=================================================================== RCS file: /home/cvs/OpenXM/src/ox_math/documents/samplelog-sm1.txt,v retrieving revision 1.1 retrieving revision 1.3 diff -u -p -r1.1 -r1.3 --- OpenXM/src/ox_math/documents/samplelog-sm1.txt 1999/11/05 03:00:34 1.1 +++ OpenXM/src/ox_math/documents/samplelog-sm1.txt 1999/11/08 00:36:56 1.3 @@ -1,4 +1,4 @@ -%% $OpenXM$ +%% $OpenXM: OpenXM/src/ox_math/documents/samplelog-sm1.txt,v 1.2 1999/11/07 00:19:44 takayama Exp $ samplelog-sm1.txt : sm1 から, ox_math を呼び出す例. 例題は, Mathematica Book (S.Wolfram) A Tour of Mathematica より とった. @@ -74,14 +74,316 @@ 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: samplelog-sm1.txt,v $ -[ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ Revision 1.1 1999/11/05 03:00:34 takayama -[ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ A sample log of using ox_math from kan/sm1. +[ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ Revision 1.3 1999/11/08 00:36:56 takayama +[ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ An example of computation of Grobner basis in D is given. +[ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ Here, actual computation is done on ox_sm1 and Mathematica is used as +[ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ a front-end. The last example is the elimination in D. [ $Plus$ , [ $Times$ , -1 , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $ArcTan$ , [ $Times$ , [ $Power$ , 3 , [ $Rational$ , -1 , 2 ] ] , [ $Plus$ , 1 , [ $Times$ , 2 , Class.indeterminate $x$ ] ] ] ] ] , [ $Times$ , [ $Rational$ , -1 , 3 ] , [ , [ $Plus$ , -1 , Class.indeterminate $x$ ] ] ] , [ $Times$ , [ $Rational$ , 1 , 6 ] , [ $Log: samplelog-sm1.txt,v $ -[ $Plus$ , [ $Times$ , -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 ] , [ Revision 1.1 1999/11/05 03:00:34 takayama -[ $Plus$ , [ $Times$ , -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 ] , [ A sample log of using ox_math from kan/sm1. +[ $Plus$ , [ $Times$ , -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 ] , [ Revision 1.3 1999/11/08 00:36:56 takayama +[ $Plus$ , [ $Times$ , -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 ] , [ An example of computation of Grobner basis in D is given. +[ $Plus$ , [ $Times$ , -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 ] , [ Here, actual computation is done on ox_sm1 and Mathematica is used as +[ $Plus$ , [ $Times$ , -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 ] , [ a front-end. The last example is the elimination in D. [ $Plus$ , [ $Times$ , -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 ] , [ , [ $Plus$ , 1 , Class.indeterminate $x$ , [ $Power$ , Class.indeterminate $x$ , 2 ] ] ] ] ] sm1>@@@.oxmath ( <@@@.oxmath oxpopcmo :: Class.indeterminate $$Failed$ ファイルは読み込めない. + +--------- 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 $), +In[4]:= OxPopString[] + +Out[4]= 2 + +In[5]:= Quit +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. +oxSocketSelect0() returns 1, but there is no data. You peer may be killed. + +[control] control function_id is -1 +Sending the kill signal to the child. + +sm1 の gb (グレブナ基底計算), deRham ( de Rham コホモロジ計算) +を呼び出す例. + +bash$ 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 での左イデアル + の GB を weight (x,y,Dx,Dy) = (0,0,1,1) で求める. + +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 $), +In[4]:= OxPopString[] + +Out[4]= [ [ x*dx+y*dy-2 , -y^2*dy^2-2*x*dx ] , [ x*dx+y*dy , -y^2*dy^2 ] \ + +> ] + これが GB こちらが weight vector + での主部 (特性多様体) + + H^i( C^2 \setminus V(x^3-y^2) , C) の次元 +In[5]:= OxExecute[" [(x^3-y^2) (x,y)] deRham "] + +Out[5]= 0 + +In[6]:= (CMO_STRING[4],[size=26],$ [(x^3-y^2) (x,y)] deRham $),[ [ -3*y*dx^2+2*x*dy , -2*x*dx-3*y*dy+1 ] , [ x , y ] ] bfm +sm1>sm1>b-function is -216*s^3+432*s^2-264*s+48 +[ [ -3*y*dx^2+2*x*dy , -2*x*dx-3*y*dy+1 ] , [ x , y ] , 1 , 2 ] restall1_s +Computing a free resolution ... +A free resolution obtained. +0-th cohomology: [ 0 , [ ] ] +sm1>-1-th cohomology: [ 1 , [ ] ] +sm1>-2-th cohomology: [ 2 , [ -1 ] ] + +In[6]:= OxPopString[] + +Out[6]= [ 1 , 1 , 0 ] + +In[7]:= OxClose[] + +[control] control function_id is 1024 +[control] control_kill + +I have closed the connection to an Open XM server. + +Out[7]= 0 + +In[8]:= In[8]:= Sending the kill signal to the child. + +In[8]:= Quit +bash$ + + +これは失敗例. +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 の array をあらわす [ ] を { } に変えて +--------------- sm1 の出力を ToExpression で読み込む例 +[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 + 省略 +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 "] + [ を { へ, ] を } へ. + +Out[10]= 0 + +In[11]:= (CMO_STRING[4],[size=74],$ [(LeftBracket) ({)] system_variable [(RightBracket) (})] system_variable $), +In[11]:= OxExecute[" [[(x dx + y dy + 1) (x dx x dx - y dy)] (x,y) + [[(dx) 1 (dy) 1]]] gb "] + グレブナ基底を Q で. weight は dx=1, dy=1. + +Out[11]= 0 + +In[12]:= (CMO_STRING[4],[size=81],$ [[(x dx + y dy + 1) (x dx x dx - y dy)] (x,y) [[(dx) 1 (dy) 1]]] gb $), +In[12]:= ans = OxPopString[] + +Out[12]= {{x*dx+y*dy+1 , -y^2*dy^2+x*dx-y*dy} , {x*dx+y*dy , -y^2*dy^2}} + グレブナ基底が文字列でかえる. + 最初が Groebner, 2 番目が weight dx=1, dy=1 での主要部. + +In[13]:= ans2 = ToExpression[ans] + Mathematica の多項式に変換. + 2 2 2 2 +Out[13]= {{1 + dx x + dy y, dx x - dy y - dy y }, {dx x + dy y, -(dy y )}} + + +In[17]:= OxExecute[" [[(x dx x dx + y dy y dy -4) (x dx y dy -1)] (x,y) + [[(dx) 1]]] gb "] + + dx の weight を 1 にして, グレブナ基底を計算. + ****** dx の 消去法 + +Out[17]= 0 + +In[18]:= (CMO_STRING[4],[size=79],$ [[(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 を含まない微分作用素があるのに注意!! つまり dy についての + 常微分方程式がでた. + +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]:=