File: [local] / OpenXM / src / ox_math / documents / samplelog-sm1.txt (download)
Revision 1.3, Mon Nov 8 00:36:56 1999 UTC (24 years, 6 months ago) by takayama
Branch: MAIN
CVS Tags: maekawa-ipv6, R_1_3_1-2, RELEASE_20000124, RELEASE_1_3_1_13b, RELEASE_1_2_3_12, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, RELEASE_1_1_3, RELEASE_1_1_2, KNOPPIX_2006, HEAD, DEB_REL_1_2_3-9
Changes since 1.2: +100 -1
lines
An example of computation of Grobner basis in D is given.
Here, actual computation is done on ox_sm1 and Mathematica is used as
a front-end. The last example is the elimination in D.
|
%% $OpenXM: OpenXM/src/ox_math/documents/samplelog-sm1.txt,v 1.3 1999/11/08 00:36:56 takayama Exp $
samplelog-sm1.txt : sm1 $B$+$i(B, ox_math $B$r8F$S=P$9Nc(B.
$BNcBj$O(B, Mathematica Book (S.Wolfram) A Tour of Mathematica $B$h$j(B
$B$H$C$?(B.
1999, 11/5 Fri, 11:20:
[nobuki@yama nobuki]$ sm1
Kan/StackMachine1 1991 April --- 1998.
Release 2.991030 (C) N. Takayama
gc 4.14 (C) Boehm, Demers, GNU MP 2.0.2 (C) Free Software Foundation,
Open XM.
This software may be freely distributed as is with no warranty expressed.
Info: http://www.math.kobe-u.ac.jp/KAN, kan@math.kobe-u.ac.jp. ? for help.
Ready
sm1>macro package : dr.sm1, 9/26,1995 --- Version 9/8, 1999.
sm1>macro package : module1.sm1, 1994 -- Nov 8, 1998
sm1>(ox.sm1) run ;
ox.sm1, --- open sm1 protocol module 10/1,1999 (C) N.Takayama. oxhelp for help
sm1>(ox_launch) usage ;
[remote remote-OpenXM-bin remote-ox-server remote-login-name myhostname]
ox_launch client
Example 1:
[(tau.math.kobe-u.ac.jp) (/home/taka/OpenXM/bin)
(/home/taka/OpenXM/src/ox_math/ox_math) (taka) (dc4.math.kobe-u.ac.jp)
] ox_launch /@@@.oxmath set
sm1> [(tau.math.kobe-u.ac.jp) (/home/taka/OpenXM/bin)
(/home/taka/OpenXM/src/ox_math/ox_math) (taka) (yama.math.kobe-u.ac.jp)
] ox_launch /@@@.oxmath set ;
Hello from open. serverName is yama.math.kobe-u.ac.jp and portnumber is 0
Done the initialization. port =1026
[ 4 , 1026 , 3 , 1024 ]
Executing the command : ssh -f tau.math.kobe-u.ac.jp -l taka "/home/taka/OpenXM/bin/oxlog /usr/X11R6/bin/xterm -icon -e /home/taka/OpenXM/bin/ox -reverse -ox /home/taka/OpenXM/src/ox_math/ox_math -host yama.math.kobe-u.ac.jp -data 1026 -control 1024 -pass 269770415 "
[
taka@tau.math.kobe-u.ac.jp's password:
Trying to accept... Accepted.
Trying to accept... Accepted.
Control port 1024 : Connected.
Stream port 1026 : Connected.
Byte order for control process is network byte order.
Byte order for engine process is network byte order.
sm1>@@@.oxmath (N[Sqrt[10],40]) oxsubmit ;
sm1>@@@.oxmath oxpopcmo ::
$3.16227766016837933199889354443271853372$
sm1>@@@.oxmath (FindRoot[BesselJ[0,x],{x,10.5}) oxsubmit ;
sm1>@@@.oxmath ::
[ $client$ , Name=Buffered IO by FILE2, FILE *=82d2000 , 1026 , 5 , 1024 , 0 , 0 , 0 , 0 , 0 , %[null] , 0 , 0 ]
sm1>@@@.oxmath oxpopcmo ::
Class.indeterminate $$Failed$
sm1>@@@.oxmath (FindRoot[BesselJ[0,x],{x,10.5}]) oxsubmit ;
sm1>@@@.oxmath oxpopcmo ::
[ $List$ , [ $Rule$ , Class.indeterminate $x$ , $18.071063872589566$ ] ]
sm1>@@@.oxmath (NIntegrate[Sin[Sin[x]], {x,0,Pi}]) oxsubmit ;
sm1>@@@.oxmath oxpopcmo ::
$1.7864874819500596$
sm1>@@@.oxmath (FactorInteger[ 20654065386]) oxsubmit ;
sm1>@@@.oxmath oxpopcmo ::
[ $List$ , [ $List$ , 2 , 1 ] , [ $List$ , 3 , 2 ] , [ $List$ , 43 , 1 ] , [ $List$ , 26684839 , 1 ] ]
sm1>@@@.oxmath (Plot[Sin[x^3],{x,-2,2}]) oxsubmit ;
Plot $B$rMj$`$H(B Mathematica $B$O0J2<$N$h$&$J5pBg$J%G!<%?$r$*$/$j$+$($7$F$-$F(B
$B$/$l$k(B.
..........
$0.058848715846176042$ , $0.00020380318568878926$ ] , [ $List$ , $0.063925582957708782$ , $0.00026123062327715319$ ] , [ $List$ , $0.075483797260236019$ , $0.00043009184219683475$ ] , [ $List$ , $0.085389058362520226$ , $0.00062259645710993009$ ] , [ $List$ , $0.094800203092095747$ , $0.00085197676453212636$ ] , [ $List$ , $0.1124643743927272$ , $0.001422475413813041$ ] , [ $List$ , $0.13147941741224145$ , $0.0022728613274591624$ ] , [ $List$ , $0.15222475922816323$ , $0.0035274022435660929$ ] , [ $List$ , $0.17456638178891035$ , $0.0053196098687267566$ ] , [ $List$ , $0.19560281767103044$ , $0.0074837843683483452$ ] , [ $List$ , $0.2349136621617281$ , $0.012963213138804636$ ] , [ $List$ , $0.27724798215631957$ , $0.021309453311807332$ ] , [ $List$ , $0.32301927231130739$ , $0.033697918471413596$ ] , [ $List$ , $0.36298144245228797$ , $0.047806582612823653$ ] , [ $List$ , $0.40682416150617157$ , $0.06728093428390626$ ] , [ $List$ , $0.49531661779027614$ , $0.12122139733321755$ ] , [ $List$ , $0.577319191041195$ , $0.19123382135485076$ ] , [ $List$ , $0.66518232937340627$ , $0.29009067257088256$ ] , [ $List$ , $0.83898250724819956$ , $0.55682026463112355$ ] , [ $List$ , $0.92597335379970913$ , $0.71313087969680655$ ] , [ $List$ , $1.0064165849354911$ , $0.85177998519206055$ ] , [ $List$ , $1.0467183689036557$ , $0.91145412211964616$ ] , [ $List$ , $1.0845351444477094$ , $0.95675903914962124$ ] , [ $List$ , $1.1035191959241926$ , $0.97435028116126077$ ] , [ $List$ , $1.1239738197801938$ , $0.98864205621250267$ ] , [ $List$ , $1.1350366272041006$ , $0.99411754672915609$ ] , [ $List$ , $1.14059782862615$ , $0.99622480932896185$ ] , [ $List$ , $1.1466780326819648$ , $0.99801217555180666$ ] , [ $List$ , $1.1518918871031776$ , $0.9991011313229109$ ] , [ $List$ , $1.1548094669240425$ , $0.99952695300130912$ ] , [ $List$ , $1.1574591361017637$ , $0.99979730104303988$ ] , [ $List$ , $1.1626173398883621$ , $0.99999976249588263$ ] , [ $List$ , $1.167484562435281$ , $0.99978970359145969$ ] , [ $List$ , $1.1723357744205902$ , $0.99918289320997544$ ] , [ $List$ , $1.1775447829536554$ , $0.99807854960111486$ ] , [ $List$ , $1.1824617391562282$ , $0.99659548150788801$ ] , [ $List$ , $1.1869521986730704$ , $0.99485858038227182$ ] , [ $List$ , $1.1979348243966028$ , $0.98902406922202202$ ] , [ $List$ , $1.2083558624748583$ , $0.98132703485916639$ ] , [ $List$ , $1.2190984883554299$ ,
......
sm1>
@@@.oxmath (Integrate[x/(1-x^3),x]) oxsubmit ;
sm1>@@@.oxmath oxpopcmo ::
[ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ $Log$ , [ $Plus$ , -1 , Class.indeterminate $x$ ] ] ] , [ $Times$ , [ $Rational$ , 1 , 6 ] , [ $Log$ , [ $Plus$ , 1 , Class.indeterminate $x$ , [ $Power$ , Class.indeterminate $x$ , 2 ] ] ] ] ]
sm1>@@@.oxmath ( <<Polyhedra.m ) oxsubmit ;
sm1>@@@.oxmath oxpopcmo ::
Class.indeterminate $$Failed$ $B%U%!%$%k$OFI$_9~$a$J$$(B.
--------- From mathematica to sm1
bash$ pwd
/home/taka/OpenXM/src/ox_math
bash$ uname -a
SunOS tau 5.7 Generic sun4u sparc SUNW,Ultra-5_10
bash$ date
Sun Nov 7 09:03:55 JST 1999
bash$ math
couldn't set locale correctly
Mathematica 3.0 for Solaris
Copyright 1988-97 Wolfram Research, Inc.
-- Terminal graphics initialized --
In[1]:= Install["math2ox"]
couldn't set locale correctly
Out[1]= LinkObject['./math2ox', 1, 1]
In[2]:= OxStart["../bin/ox_sm1"]
Trying to connect port 53613, ip=ffbef06c
connected.
Trying to connect port 53614, ip=ffbef06c
connected.
Socket#18: login!.
password = (otpasswd), 9 bytes.
received = (otpasswd), 9 bytes.
Socket#20: login!.
password = (otpasswd), 9 bytes.
received = (otpasswd), 9 bytes.
sm1>macro package : dr.sm1, 9/26,1995 --- Version 9/8, 1999.
sm1>macro package : module1.sm1, 1994 -- Nov 8, 1998
sm1>---------------------------------------------------
open (localhost)
Out[2]= 0
In[3]:= OxExecute["1 1 add "]
Out[3]= 0
In[4]:= (CMO_STRING[4],[size=8],$1 1 add $),
In[4]:= OxPopString[]
Out[4]= 2
In[5]:= Quit
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
oxSocketSelect0() returns 1, but there is no data. You peer may be killed.
[control] control function_id is -1
Sending the kill signal to the child.
sm1 $B$N(B gb ($B%0%l%V%J4pDl7W;;(B), deRham ( de Rham $B%3%[%b%m%87W;;(B)
$B$r8F$S=P$9Nc(B.
bash$ math
couldn't set locale correctly
Mathematica 3.0 for Solaris
Copyright 1988-97 Wolfram Research, Inc.
-- Terminal graphics initialized --
In[1]:= Install["math2ox"]
couldn't set locale correctly
Out[1]= LinkObject['./math2ox', 1, 1]
In[2]:= OxStart["../lib/sm1/bin/ox_sm1_forAsir"]
Trying to connect port 53620, ip=ffbef05c
connected.
Trying to connect port 53621, ip=ffbef05c
connected.
Socket#18: login!.
password = (otpasswd), 9 bytes.
received = (otpasswd), 9 bytes.
Socket#20: login!.
password = (otpasswd), 9 bytes.
received = (otpasswd), 9 bytes.
sm1>macro package : dr.sm1, 9/26,1995 --- Version 9/8, 1999.
sm1>macro package : module1.sm1, 1994 -- Nov 8, 1998
sm1>cohom.sm1 is the top of an experimental package to compute restrictions
of all degrees based on restall.sm1 and restall_s.sm1
See, http://www.math.kobe-u.ac.jp to get these files of the latest version.
Note that the package b-function.sm1 cannot be used with this package.
r-interface.sm1 (C) N.Takayama, restriction, deRham
hol.sm1, basic package for holonomic systems (C) N.Takayama, 1999, 6/05
rank characteristic ch rrank gb pgb syz genericAnn annfs
sm1>gkz.sm1 generates gkz systems (C) N.Takayama, 1998, 11/8, cf. rrank in hol.sm1
gkz
sm1>appell.sm1 generates Appell hypergeometric differential equations (C) N.Takayama, 1998, 11/8, cf. rank in hol.sm1
appell1 appell4
sm1>resol0.sm1, package to construct schreyer resolutions -- not minimal
(C) N.Takayama, 1999, 5/18. resol0, resol1
complex.sm1 : 1999, 9/28, res-div, res-solv, res-kernel-image, res-dual
In this package, complex is expressed in terms of matrices.
restall.sm1 ... compute all the cohomology groups of the restriction
of a D-module to tt = (t_1,...,t_d) = (0,...,0).
non-Schreyer Version: 19980415 by T.Oaku
usage: [(P1)...] [(t1)...] bfm --> the b-function
[(P1)...] [(t1)...] k0 k1 deg restall --> cohomologies of restriction
[(P1)...] [(t1)...] intbfm --> the b-function for integration
[(P1)...] [(t1)...] k0 k1 deg intall --> cohomologies of integration
restall_s.sm1...compute all the cohomology groups of the restriction
of a D-module to tt = (t_1,...,t_d) = (0,...,0).
Schreyer Version: 19990521 by N.Takayama & T.Oaku
usage: [(P1)...] [(t1)...] k0 k1 deg restall_s -> cohomologies of restriction
[(P1)...] [(t1)...] k0 k1 deg intall_s --> cohomologies of integration
No truncation from below in restall
The variable Schreyer is set to 2.
Loading tower.sm1 in the standard context. You cannot use Schyrer 1. It is controlled from cohom.sm1
SSkan/lib/callsm1.sm1, 1999/6/23.
---------------------------------------------------
open (localhost)
Out[2]= 0
D $B$G$N:8%$%G%"%k(B <x Dx + y Dy -1, (x Dx)^2 + d Dy>
$B$N(B GB $B$r(B weight (x,y,Dx,Dy) = (0,0,1,1) $B$G5a$a$k(B.
In[3]:= OxExecute[" [[(x dx + y dy-2) ( x dx x dx + y dy)] (x,y) [[(dx) 1 (dy) 1]]] gb "]
Out[3]= 0
In[4]:= (CMO_STRING[4],[size=68],$ [[(x dx + y dy-2) ( x dx x dx + y dy)] (x,y) [[(dx) 1 (dy) 1]]] gb $),
In[4]:= OxPopString[]
Out[4]= [ [ x*dx+y*dy-2 , -y^2*dy^2-2*x*dx ] , [ x*dx+y*dy , -y^2*dy^2 ] \
> ]
$B$3$l$,(B GB $B$3$A$i$,(B weight vector
$B$G$N<gIt(B ($BFC@-B?MMBN(B)
H^i( C^2 \setminus V(x^3-y^2) , C) $B$N<!85(B
In[5]:= OxExecute[" [(x^3-y^2) (x,y)] deRham "]
Out[5]= 0
In[6]:= (CMO_STRING[4],[size=26],$ [(x^3-y^2) (x,y)] deRham $),[ [ -3*y*dx^2+2*x*dy , -2*x*dx-3*y*dy+1 ] , [ x , y ] ] bfm
sm1>sm1>b-function is -216*s^3+432*s^2-264*s+48
[ [ -3*y*dx^2+2*x*dy , -2*x*dx-3*y*dy+1 ] , [ x , y ] , 1 , 2 ] restall1_s
Computing a free resolution ...
A free resolution obtained.
0-th cohomology: [ 0 , [ ] ]
sm1>-1-th cohomology: [ 1 , [ ] ]
sm1>-2-th cohomology: [ 2 , [ -1 ] ]
In[6]:= OxPopString[]
Out[6]= [ 1 , 1 , 0 ]
In[7]:= OxClose[]
[control] control function_id is 1024
[control] control_kill
I have closed the connection to an Open XM server.
Out[7]= 0
In[8]:= In[8]:= Sending the kill signal to the child.
In[8]:= Quit
bash$
$B$3$l$O<:GTNc(B.
bash$ math
couldn't set locale correctly
Mathematica 3.0 for Solaris
Copyright 1988-97 Wolfram Research, Inc.
-- Terminal graphics initialized --
In[1]:= Install["../bin/ox_sm1"]
couldn't set locale correctly
sm1 version : 2.991106
sm1 url : http://www.math.kobe-u.ac.jp/KAN
name = ox_sm1
engineByteOrder=0
Interrupt during LinkConnect> abort
??
Your options are:
continue (or c) to continue
exit (or quit) to exit Mathematica
back out (or b) to back out of the MathLink call--the link may die.
Interrupt during LinkConnect> quit
--------------- sm1 $B$N(B array $B$r$"$i$o$9(B [ ] $B$r(B { } $B$KJQ$($F(B
--------------- sm1 $B$N=PNO$r(B ToExpression $B$GFI$_9~$`Nc(B
[tau]bash
bash$ cd OpenXM
bash$ cd src/ox_math
bash$ math
couldn't set locale correctly
Mathematica 3.0 for Solaris
Copyright 1988-97 Wolfram Research, Inc.
-- Motif graphics initialized --
In[1]:= Install["math2ox"]
couldn't set locale correctly
Out[1]= LinkObject['./math2ox', 1, 1]
In[2]:= OxStart["/home/taka/OpenXM/lib/sm1/bin/ox_sm1_forAsir"]
Trying to connect port 53755, ip=ffbef02c
connected.
Trying to connect port 53756, ip=ffbef02c
connected.
Socket#18: login!.
password = (otpasswd), 9 bytes.
received = (otpasswd), 9 bytes.
Socket#20: login!.
password = (otpasswd), 9 bytes.
received = (otpasswd), 9 bytes.
sm1>macro package : dr.sm1, 9/26,1995 --- Version 11/8, 1999.
sm1>macro package : module1.sm1, 1994 -- Nov 8, 1998
sm1>cohom.sm1 is the top of an experimental package to compute restrictions
$B>JN,(B
Loading tower.sm1 in the standard context. You cannot use Schyrer 1. It is controlled from cohom.sm1
SSkan/lib/callsm1.sm1, 1999/6/23.
---------------------------------------------------
open (localhost)
Out[2]= 0
In[10]:= OxExecute[" [(LeftBracket) ({)] system_variable [(RightBracket) (})] system_variable "]
[ $B$r(B { $B$X(B, ] $B$r(B } $B$X(B.
Out[10]= 0
In[11]:= (CMO_STRING[4],[size=74],$ [(LeftBracket) ({)] system_variable [(RightBracket) (})] system_variable $),
In[11]:= OxExecute[" [[(x dx + y dy + 1) (x dx x dx - y dy)] (x,y)
[[(dx) 1 (dy) 1]]] gb "]
$B%0%l%V%J4pDl$r(B Q<x,y,dx,dy> $B$G(B. weight $B$O(B dx=1, dy=1.
Out[11]= 0
In[12]:= (CMO_STRING[4],[size=81],$ [[(x dx + y dy + 1) (x dx x dx - y dy)] (x,y) [[(dx) 1 (dy) 1]]] gb $),
In[12]:= ans = OxPopString[]
Out[12]= {{x*dx+y*dy+1 , -y^2*dy^2+x*dx-y*dy} , {x*dx+y*dy , -y^2*dy^2}}
$B%0%l%V%J4pDl$,J8;zNs$G$+$($k(B.
$B:G=i$,(B Groebner, 2 $BHVL\$,(B weight dx=1, dy=1 $B$G$N<gMWIt(B.
In[13]:= ans2 = ToExpression[ans]
Mathematica $B$NB?9`<0$KJQ49(B.
2 2 2 2
Out[13]= {{1 + dx x + dy y, dx x - dy y - dy y }, {dx x + dy y, -(dy y )}}
In[17]:= OxExecute[" [[(x dx x dx + y dy y dy -4) (x dx y dy -1)] (x,y)
[[(dx) 1]]] gb "]
dx $B$N(B weight $B$r(B 1 $B$K$7$F(B, $B%0%l%V%J4pDl$r7W;;(B.
****** dx $B$N(B $B>C5nK!(B
Out[17]= 0
In[18]:= (CMO_STRING[4],[size=79],$ [[(x dx x dx + y dy y dy -4) (x dx y dy -1)] (x,y) [[(dx) 1]]] gb $),
In[18]:= ans = OxPopString[]
Out[18]= {{x*dx+y^3*dy^3+3*y^2*dy^2-3*y*dy ,\
> -y^4*dy^4-6*y^3*dy^3-3*y^2*dy^2+3*y*dy-1} , {x*dx ,\
> -y^4*dy^4-6*y^3*dy^3-3*y^2*dy^2+3*y*dy-1}}
dx $B$r4^$^$J$$HyJ,:nMQAG$,$"$k$N$KCm0U(B!! $B$D$^$j(B dy $B$K$D$$$F$N(B
$B>oHyJ,J}Dx<0$,$G$?(B.
In[19]:= ToExpression[ans]
2 2 3 3
Out[19]= {{dx x - 3 dy y + 3 dy y + dy y ,
2 2 3 3 4 4
> -1 + 3 dy y - 3 dy y - 6 dy y - dy y },
2 2 3 3 4 4
> {dx x, -1 + 3 dy y - 3 dy y - 6 dy y - dy y }}
In[20]:=
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to samplelog-sm1.txt CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / ox_math / documents