Annotation of OpenXM/src/kan96xx/Doc/oxasir.sm1, Revision 1.1
1.1 ! maekawa 1: %% kxx/oxasir.sm1 1998, 2/12 (this version is at Old/oxasir.sm1.19980212
! 2: %% 3/1, 1995, 11/5, 11/21
! 3: %% This file is error clean.
! 4: %%%%%%% How to install.
! 5: %%% Set ASIR_LIBDIR if necessary. Ex. /u/nobuki/lib/asir
! 6: %%% write ~/.asirrc : load("gr")$ load("primdec")$ end$
! 7: %%% oxasir.asir must be in
! 8: %%% LOAD_SM1_PATH or oxasirpath.asirlib
! 9: %%% Edit below
! 10: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! 11: %%% /usr/local/lib/sm1, SM1_LOAD_PATH, /usr/local/lib/asir, ASIR_LOAD_PATH
! 12: /oxasirpath.oxasir (ox_asir) def %% loadmethod is 1
! 13: /oxasirpath.asirlib (oxasir.asir) def
! 14:
! 15: /ox_asirConnectMethod { asirconnectr /oxasir.ccc set } def
! 16: %/ox_asirConnectMethod { asirconnect2 } def
! 17:
! 18: %% Old path
! 19: %/oxasirpath.oxasir (/home/nobuki/kxx/ox_asir) def %% loadmethod is 1
! 20: %/oxasirpath.asirlib (/home/nobuki/kxx/oxasir.asir) def
! 21: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! 22: /oxasir.loadmethod 1 def %% "..." oxsendcmo (load) ox...
! 23: %/oxasir.loadmethod 0 def %% load("..."); %% at MSRI
! 24: %%%%%%%%%%%%%%%% end of configuration.
! 25: /initializePathNamesForOxAsir {
! 26: [oxasirpath.oxasir] getPathNameAsir /oxasirpath.oxasir set
! 27: [oxasirpath.asirlib] getPathNameSm1 /oxasirpath.asirlib set
! 28: } def
! 29:
! 30:
! 31: /oxasir.verbose 0 def
! 32: /oxasir.version (2.981105) def
! 33: oxasir.version [(Version)] system_variable gt
! 34: { [(This package requires the latest version of kan/sm1) nl
! 35: (Please get it from http://www.math.kobe-u.ac.jp/KAN) ] cat
! 36: error
! 37: } { } ifelse
! 38: (oxasir.sm1, --- open asir protocol module 3/1 1998, 6/5 1999) message-quiet
! 39: ( asirconnect, asir, fctr, primadec, (C) M.Noro, N.Takayama ) message-quiet
! 40:
! 41: /oxasir.ccc load isArray
! 42: { }
! 43: { /oxasir.ccc [ ] def } ifelse
! 44:
! 45: [(parse) (ox.sm1) pushfile] extension pop
! 46: oxasir.verbose {
! 47: (type in asirconnect to connect, asir is used to execute asir command. )
! 48: message
! 49: (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] )
! 50: message
! 51: } { } ifelse
! 52:
! 53: /loadAsirFile {
! 54: /arg1 set
! 55: [/in-loadAsirFile /peer /fname] pushVariables
! 56: [
! 57: /peer arg1 0 get def
! 58: /fname arg1 1 get def
! 59: oxasir.loadmethod {
! 60: peer fname oxsendcmo peer 1 oxsendcmo
! 61: peer (load) oxexec
! 62: }{
! 63: peer [$load("$ fname $");$] cat oxsubmit
! 64: }ifelse
! 65: ] pop
! 66: popVariables
! 67: } def
! 68: [(loadAsirFile)
! 69: [$[client fname] loadAsirFile (ox_asir function)$
! 70: $Load a file into the client$
! 71: ]] putUsages
! 72:
! 73: /asirinit {
! 74: %% gr and primdec are loaded by .asirrc
! 75: /asirinit.peer set
! 76: [asirinit.peer oxasirpath.asirlib] loadAsirFile
! 77: } def
! 78: /asirconnect {
! 79: [(localhost) 1300 1200] oxconnect /oxasir.ccc set
! 80: /ccc oxasir.ccc def %% for compatibility.
! 81: oxasir.ccc asirinit
! 82: } def
! 83: /asirconnect2 {
! 84: [oxpath.oxlog.xterm oxpath.ox ( -ox ) oxasirpath.oxasir
! 85: oxpath.null
! 86: ( & )] cat system
! 87: % (xterm -e /home/nobuki/kxx/ox -ox /home/nobuki/kxx/ox_asir &) system
! 88: % (kterm -iconic -e /home/nobuki/kxx/ox -ox /home/nobuki/kxx/ox_asir &) system
! 89: % For MSRI
! 90: % Eterm is also nice (including kanji). rxvt is also nice.
! 91: %(xterm -icon -e /u/nobuki/tmp/kxx/ox -ox /u/nobuki/tmp/Ox/ox_asir2 &) system
! 92: %(kterm2 -e /u/nobuki/tmp/kxx/ox -ox /u/nobuki/tmp/Ox/ox_asir2 &) system
! 93: % (If you start the server automatically, you may have a trouble to) message
! 94: % (oxreset. In order to avoid this trouble, start the server by hand.) message
! 95: (sleep 5) system
! 96: [(localhost) 1300 1200] oxconnect /oxasir.ccc set
! 97: /ccc oxasir.ccc def %% for compatibility.
! 98: oxasir.ccc asirinit
! 99: } def
! 100:
! 101: [(asirconnect2)
! 102: [(asirconnect2 starts ox_asir server. (ox_asir function))
! 103: (Open xxx protocol is used for the communication between sm1 and ox_asir.)
! 104: (cf. oxhelp, asir.)
! 105: (You need to install ox_asir server to use this function. cf. oxasir)
! 106: ]] putUsages
! 107:
! 108: /asirconnect3 {
! 109: [oxpath.oxlog.xterm oxpath.ox ( -ox ) oxasirpath.oxasir
! 110: ( -data 2300 -control 2200) oxpath.null
! 111: ( & )] cat system
! 112: % (If you start the server automatically, you may have a trouble to) message
! 113: % (oxreset. In order to avoid this trouble, start the server by hand.) message
! 114: (sleep 5) system
! 115: [(localhost) 2300 2200] oxconnect /oxasir.ccc2 set
! 116: /ccc2 oxasir.ccc2 def %% for compatibility.
! 117: oxasir.ccc2 asirinit
! 118: (The client is stored in oxasir.ccc2.) message
! 119: } def
! 120:
! 121: [(asir)
! 122: [(pid [asir-command, asir-arg1, asir-arg2, ...] asir result (ox_asir function))
! 123: (Call open asir server. You need to install ox_asir on your system)
! 124: (to use this function. cf. primadec, fctr, asirconnect2, asirconnectr.)
! 125: (If you interrupted the computation by typing ctrl-C, type in )
! 126: ( oxasir.ccc oxreset ; )
! 127: (to interrupt the ox_asir server.)
! 128: (Example: oxasir.ccc [(fctr) (x^10-1).] asir )
! 129: ( )
! 130: (This function requires plugins cmo, socket and ox_asir server. cf. oxasir)
! 131: (See, ftp://endeavor.fujitsu.co.jp/pub/isis/asir on asir)
! 132: ]
! 133: ] putUsages
! 134:
! 135: /asir {
! 136: /arg2 set
! 137: /arg1 set
! 138: [/pid /asir-comm /comm /n /i /rr] pushVariables
! 139: [(CurrentRingp)] pushEnv
! 140: [
! 141: /pid arg1 def
! 142: /asir-comm arg2 def
! 143: pid tag 6 eq { } { (Invalid pid. See asir.) error } ifelse
! 144: pid 0 get (client) eq { } { (Invalid pid. See asir.) error } ifelse
! 145: asir-comm tag 6 eq { } { (Invalid argument asir-comm. See asir) error } ifelse
! 146:
! 147: [ %% Change the current ring if necessary to send a correct OxVlist.
! 148: asir-comm oxasir.changeRing
! 149: ] pop
! 150: %%% Setting OxVlist to tell asir a way to change dist-poly <==> poly.
! 151: (OxVlist=) getVlist2 toString (;) 3 cat_n /comm set
! 152: %% comm message
! 153: pid comm oxsubmit
! 154: pid (print(OxVlist);) oxsubmit
! 155:
! 156:
! 157: /n asir-comm length def
! 158: n 1 sub -1 1 {
! 159: /i set
! 160: pid asir-comm i get oxsendcmo
! 161: pid 1 oxsendcmo pid (ox_dtop) oxexec
! 162: } for
! 163: pid n 1 sub oxsendcmo
! 164: pid asir-comm 0 get oxexec
! 165:
! 166: pid 1 oxsendcmo pid (ox_ptod) oxexec
! 167: pid oxpopcmo /arg1 set
! 168:
! 169:
! 170: ] pop
! 171: popEnv
! 172: popVariables
! 173: arg1
! 174: } def
! 175:
! 176: /oxasir.changeRing {
! 177: /arg1 set
! 178: [/in-oxasir.changeRing /f /rr] pushVariables
! 179: [
! 180: /f arg1 def
! 181: f isArray {
! 182: f {oxasir.changeRing} map
! 183: }{
! 184: f isPolynomial {
! 185: f (0). eq { }
! 186: { f (ring) dc /rr set [(CurrentRingp) rr] system_variable } ifelse
! 187: } { } ifelse
! 188: } ifelse
! 189: ] pop
! 190: popVariables
! 191: } def
! 192:
! 193: /fctr {
! 194: /arg1 set
! 195: [/f /comm /vv] pushVariables
! 196: [(CurrentRingp)] pushEnv
! 197: [
! 198: /f arg1 def
! 199: oxasir.ccc [ ] eq {
! 200: (Starting ox_asir server.) message
! 201: ox_asirConnectMethod
! 202: } { } ifelse
! 203:
! 204: f isPolynomial not {
! 205: /vv f 1 get def
! 206: vv isArray { /vv vv from_records def } { } ifelse
! 207: /f f 0 get def
! 208: [vv ring_of_polynomials 0] define_ring
! 209: f . /f set
! 210: }{ } ifelse
! 211: oxasir.ccc [(fctr) f] asir /arg1 set
! 212: ] pop
! 213: popEnv
! 214: popVariables
! 215: arg1
! 216: } def
! 217:
! 218: [(fctr)
! 219: [(You need to install ox_asir server to use this function. (ox_asir function))
! 220: (f fctr g)
! 221: (poly f; array g;)
! 222: ([f v] fctr g ; string f, string or array of string v)
! 223: (This function factors the polynomial f over Q.)
! 224: ( )
! 225: (Example 1: [(x^10-y^10) (x,y)] fctr ::)
! 226: (Example 2: (x^10-1). fctr ::)
! 227: ( )
! 228: (If you interrupted the computation by typing ctrl-C, type in )
! 229: ( oxasir.ccc oxreset ; )
! 230: (to interrupt the ox_asir server.)
! 231: ( )
! 232: (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)
! 233: ]] putUsages
! 234:
! 235:
! 236: [(primadec)
! 237: [(You need to install ox_asir server to use this function. (ox_asir function))
! 238: ([ ii ] primadec [[q1 p1] [q2 p2] ... ] )
! 239: ( array of poly ii; array of poly q1, p1, q2, p2 ...;)
! 240: ( q1, q2, ... are primary components of the primary ideal decomposition)
! 241: ( of the ideal generated by << ii >>.)
! 242: ( )
! 243: ([ ii v ] primadec [[q1 p1] [q2 p2] ... ] )
! 244: ( array of poly or string ii; array of string v; array of poly q1, p1, q2, p2 ...;)
! 245: (<< v >> is an array of independent variables.)
! 246: ( )
! 247: ([ ii v ] primadec [[q1 p1] [q2 p2] ... ] )
! 248: ( array of poly or string ii; array of string v; array of poly q1, p1, q2, p2 ...;)
! 249: ( v is a string of variables separated by , )
! 250: ( )
! 251: (Example: [(x,y) ring_of_polynomials 0] define_ring)
! 252: ( [ [(x^2-1). (x y).] ] primadec pmat ;)
! 253: ( )
! 254: (Example: [ [(x^2-1) (x y)] [(x) (y)]] primadec pmat ;)
! 255: ( )
! 256: (If you interrupted the computation by typing ctrl-C, type in )
! 257: ( oxasir.ccc oxreset ; )
! 258: (to interrupt the ox_asir server.)
! 259: ( )
! 260: (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)
! 261: ]] putUsages
! 262:
! 263: /primadec {
! 264: /arg1 set
! 265: [/in-primadec /aa /f /comm /vvv /r /setarg] pushVariables
! 266: [(CurrentRingp)] pushEnv
! 267: [
! 268: /aa arg1 def
! 269: aa isArray { } { (<<array>> primadec) error } ifelse
! 270: /setarg 0 def
! 271: oxasir.ccc [ ] eq {
! 272: (Starting ox_asir server.) message
! 273: ox_asirConnectMethod
! 274: } { } ifelse
! 275: aa { tag } map /typev set
! 276: typev [ ArrayP ] eq
! 277: { /f aa 0 get def
! 278: f 0 get (ring) dc /r set
! 279: [(CurrentRingp) r] system_variable
! 280: /vvv getVariableNames def
! 281: /setarg 1 def
! 282: } { } ifelse
! 283: typev [ArrayP StringP] eq
! 284: { /f aa 0 get def
! 285: /vvv [ aa 1 get to_records pop ] def
! 286: /setarg 1 def
! 287: } { } ifelse
! 288: typev [ArrayP ArrayP] eq
! 289: { /f aa 0 get def
! 290: /vvv aa 1 get {toString} map def
! 291: /setarg 1 def
! 292: } { } ifelse
! 293: setarg { } { (primadec : Argument mismatch) error } ifelse
! 294:
! 295: f 0 get isPolynomial {
! 296: /r f 0 get (ring) dc def
! 297: /vvv vvv { r ,, } map def
! 298: }
! 299: {
! 300: [vvv from_records ring_of_polynomials 0] define_ring
! 301: f { toString . } map /f set
! 302: vvv { . } map /vvv set
! 303: } ifelse
! 304: oxasir.ccc [(primadec) f vvv] asir /arg1 set
! 305: ] pop
! 306: popEnv
! 307: popVariables
! 308: arg1
! 309: } def
! 310:
! 311:
! 312: /getVlist2 {
! 313: [/n /i ] pushVariables
! 314: [
! 315: /n [(N)] system_variable def
! 316: [
! 317: 0 1 n 1 sub { /i set (x) i (dollar) dc 2 cat_n } for
! 318: 0 1 n 1 sub { /i set (d) i (dollar) dc 2 cat_n } for
! 319: ] /arg1 set
! 320: ] pop
! 321: popVariables
! 322: arg1
! 323: } def
! 324:
! 325: %%%%%%%%%%%%%%%%%%%
! 326: /getVlist {
! 327: [/n /i ] pushVariables
! 328: [
! 329: /n [(N)] system_variable def
! 330: [
! 331: 0 1 n 1 sub { /i set [(x) (var) i] system_variable } for
! 332: 0 1 n 1 sub { /i set [(D) (var) i] system_variable } for
! 333: ] /arg1 set
! 334: ] pop
! 335: popVariables
! 336: arg1
! 337: } def
! 338:
! 339: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! 340: [(chattr) 0 /findIntegralRoots] extension pop
! 341: oxasir.verbose {
! 342: (Overloaded on findIntegralRoots.) message
! 343: } { } ifelse
! 344: /findIntegralRoots {
! 345: /arg1 set
! 346: [/in-findIntegralRoots /pp ] pushVariables
! 347: [
! 348: /pp arg1 def
! 349: oxasir.ccc [ ] eq {
! 350: (Starting ox_asir server.) message
! 351: ox_asirConnectMethod
! 352: } { } ifelse
! 353: oxasir.ccc oxIsServerReady
! 354: { pp findIntegralRoots.oxasir /arg1 set}
! 355: { pp findIntegralRoots.slow /arg1 set} ifelse
! 356: ] pop
! 357: popVariables
! 358: arg1
! 359: } def
! 360:
! 361: /findIntegralRoots.oxasir {
! 362: /arg1 set
! 363: [/in-findIntegralRoots /f /r /g /aa /rlist] pushVariables
! 364: [(CurrentRingp) (KanGBmessage)] pushEnv
! 365: [
! 366: /f arg1 def
! 367: [(s) ring_of_polynomials 0] define_ring
! 368: f toString . /f set
! 369: f fctr rest /g set
! 370: g {
! 371: 0 get /aa set
! 372: aa (s). degree 1 eq {
! 373: aa (s). coeff 1 get /aa set
! 374: aa length 1 eq { 0 }
! 375: { aa 0 get (1). eq {
! 376: 0 << aa 1 get (integer) dc >> sub
! 377: } { } ifelse
! 378: } ifelse
! 379: }{ } ifelse
! 380: } map
! 381: /rlist set
! 382: %% rlist ::
! 383: [-1000000] rlist join shell rest /arg1 set
! 384: ] pop
! 385: popEnv
! 386: popVariables
! 387: arg1
! 388: } def
! 389:
! 390:
! 391: %%%%%%%%%%%%%%%%%%%%%%%%%%
! 392:
! 393: /asirconnectr {
! 394: [/in-asirconnectr /pass /peer /data /control /oxasir] pushVariables
! 395: [
! 396: /pass [(oxGenPass)] extension def
! 397: /peer [(oxGetPort) (localhost)] extension def
! 398: /data peer 1 get toString def
! 399: /control peer 3 get toString def
! 400: peer message
! 401: [oxpath.oxlog.xterm oxpath.ox ( -reverse -ox ) oxasirpath.oxasir
! 402: ( -data ) data ( -control ) control ( -pass ) pass
! 403: oxpath.null
! 404: ( &)] cat system
! 405: [(oxCreateClient2) peer 0 pass] extension /oxasir set
! 406: %% 0 means connect from only localhost.
! 407: oxasir asirinit
! 408: /arg1 oxasir def
! 409: ] pop
! 410: popVariables
! 411: arg1
! 412: } def
! 413: [(asirconnectr)
! 414: [(asirconnectr server (ox_asir function))
! 415: (array server;)
! 416: (Example: asirconnectr /oxasir.ccc set)
! 417: ]] putUsages
! 418:
! 419:
! 420: %%%%%%%%%%%%% From gbhg3/Int/intw.sm1
! 421: %% This function needs solv1.asir and ox_asir.
! 422: %% See solv1.asir for the usage of this function.
! 423: /rationalRoots2 {
! 424: /arg1 set
! 425: [/in-rationalRoots2 /aa /f /comm /vvv /r /setarg
! 426: /w /ans
! 427: ] pushVariables
! 428: [(CurrentRingp) (KanGBmessage)] pushEnv
! 429: [
! 430: /aa arg1 def
! 431: aa isArray { } { (<<array>> rationalRoots2) error } ifelse
! 432: /setarg 0 def
! 433: oxasir.ccc [ ] eq {
! 434: (Starting ox_asir server.) message
! 435: ox_asirConnectMethod
! 436: } { } ifelse
! 437: aa { tag } map /typev set
! 438: typev [ArrayP StringP ArrayP] eq
! 439: { /f aa 0 get def
! 440: /vvv [ aa 1 get to_records pop ] def
! 441: /w aa 2 get def
! 442: /setarg 1 def
! 443: } { } ifelse
! 444: typev [ArrayP ArrayP ArrayP] eq
! 445: { /f aa 0 get def
! 446: /vvv aa 1 get {toString} map def
! 447: /setarg 1 def
! 448: /w aa 2 get def
! 449: } { } ifelse
! 450: setarg { } { (rationalRoots2 : Argument mismatch) error } ifelse
! 451:
! 452:
! 453: [vvv from_records ring_of_polynomials 0] define_ring
! 454: f { toString . } map /f set
! 455: vvv { . } map /vvv set
! 456: w { toString . } map /w set
! 457:
! 458: (rationalRoots2 -- f = ) messagen f messagen
! 459: ( , vvv= ) messagen vvv messagen ( , w = ) messagen w message
! 460:
! 461: vvv length 1 eq w 0 get (1). eq and
! 462: {
! 463: [(KanGBmessage) 0] system_variable
! 464: [f] groebner_sugar 0 get /f set
! 465: vvv 0 get toString (s) eq {
! 466: }{ [[vvv 0 get toString (s)] from_records ring_of_polynomials 0] define_ring}
! 467: ifelse
! 468: f 0 get toString . [[vvv 0 get toString . (s).]] replace
! 469: findIntegralRoots /ans set
! 470: }
! 471: {
! 472: oxasir.ccc [(sm1_rationalRoots2) f vvv w] asir
! 473: {(integer) dc} map
! 474: /ans set
! 475: } ifelse
! 476:
! 477: /arg1 ans def
! 478: ] pop
! 479: popEnv
! 480: popVariables
! 481: arg1
! 482: } def
! 483: [(rationalRoots2)
! 484: [(rationalRoots2 (ox_asir function) called from intw.sm1 to analyze integral)
! 485: (roots.)
! 486: ]] putUsages
! 487:
! 488: /ptozp_subst {
! 489: /arg1 set
! 490: [/in-ptozp_subst /aaa /fff /xxx /vvv /vlist] pushVariables
! 491: [(CurrentRingp)] pushEnv
! 492: [
! 493: /aaa arg1 def
! 494: /fff aaa 0 get def
! 495: /xxx aaa 1 get toString def
! 496: /vvv aaa 2 get {toString ..} map def
! 497: aaa length 4 eq {
! 498: /vlist aaa 3 get def
! 499: } {
! 500: /vlist 0 def
! 501: } ifelse
! 502: oxasir.ccc [ ] eq {
! 503: (Starting ox_asir server.) message
! 504: ox_asirConnectMethod
! 505: } { } ifelse
! 506: fff isPolynomial {
! 507: fff (ring) dc ring_def
! 508: fff toString /fff set
! 509: }
! 510: { vlist isInteger { (ptozp_subst: need variable names.) error } { } ifelse
! 511: [vlist ring_of_differential_operators 0] define_ring
! 512: } ifelse
! 513: oxasir.ccc [(sm1_ptozp_subst) fff . xxx . vvv] asir
! 514: /arg1 set
! 515: ] pop
! 516: popEnv
! 517: popVariables
! 518: arg1
! 519: } def
! 520:
! 521: [(ptozp_subst)
! 522: [$[f s [p q] v] ptozp_subst g (ox_asir function)$
! 523: $It returns ptozp(subst(f,s,p/q))$
! 524: $Example 1: [ (x Dx - s) (s) [2 3] (x,s)] ptozp_subst $
! 525: $ ===> 3 x Dx - 2 $
! 526: ]] putUsages
! 527:
! 528: /reduceByAsir {
! 529: /arg1 set
! 530: [/in-reduceByAsir /aaa /fff /fff0 /fff1 /vlist] pushVariables
! 531: [(CurrentRingp)] pushEnv
! 532: [
! 533: /aaa arg1 def
! 534: /fff aaa 0 get def
! 535: aaa length 2 eq {
! 536: /vlist aaa 1 get def
! 537: } {
! 538: /vlist 0 def
! 539: } ifelse
! 540: oxasir.ccc [ ] eq {
! 541: (Starting ox_asir server.) message
! 542: ox_asirConnectMethod
! 543: } { } ifelse
! 544: fff isArray {
! 545: fff length 2 eq {
! 546: /fff0 fff 0 get def
! 547: /fff1 fff 1 get def
! 548: } {
! 549: ([ << [f g] >> vlist ] reduceByAsir ) error
! 550: } ifelse
! 551: } {
! 552: ([ << [f g] >> vlist ] reduceByAsir ) error
! 553: } ifelse
! 554: fff0 isPolynomial fff1 isPolynomial and {
! 555: fff0 (ring) dc ring_def
! 556: fff0 toString . /fff0 set
! 557: fff1 (ring) dc ring_def
! 558: fff1 toString . /fff1 set
! 559: }
! 560: { vlist isInteger { (reduceByAsir: need variable names.) error } { } ifelse
! 561: [vlist ring_of_differential_operators 0] define_ring
! 562: fff0 toString . /fff0 set
! 563: fff1 toString . /fff1 set
! 564: } ifelse
! 565: oxasir.ccc [(sm1_rat2plist2) [fff0 fff1]] asir
! 566: /arg1 set
! 567: ] pop
! 568: popEnv
! 569: popVariables
! 570: arg1
! 571: } def
! 572:
! 573: [(reduceByAsir)
! 574: [$ [[f g] v] reduceByAsir [ff gg] (ox_asir function)$
! 575: $ [[f g]] reduceByAsir [ff gg] $
! 576: $Example 1: [[(2 x -2) (4 x - 8)] (x)] reduceByAsir $
! 577: (Note that there may be a gcd that is more than 1 among the coefficients.)
! 578: ]] putUsages
! 579:
! 580: /oxasir.sm1.loaded 1 def
! 581: initializePathNamesForOxAsir %% This should be the last.
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