IntegerP eq { (universalNumber) dc } { } ifelse } map /wt set
776: wt /arg1 set
777: ] pop
778: popVariables
779: arg1
780: } def
1.1 maekawa 781:
782: /oxasir.sm1.loaded 1 def
1.3 takayama 783: [(ostype)] extension 0 get (windows) eq {
784: [(parse) (oxasir-win.sm1) pushfile ] extension
785: }{
786: initializePathNamesForOxAsir %% This should be the last.
787: } ifelse
1.12 ! takayama 788:
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