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Diff for /OpenXM/src/kan96xx/Doc/oxasir.sm1 between version 1.12 and 1.13

version 1.12, 2003/01/01 02:03:42 version 1.13, 2003/07/21 07:32:00
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 % $OpenXM: OpenXM/src/kan96xx/Doc/oxasir.sm1,v 1.11 2002/11/09 01:24:08 takayama Exp $  % $OpenXM: OpenXM/src/kan96xx/Doc/oxasir.sm1,v 1.12 2003/01/01 02:03:42 takayama Exp $
 %% kxx/oxasir.sm1   1998, 2/12 (this version is at Old/oxasir.sm1.19980212  [(parse) (ox.sm1) pushfile] extension
 %%   3/1, 1995, 11/5, 11/21  
 %% This file is error clean.  
 %%%%%%% How to install.  
 %%%  Set ASIR_LIBDIR if necessary. Ex. /u/nobuki/lib/asir  
 %%%  write  ~/.asirrc  :    load("gr")$ load("primdec")$ load("bfct")$ end$  
 %%%  or it is written in OpenXM/rc/asirrc in OpenXM env, it's fine.  
 %%%  oxasir.asir  must be in  
 %%%  LOAD_SM1_PATH or oxasirpath.asirlib  
 %%%  Edit below  
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 %%% /usr/local/lib/sm1, SM1_LOAD_PATH, /usr/local/lib/asir, ASIR_LOAD_PATH  
 /oxasirpath.oxasir (ox_asir) def     %% loadmethod is 1  
 /oxasirpath.asirlib (oxasir.asir) def  
   
 /ox_asirConnectMethod { asirconnectr /oxasir.ccc set } def  
 %/ox_asirConnectMethod { asirconnect2  } def  
   
 %% Old path  
 %/oxasirpath.oxasir (/home/nobuki/kxx/ox_asir) def     %% loadmethod is 1  
 %/oxasirpath.asirlib (/home/nobuki/kxx/oxasir.asir) def  
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 /oxasir.loadmethod 1 def   %% "..." oxsendcmo (load) ox...  
 %/oxasir.loadmethod 0 def  %% load("...");  %% at MSRI  
 %%%%%%%%%%%%%%%% end of configuration.  
 /initializePathNamesForOxAsir  {  
    [oxasirpath.oxasir] getPathNameAsir /oxasirpath.oxasir set  
    [oxasirpath.asirlib] getPathNameSm1 /oxasirpath.asirlib set  
 } def  
   
   
 /oxasir.verbose 0   def  
 /oxasir.version (2.981105) def  
 oxasir.version [(Version)] system_variable gt  
 { [(This package requires the latest version of kan/sm1) nl  
    (Please get it from http://www.math.kobe-u.ac.jp/KAN) ] cat  
   error  
 } { } ifelse  
 (oxasir.sm1, --- open asir protocol module 3/1 1998, 6/5 1999) message-quiet  
 (   asirconnect, asir, fctr, primadec, (C) M.Noro, N.Takayama ) message-quiet  
   
 /oxasir.ccc load isArray  
 { }  
 { /oxasir.ccc [ ] def } ifelse  
   
 [(parse) (ox.sm1) pushfile] extension pop  
 oxasir.verbose {  
   (type in  asirconnect to connect,  asir is used to execute asir command. )  
    message  
   (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] )  
    message  
 } { } ifelse  
   
 /loadAsirFile {  
   /arg1 set  
   [/in-loadAsirFile /peer /fname] pushVariables  
   [  
     /peer arg1 0 get def  
     /fname arg1 1 get def  
     oxasir.loadmethod  {  
       peer  fname oxsendcmo peer 1 oxsendcmo  
       peer (load) oxexec  
     }{  
       peer  [$load("$ fname $");$] cat oxsubmit  
     }ifelse  
   ] pop  
   popVariables  
 } def  
 [(loadAsirFile)  
 [$[client fname] loadAsirFile   (ox_asir function)$  
  $Load a file into the client$  
 ]] putUsages  
   
 /asirinit {  
  %% gr and primdec are loaded by .asirrc  
  /asirinit.peer set  
  [(ostype)] extension  0 get (windows) eq {  
   [(getenv) (OSTYPE)] extension tag 0 eq {  
     [asirinit.peer (oxasir-win.rr)] oxasirParseFile  
   }{  
    [(getenv) (OSTYPE)] extension (cygwin) eq {  
      [asirinit.peer  oxasirpath.asirlib] loadAsirFile  
    }{  
      [asirinit.peer  (oxasir-win.rr)] oxasirParseFile  
    } ifelse  
   } ifelse  
  }{  
    [asirinit.peer  oxasirpath.asirlib] loadAsirFile  
  } ifelse  
  asirinit.peer oxmathcap  
  asirinit.peer oxsetmathcap  
  (Ox103_loaded) boundp  
  {  
    asirinit.peer ox103_asir_init  
  }{  } ifelse  
 } def  
 /asirconnect {  
  [(localhost) 1300 1200] oxconnect /oxasir.ccc set  
  /ccc oxasir.ccc def   %% for compatibility.  
  oxasir.ccc asirinit  
 } def  
 /asirconnect2 {  
 [oxpath.oxlog.xterm oxpath.ox ( -ox ) oxasirpath.oxasir  
  oxpath.null  
  ( & )] cat system-csh  
 % (xterm -e /home/nobuki/kxx/ox -ox /home/nobuki/kxx/ox_asir &) system-csh  
 % (kterm -iconic -e /home/nobuki/kxx/ox -ox /home/nobuki/kxx/ox_asir &) system-csh  
 % For MSRI  
 % Eterm is also nice (including kanji). rxvt is also nice.  
 %(xterm -icon -e /u/nobuki/tmp/kxx/ox -ox /u/nobuki/tmp/Ox/ox_asir2 &) system-csh  
 %(kterm2 -e /u/nobuki/tmp/kxx/ox -ox /u/nobuki/tmp/Ox/ox_asir2 &) system-csh  
 % (If you start the server automatically, you may have a trouble to) message  
 % (oxreset. In order to avoid this trouble, start the server by hand.) message  
  (sleep 5) system-csh  
  [(localhost) 1300 1200] oxconnect /oxasir.ccc set  
  /ccc oxasir.ccc def   %% for compatibility.  
  oxasir.ccc asirinit  
 } def  
   
 [(asirconnect2)  
  [(asirconnect2 starts ox_asir server.  (ox_asir function))  
   (Open xxx protocol is used for the communication between sm1 and ox_asir.)  
   (cf. oxhelp,  asir.)  
   (You need to install ox_asir server to use this function. cf. oxasir)  
 ]] putUsages  
   
 /asirconnect3 {  
 [oxpath.oxlog.xterm oxpath.ox ( -ox ) oxasirpath.oxasir  
  ( -data 2300 -control 2200) oxpath.null  
  ( & )] cat system-csh  
 % (If you start the server automatically, you may have a trouble to) message  
 % (oxreset. In order to avoid this trouble, start the server by hand.) message  
  (sleep 5) system-csh  
  [(localhost) 2300 2200] oxconnect /oxasir.ccc2 set  
  /ccc2 oxasir.ccc2 def   %% for compatibility.  
  oxasir.ccc2  asirinit  
  (The client is stored in oxasir.ccc2.) message  
 } def  
   
 [(asir)  
  [(pid [asir-command, asir-arg1, asir-arg2, ...] asir result  (ox_asir function))  
   (Call open asir server. You need to install ox_asir on your system)  
   (to use this function. cf. primadec, fctr, asirconnect2, asirconnectr.)  
   (If you interrupted the computation by typing ctrl-C, type in )  
   (   oxasir.ccc oxreset  ; )  
   (to interrupt the ox_asir server.)  
   (Example: oxasir.ccc [(fctr) (x^10-1).] asir )  
   (  )  
   (This function requires plugins cmo, socket and ox_asir server. cf. oxasir)  
   (See, ftp://endeavor.fujitsu.co.jp/pub/isis/asir on asir)  
  ]  
 ] putUsages  
   
 /asir {  
   /arg2 set  
   /arg1 set  
   [/pid  /asir-comm /comm /n /i /rr] pushVariables  
   [(CurrentRingp)] pushEnv  
   [  
      /pid arg1 def  
      /asir-comm arg2 def  
      pid tag 6 eq {  } { (Invalid pid. See asir.) error } ifelse  
      pid 0 get (client) eq { } { (Invalid pid. See asir.) error } ifelse  
      asir-comm tag 6 eq {  } { (Invalid argument asir-comm. See asir) error } ifelse  
   
     [ %% Change the current ring if necessary to send a correct OxVlist.  
       asir-comm oxasir.changeRing  
     ] pop  
     %%% Setting OxVlist to tell asir a way to change dist-poly <==> poly.  
     (OxVlist=) getVlist2 toString (;) 3 cat_n /comm set  
      %% comm message  
      pid comm oxsubmit  
      pid (print(OxVlist);) oxsubmit  
   
   
      /n asir-comm length def  
      n 1 sub -1 1 {  
        /i set  
        pid asir-comm i get oxsendcmo  
        pid 1 oxsendcmo pid (ox_dtop) oxexec  
      } for  
      pid n 1 sub oxsendcmo  
      pid asir-comm 0 get oxexec  
   
      pid 1 oxsendcmo pid (ox_ptod) oxexec  
      pid oxpopcmo /arg1 set  
   
   
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
 /oxasir.changeRing {  
   /arg1 set  
   [/in-oxasir.changeRing /f /rr] pushVariables  
   [  
      /f arg1 def  
      f isArray {  
        f {oxasir.changeRing} map  
      }{  
        f isPolynomial {  
          f (0). eq { }  
          { f (ring) dc /rr set [(CurrentRingp) rr] system_variable } ifelse  
        } {  } ifelse  
      } ifelse  
   ] pop  
   popVariables  
 } def  
   
 /fctr {  
   /arg1 set  
   [/f /comm /vv] pushVariables  
   [(CurrentRingp)] pushEnv  
   [  
     /f arg1 def  
     oxasir.ccc [ ] eq {  
        (Starting ox_asir server.) message  
         ox_asirConnectMethod  
     } {  } ifelse  
   
     f isPolynomial not {  
       /vv f 1 get def  
       vv isArray { /vv vv from_records  def } {  } ifelse  
       /f f 0 get def  
       [vv ring_of_polynomials 0] define_ring  
       f . /f set  
     }{ } ifelse  
     oxasir.ccc [(fctr) f] asir /arg1 set  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
 [(fctr)  
  [(You need to install ox_asir server to use this function. (ox_asir function))  
   (f fctr g)  
   (poly f; array g;)  
   ([f v] fctr g ;  string f, string or array of string v)  
   (This function factors the polynomial f over Q.)  
   ( )  
   (Example 1:  [(x^10-y^10) (x,y)] fctr ::)  
   (Example 2:  (x^10-1). fctr ::)  
   ( )  
   (If you interrupted the computation by typing ctrl-C, type in )  
   (   oxasir.ccc oxreset  ; )  
   (to interrupt the ox_asir server.)  
   (  )  
   (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)  
 ]] putUsages  
   
   
 [(primadec)  
  [(You need to install ox_asir server to use this function. (ox_asir function))  
   ([ ii ] primadec [[q1 p1] [q2 p2] ... ] )  
   ( array of poly ii; array of poly q1, p1, q2, p2 ...;)  
   ( q1, q2, ... are primary components of the primary ideal decomposition)  
   ( of the ideal generated by << ii >>.)  
   (  )  
   ([ ii v ] primadec [[q1 p1] [q2 p2] ... ] )  
   ( array of poly or string ii; array of string v; array of poly q1, p1, q2, p2 ...;)  
   (<< v >> is an array of independent variables.)  
   (  )  
   ([ ii v ] primadec [[q1 p1] [q2 p2] ... ] )  
   ( array of poly or string ii; array of string v; array of poly q1, p1, q2, p2 ...;)  
   ( v  is a string of variables separated by , )  
   (  )  
   (Example:  [(x,y) ring_of_polynomials 0] define_ring)  
   (          [ [(x^2-1). (x y).] ] primadec pmat ;)  
   (  )  
   (Example:  [ [(x^2-1) (x y)] [(x) (y)]] primadec pmat ;)  
   (  )  
   (If you interrupted the computation by typing ctrl-C, type in )  
   (   oxasir.ccc oxreset  ; )  
   (to interrupt the ox_asir server.)  
   (  )  
   (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)  
 ]] putUsages  
   
 /primadec {  
   /arg1 set  
   [/in-primadec /aa /f  /comm /vvv /r /setarg] pushVariables  
   [(CurrentRingp)] pushEnv  
   [  
     /aa arg1 def  
     aa isArray { } { (<<array>> primadec) error } ifelse  
     /setarg 0 def  
     oxasir.ccc [ ] eq {  
        (Starting ox_asir server.) message  
         ox_asirConnectMethod  
     } {  } ifelse  
     aa { tag } map /typev set  
     typev [ ArrayP ] eq  
     {  /f aa 0 get def  
        f 0 get (ring) dc /r set  
        [(CurrentRingp) r] system_variable  
        /vvv getVariableNames def  
        /setarg 1 def  
     } { } ifelse  
     typev [ArrayP StringP] eq  
     {  /f aa 0 get def  
        /vvv [ aa 1 get to_records pop ] def  
        /setarg 1 def  
     } { } ifelse  
     typev [ArrayP ArrayP] eq  
     {  /f aa 0 get def  
        /vvv aa 1 get {toString} map def  
        /setarg 1 def  
     } { } ifelse  
     setarg { } { (primadec : Argument mismatch) error } ifelse  
   
     f 0 get isPolynomial {  
       /r f 0 get (ring) dc def  
       /vvv vvv { r ,, } map def  
     }  
     {  
       [vvv from_records ring_of_polynomials 0] define_ring  
       f { toString . } map /f set  
       vvv { . } map /vvv set  
     } ifelse  
     oxasir.ccc [(primadec) f vvv] asir /arg1 set  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
   
 /getVlist2 {  
   [/n  /i ] pushVariables  
   [  
     /n [(N)] system_variable def  
     [  
       0 1 n 1 sub { /i set (x) i (dollar) dc 2 cat_n } for  
       0 1 n 1 sub { /i set (d) i (dollar) dc 2 cat_n } for  
     ] /arg1 set  
   ] pop  
   popVariables  
   arg1  
 } def  
   
 %%%%%%%%%%%%%%%%%%%  
 /getVlist {  
   [/n  /i ] pushVariables  
   [  
     /n [(N)] system_variable def  
     [  
       0 1 n 1 sub { /i set [(x) (var) i] system_variable } for  
       0 1 n 1 sub { /i set [(D) (var) i] system_variable } for  
     ] /arg1 set  
   ] pop  
   popVariables  
   arg1  
 } def  
   
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 [(chattr) 0 /findIntegralRoots] extension pop  
 oxasir.verbose {  
   (Overloaded on findIntegralRoots.) message  
 } { } ifelse  
 /findIntegralRoots {  
   /arg1 set  
   [/in-findIntegralRoots /pp ] pushVariables  
   [  
     /pp arg1 def  
     oxasir.ccc [ ] eq {  
       (Starting ox_asir server.) message  
        ox_asirConnectMethod  
     } {  } ifelse  
     oxasir.ccc oxIsServerReady  
     { pp findIntegralRoots.oxasir /arg1 set}  
     { pp findIntegralRoots.slow /arg1 set} ifelse  
   ] pop  
   popVariables  
   arg1  
 } def  
   
 /findIntegralRoots.oxasir {  
   /arg1 set  
   [/in-findIntegralRoots /f /r /g /aa /rlist] pushVariables  
   [(CurrentRingp) (KanGBmessage)] pushEnv  
   [  
     /f arg1 def  
     [(s) ring_of_polynomials 0] define_ring  
     f toString . /f set  
     f fctr rest /g set  
     g {  
          0 get /aa set  
          aa (s). degree 1 eq {  
            aa (s). coeff 1 get /aa set  
            aa length 1 eq { 0 }  
            {  aa 0 get (1). eq {  
                  0 << aa 1 get (integer) dc >> sub  
               } { } ifelse  
            } ifelse  
          }{ } ifelse  
      } map  
     /rlist set  
     %% rlist ::  
     [-1000000] rlist join shell rest /arg1 set  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
   
 %%%%%%%%%%%%%%%%%%%%%%%%%%  
   
 /asirconnectr {  
  [/in-asirconnectr /pass /peer /data /control /oxasir] pushVariables  
  [  
  /pass [(oxGenPass)] extension def  
  /peer [(oxGetPort) (localhost)] extension def  
  /data peer 1 get toString def  
  /control peer 3 get toString def  
  peer message  
  [oxpath.oxlog.xterm  oxpath.ox ( -reverse -ox ) oxasirpath.oxasir  
   ( -data ) data ( -control ) control  ( -pass ) pass  
   oxpath.null  
   ( &)] cat system-csh  
  [(oxCreateClient2) peer 0 pass] extension /oxasir set  
                      %% 0 means connect from only localhost.  
  oxasir asirinit  
  /arg1 oxasir def  
  ] pop  
  popVariables  
  arg1  
 } def  
 [(asirconnectr)  
  [(asirconnectr server  (ox_asir function))  
   (array server;)  
   (Example: asirconnectr /oxasir.ccc set)  
 ]] putUsages  
   
   
 %%%%%%%%%%%%%   From gbhg3/Int/intw.sm1  
 %% This function needs solv1.asir and ox_asir.  
 %% See solv1.asir for the usage of this function.  
 /rationalRoots2 {  
   /arg1 set  
   [/in-rationalRoots2 /aa /f  /comm /vvv /r /setarg  
    /w /ans  
   ] pushVariables  
   [(CurrentRingp) (KanGBmessage)] pushEnv  
   [  
     /aa arg1 def  
     aa isArray { } { (<<array>> rationalRoots2) error } ifelse  
     /setarg 0 def  
     oxasir.ccc [ ] eq {  
        (Starting ox_asir server.) message  
         ox_asirConnectMethod  
     } {  } ifelse  
     aa { tag } map /typev set  
     typev [ArrayP StringP ArrayP] eq  
     {  /f aa 0 get def  
        /vvv [ aa 1 get to_records pop ] def  
        /w aa 2 get def  
        /setarg 1 def  
     } { } ifelse  
     typev [ArrayP ArrayP ArrayP] eq  
     {  /f aa 0 get def  
        /vvv aa 1 get {toString} map def  
        /setarg 1 def  
        /w aa 2 get def  
     } { } ifelse  
     setarg { } { (rationalRoots2 : Argument mismatch) error } ifelse  
   
   
     [vvv from_records ring_of_polynomials 0] define_ring  
     f { toString . } map /f set  
     vvv { . } map /vvv set  
     w { toString . } map /w set  
   
     (rationalRoots2 -- f = ) messagen f messagen  
     ( , vvv= ) messagen vvv messagen ( , w = ) messagen w message  
   
     vvv length 1 eq w 0 get (1). eq and  
     {  
        [(KanGBmessage) 0] system_variable  
        [f] groebner_sugar 0 get /f set  
        vvv 0 get toString (s) eq {  
        }{ [[vvv 0 get toString (s)] from_records ring_of_polynomials 0] define_ring}  
        ifelse  
        f 0 get toString . [[vvv 0 get toString . (s).]] replace  
        findIntegralRoots /ans set  
     }  
     {  
       oxasir.ccc [(sm1_rationalRoots2) f vvv w] asir  
       {(integer) dc} map  
       /ans set  
     } ifelse  
   
     /arg1 ans def  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
 [(rationalRoots2)  
 [(rationalRoots2  (ox_asir function) called from intw.sm1 to analyze integral)  
  (roots.)  
 ]] putUsages  
   
 /ptozp_subst  {  
   /arg1 set  
   [/in-ptozp_subst /aaa /fff /xxx /vvv /vlist] pushVariables  
   [(CurrentRingp)] pushEnv  
   [  
      /aaa arg1 def  
      /fff aaa 0 get def  
      /xxx aaa 1 get toString def  
      /vvv aaa 2 get {toString ..} map def  
      aaa length 4 eq {  
        /vlist aaa 3 get def  
      } {  
        /vlist 0 def  
      } ifelse  
      oxasir.ccc [ ] eq {  
         (Starting ox_asir server.) message  
         ox_asirConnectMethod  
      } {  } ifelse  
      fff isPolynomial {  
        fff (ring) dc ring_def  
        fff toString /fff set  
      }  
      { vlist isInteger { (ptozp_subst: need variable names.) error } {  } ifelse  
        [vlist ring_of_differential_operators 0] define_ring  
      } ifelse  
      oxasir.ccc [(sm1_ptozp_subst) fff . xxx .  vvv] asir  
      /arg1 set  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
 [(ptozp_subst)  
  [$[f  s  [p q] v] ptozp_subst g   (ox_asir function)$  
   $It returns ptozp(subst(f,s,p/q))$  
   $Example 1:  [ (x Dx - s) (s) [2 3] (x,s)] ptozp_subst $  
   $   ===>     3 x Dx - 2 $  
 ]] putUsages  
   
 /reduceByAsir  {  
   /arg1 set  
   [/in-reduceByAsir /aaa /fff /fff0 /fff1 /vlist] pushVariables  
   [(CurrentRingp)] pushEnv  
   [  
      /aaa arg1 def  
      /fff aaa 0 get def  
      aaa length 2 eq {  
        /vlist aaa 1 get def  
      } {  
        /vlist 0 def  
      } ifelse  
      oxasir.ccc [ ] eq {  
         (Starting ox_asir server.) message  
         ox_asirConnectMethod  
      } {  } ifelse  
      fff isArray {  
        fff length 2 eq {  
          /fff0 fff 0 get def  
          /fff1 fff 1 get def  
        } {  
          ([ << [f g] >> vlist ] reduceByAsir ) error  
        } ifelse  
      } {  
        ([ << [f g] >> vlist ] reduceByAsir ) error  
      } ifelse  
      fff0 isPolynomial fff1 isPolynomial and {  
        fff0 (ring) dc ring_def  
        fff0 toString . /fff0 set  
        fff1 (ring) dc ring_def  
        fff1 toString . /fff1 set  
      }  
      { vlist isInteger { (reduceByAsir: need variable names.) error } {  } ifelse  
        [vlist ring_of_differential_operators 0] define_ring  
        fff0 toString . /fff0 set  
        fff1 toString . /fff1 set  
      } ifelse  
      oxasir.ccc [(sm1_rat2plist2) [fff0 fff1]] asir  
      /arg1 set  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
 [(reduceByAsir)  
 [$ [[f g] v] reduceByAsir [ff gg]   (ox_asir function)$  
  $ [[f g]] reduceByAsir [ff gg]  $  
  $Example 1: [[(2 x -2) (4 x - 8)] (x)] reduceByAsir $  
  (Note that there may be a gcd that is more than 1 among the coefficients.)  
 ]] putUsages  
   
 %% File should be preprocessed by OpenXM/misc/packages/Windows/oxpp  
 %% and ./oxapp --removeSharp  
 [(oxasirParseFile)  
 [$[peer filename] oxasirParseFile $  
  $File should be preprocessed by OpenXM/misc/packages/Windows/oxpp$  
  $and ./oxapp --removeSharp $  
 ]] putUsages  
   
 /oxasirParseFile {  
   /arg1 set  
   [/in-oxasirParseFile /fname /sss] pushVariables  
   [  
     /fname arg1 1 get def  
     /peer  arg1 0 get def  
     fname pushfile /sss set  
     peer  
     [$if (1) { ; $ sss (}$)] cat  
     oxsubmit  
   ] pop  
   popVariables  
 } def  
   
 [(bfct)  
  [  
   ( f bfct b )  
   ( poly f; poly b)  
   ([f v] bfct b)  
   ( string f )  
   ( b is the global b-function of the polynomial f.)  
   (Example: [(x^3-y^2) (x,y)] bfct fctr :: )  
   (Algorithm: M.Noro, Mathematical Software, icms 2002, pp.147--157.)  
   (  )  
   (If you interrupted the computation by typing ctrl-C, type in )  
   (   oxasir.ccc oxreset  ; )  
   (to interrupt the ox_asir server.)  
   (  )  
   (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)  
   (You need to install ox_asir server to use this function. (ox_asir function))  
 ]] putUsages  
   
 /bfct {  
   /arg1 set  
   [/in-bfct /f /comm /vv] pushVariables  
   [(CurrentRingp)] pushEnv  
   [  
     /f arg1 def  
     oxasir.ccc [ ] eq {  
        (Starting ox_asir server.) message  
         ox_asirConnectMethod  
     } {  } ifelse  
   
     f isPolynomial not {  
       /vv f 1 get def  
       vv isArray { /vv vv from_records  def } {  } ifelse  
       /f f 0 get def  
       [vv ring_of_polynomials 0] define_ring  
       f . /f set  
     }{ } ifelse  
     oxasir.ccc [(oxasir_bfct) f] asir /f set  
     [(s) ring_of_polynomials 0] define_ring  
     f . /f set  
     [f f fctr] /arg1 set  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
 [(generic_bfct)  
  [  
   ( [ii weight] generic_bfct b )  
   ( list of poly ii; list weight)  
   ([ii weight variables] generic_bfct b)  
   ( list of string ii; list weight; list variables)  
   ( b is the general b-function of the ideal ii w.r.t the weight.)  
   (Example: [[(Dx^2) (Dy^2)] [(x) -1 (Dx) 1] [(x) (y)]] generic_bfct :: )  
   (Notion: Saito, Sturmfels, Takayama, Grobner deformations of hypergeometric differential equaitons)  
   (Algorithm:  M.Noro, Mathematical Software, icms 2002, pp.147--157.)  
   (  )  
   (If you interrupted the computation by typing ctrl-C, type in )  
   (   oxasir.ccc oxreset  ; )  
   (to interrupt the ox_asir server.)  
   (  )  
   (This function requires plugins cmo, socket and ox_asir server. cf.oxasir)  
   (You need to install ox_asir server to use this function. (ox_asir function))  
 ]] putUsages  
   
 /generic_bfct {  
   /arg1 set  
   [/in-generic_bfct /aa /f  /comm /vvv0 /n /vvv /ddd /r /setarg  
    /bf /wt ] pushVariables  
   [(CurrentRingp)] pushEnv  
   [  
     /aa arg1 def  
     aa isArray { } { (<<array>> generic_bfct) error } ifelse  
     /setarg 0 def  
     aa { tag } map /typev set  
     typev [ ArrayP ArrayP] eq  
     {  /f aa 0 get def  
        f 0 tag PolyP { } {  (The first argument must be a list of differential operators. Give the third variable: a list of variables) error } ifelse  
        f 0 get (ring) dc /r set  
        [(CurrentRingp) r] system_variable  
        /wt aa 1 get def  
   
        /vvv0 getVariableNames def  
        /n [(N)] system_variable def  
        /vvv vvv0 n carN rest reverse rest reverse def  
        /ddd vvv0 reverse n carN reverse  
                    rest reverse rest reverse def  
   
        /wt wt generic_bfct.aux1 def  
   
        /setarg 1 def  
     } { } ifelse  
     typev [ArrayP ArrayP StringP] eq  
     {  /f aa 0 get def  
        /vvv [ aa 2 get to_records pop ] def  
        /wt aa 1 get def  
   
        /n vvv length def  
        /ddd vvv { (D) 2 1 roll 2 cat_n } map def  
   
        /setarg 1 def  
     } { } ifelse  
     typev [ArrayP ArrayP ArrayP] eq  
     {  /f aa 0 get def  
        /vvv aa 2 get {toString} map def  
        /wt aa 1 get def  
   
        /n vvv length def  
        /ddd vvv { (D) 2 1 roll 2 cat_n } map def  
   
        /setarg 1 def  
     } { } ifelse  
     setarg { } { (generic_bfct : Argument mismatch) error } ifelse  
   
     f 0 get isPolynomial {  
   
     }  
     {  
       [vvv from_records ring_of_differential_operators 0] define_ring  
       f { toString . } map /f set  
       vvv { . } map /vvv set  
       ddd { . } map /ddd set  
       /wt wt generic_bfct.aux1 def  
     } ifelse  
     [f vvv ddd wt] message  
   
     oxasir.ccc [ ] eq {  
        (Starting ox_asir server.) message  
         ox_asirConnectMethod  
     } {  } ifelse  
   
     oxasir.ccc [(oxasir_generic_bfct) f vvv ddd wt] asir /bf set  
     [(s) ring_of_polynomials 0] define_ring  
     bf . /bf set  
     [bf bf fctr] /arg1 set  
   ] pop  
   popEnv  
   popVariables  
   arg1  
 } def  
   
 /generic_bfct.aux1 {  
   /arg1 set  
   [/in-generic_bfct.aux1 /wt /wtx /wtd /n]  pushVariables  
   [  
     arg1 /wt set  
     /n [(N)] system_variable def  
     wt { dup tag PolyP eq { toString } {    } ifelse } map /wt set  
     wt weightv /wt set  
     /wtx wt n carN rest reverse rest reverse def  
     /wtd wt reverse n carN reverse  
                    rest reverse rest reverse def  
     wtx wtd join /wt set  
     wt { dup tag IntegerP eq { (universalNumber) dc } {    } ifelse } map /wt set  
     wt /arg1 set  
   ] pop  
   popVariables  
   arg1  
 } def  
   
 /oxasir.sm1.loaded 1 def  
 [(ostype)] extension  0 get (windows) eq {  
   [(parse) (oxasir-win.sm1) pushfile ] extension  
 }{  
   initializePathNamesForOxAsir   %% This should be the last.  
 } ifelse  
   
Legend:
Removed from v.1.12  
changed lines
  Added in v.1.13
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