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Annotation of OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex, Revision 1.1

1.1     ! takayama    1: % $OpenXM$
        !             2: %% xdvi -paper a4r rims-2003-12-16-ja-ohp
        !             3: %% dvips -f -t landscape  rims-2003-12-16-ja-ohp| psnup -8 -r | lpr -Pxerox6
        !             4: \documentclass{slides}
        !             5: \usepackage{color}
        !             6: \usepackage{rgb}
        !             7: \usepackage{epsfig}
        !             8: %\def\color#1{ }
        !             9: %\def\epsffile#1{ Picture File: #1 }
        !            10: %\def\epsfxsize{ }
        !            11: %% Sample:
        !            12: %% \epsfxsize=17cm
        !            13: %% \epsffile{cz.ps}
        !            14:
        !            15: \textwidth 9.2in
        !            16: \textheight 7.2in
        !            17: \columnsep 0.33in
        !            18: \topmargin -1in
        !            19:
        !            20: \def\nnn{ {\color{red} $\bullet$}\ }    %% $B;v<B(B
        !            21: \def\eee{ {\color{magenta} Example}:\ } %% $BNc(B
        !            22: \def\ttt{ {\color{red} $\bullet$}\ }   %% $BDjM}(B
        !            23:
        !            24: \def\pagetitle#1{ \fbox{{\color{magenta} #1 }}}
        !            25:
        !            26: \newenvironment{FRAME}{\begin{trivlist}\item[]
        !            27:   \hrule
        !            28:   \hbox to \linewidth\bgroup
        !            29:   \advance\linewidth by -30pt
        !            30:   \hsize=\linewidth
        !            31:   \vrule\hfill
        !            32:   \vbox\bgroup
        !            33:     \vskip15pt
        !            34:     \def\thempfootnote{\arabic{mpfootnote}}
        !            35:     \begin{minipage}{\linewidth}}{%
        !            36:     \end{minipage}\vskip15pt
        !            37:   \egroup\hfill\vrule
        !            38:  \egroup\hrule
        !            39: \end{trivlist}}
        !            40:
        !            41: \begin{document}
        !            42: \noindent
        !            43: \begin{center}
        !            44: {\color{magenta} OpenXM $B$N?7%5!<%P(B, $B?7%W%m%H%3%k(B}
        !            45: \end{center}
        !            46: %% 2003, 12/16 (Tue),
        !            47: \begin{center}
        !            48: {\color{SlateGray} OpenXM $B3+H/%0%k!<%W(B (committers):  http://www.openxm.org }
        !            49: \end{center}
        !            50: \begin{enumerate}
        !            51: \item $B?7$7$$%5!<%P(B ntl
        !            52: \item $B?7$7$$%5!<%P(B polymake $B$H(B oxshell.
        !            53: \item OX-RFC 103 ( 100, 101 $BJd0d(B)
        !            54: \item OX-RFC 102 --- $BK\3JE*$J%5!<%P4VDL?.(B
        !            55: \end{enumerate}
        !            56: \newpage
        !            57:
        !            58: \noindent  \quad \\
        !            59: \nnn $B?t3X$G$NJBNs7W;;(B,  \\
        !            60: \nnn $B?t3X%=%U%H%&%(%"$NE}9g2=(B $B$^$?$O(B Conglomerate $B2=(B (A.Solomon) \\
        !            61: \nnn $B?t3XE*CN<1$N%^%M!<%8%a%s%H(B (Mathematical Knowledge Management) \\
        !            62: \nnn $B<B:]$K?t3X$N8&5f$d?t3X$N1~MQ$K;H$($k%Q%C%1!<%8$N3+H/(B
        !            63:
        !            64: \noindent  \quad \\
        !            65: \nnn OpenXM 1.1.1 (January 24, 2000): $B:G=i$N<B83HG(B. \\
        !            66: \nnn OpenXM 1.1.2 (March 20, 2000): $B$H$j$"$($:;H$($kHG(B. \\
        !            67: \nnn OpenXM 1.1.3 (September 26, 2000): 1.1 $B7O$N:G=*HG(B. OpenXM RFC 100 $B7A<0(B
        !            68:    $B$N%W%m%;%9LZ(B. 1077 $B8D$N?t3X4X?t$rDs6!(B.
        !            69:    $BDs6!$7$F$$$k%5!<%P$O(B {\tt ox\_asir}, {\tt ox\_sm1},
        !            70:    {\tt ox\_phc}, {\tt ox\_gnuplot}, {\tt ox\_m2}, {\tt ox\_tigers},
        !            71:    {\tt ox\_math}(ematica), {\tt OMproxy}. \\
        !            72: \nnn OpenXM 1.2.1 (March 2, 2002): Cygwin (Windows) $B$X$NBP1~3+;O(B.
        !            73:        $B%^%K%e%"%k<+F0@8@.(B(gentexi)$B$J$I(B. \\
        !            74: \nnn OpenXM 1.2.2 (May 13, 2003):  RFC 103 ($BItJ,E*(B), autoconf\\
        !            75: (\nnn) Digital formula book, OpenMath, tfb, CD (hypergeo*, weylalgebra*, intpath*),
        !            76:  $B?tCM7W;;(B.
        !            77:
        !            78: \newpage
        !            79:
        !            80: \noindent
        !            81: \pagetitle{ 1. {\color{blue} $B?7$7$$%5!<%P(B ntl}}
        !            82: http://www.shoup.net/ntl,
        !            83: {\footnotesize
        !            84: NTL is a high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors,
        !            85: matrices, and polynomials over the integers and over finite fields.
        !            86: }
        !            87:
        !            88: {\color{blue} ox\_toolkit $+$ NTL $B%i%$%V%i%j(B}
        !            89: $\Rightarrow$ {\color{red} ox\_ntl}
        !            90: {\footnotesize
        !            91: \begin{verbatim}
        !            92: [1145]= ox_launch_nox(0,"/home/taka/OX4/OpenXM/bin/ox_ntl");
        !            93: [1028] F=ntl.ex_data(4)$
        !            94: [1029] F = F * subst(F, x, x + 1)$
        !            95: [1030] ntl.factor(PID, F);  /* NTL $B$N(B knapsac factorizer */
        !            96: [[1,1],
        !            97:  [x^16+16*x^15-16*x^14-1344*x^13-4080*x^12+32576*x^11+157376*x^10-255232*x^9-2062624*x^8-249088*x^7+10702080*x^6+9126912*x^5-18643712*x^4-24167424*x^3+2712576*x^2+10653696*x+2324736,1],
        !            98: [x^16-136*x^14+6476*x^12-141912*x^10+1513334*x^8-7453176*x^6+13950764*x^4-5596840*x^2+46225,1]]
        !            99: \end{verbatim}
        !           100: }
        !           101:
        !           102: $B<BAu$K$h$jL@$i$+$K$J$C$?$3$H(B: \\
        !           103: ox\_toolkit $B$NLdBjE@$N2~A1(B, LLL $B$r$h$V$?$a$K(B CMO array $B$bI,MW(B.
        !           104:
        !           105: \rightline{$B3+H/(B: $B4d:,(B ($B>.86(B)}
        !           106: \newpage
        !           107:
        !           108:
        !           109: \noindent
        !           110: \pagetitle{2. {\color{blue} $B?7$7$$%5!<%P(B polymake $B$H(B oxshell}}
        !           111:
        !           112: {\color{red} Polymake } : $BB?LLBNMQ%=%U%H%&%(%"(B. \\
        !           113: {\tt http://www.math.tu-berlin.de/polymake},
        !           114: by Ewgenji Gawrilow, Michael Joswig. \\
        !           115: % polemake logo
        !           116: Facets, Convex hull, Triangulation, $B9=@.(B, polytope data,
        !           117: Visualization by JavaView and Povray.
        !           118:
        !           119: \newpage
        !           120: \eee
        !           121: $BE@(B $(1,0,0)$, $(1,1,0)$, $(1,0,1)$, $(1,1,1)$ $B>e$N(B cone $B$N(B facet $B$r5a$a$h(B. \\
        !           122: {\tt polymake} $B$G$O$D$.$h$&$JF~NO%U%!%$%k(B {\tt square.poly} $B$r$^$::n@.$9$k(B.
        !           123:
        !           124: {\footnotesize \color{blue} \begin{verbatim}
        !           125: POINTS
        !           126: 1 0 0
        !           127: 1 1 0
        !           128: 1 0 1
        !           129: 1 1 1
        !           130: \end{verbatim} }
        !           131:
        !           132: {\color{red} \verb@ polymake square.poly FACETS @ } \\
        !           133: $B7k2L(B:
        !           134: {\footnotesize \begin{verbatim}
        !           135: FACETS
        !           136: 0 0 1
        !           137: 0 1 0
        !           138: 1 0 -1
        !           139: 1 -1 0
        !           140: \end{verbatim} }
        !           141:
        !           142: \newpage
        !           143:
        !           144: \pagetitle{ Polymake $B$N(B OX 100, 101 $B%5!<%P2=$G2?$,LdBj$G$"$C$?$+(B?}
        !           145: %todo OX 100 $B$N35N,$,I,MW$+(B?
        !           146:
        !           147: $B?7$7$$(B OX RFC 100 $B=`5r$N%5!<%P$r:n$k>l9g$K$O(B
        !           148: $B%?!<%2%C%H$H$9$k?t3X%=%U%H%&%(%"%7%9%F%`$N%=!<%9%3!<%I$K(B OX RFC 100 $BBP1~ItJ,(B
        !           149: $B$r2C$($k:n6H$r$7$J$$$H$$$1$J$$(B.
        !           150: $B$3$N:n6H$O%=!<%9%3!<%I$NM}2r$H$+$J$j$N<j4V$rMW$9$k(B.
        !           151: C++ $B$G=q$+$l$?(B polymake $B$N%=!<%9$O@hC<E*$J(B C++ $B$N5!G=$r(B
        !           152: $BMxMQ$7$F$*$j%3%s%Q%$%k$,MF0W$G$J$$(B.
        !           153:
        !           154:
        !           155: Polymake $B$O$"$i$+$8$a%U%!%$%k$K%3%^%s%I$d%G!<%?$r=q$-=P$7$F$*$/$3$H$K$h$j(B
        !           156: unix $B$N(B shell ($B$d(B Windows $B$N%3%^%s%I%W%m%s%W%H(B)
        !           157: $B$+$iMxMQ2DG=$J$h$&$K:n$i$l$F$$$k(B: {\color{red} $B%P%C%A=hM}BP1~%"%W%j%1!<%7%g%s(B}.
        !           158: $B%5!<%P$H$NDL?.$NIQEY$OLdBj$K$h$k$,$"$kDxEYBg$-$$7W;;$N>l9g$ODL?.;~4V$OL5;k$G$-$k(B.
        !           159: Polymake $B$OBPOCE*MxMQ$OA[Dj$7$F$*$i$:%5!<%P$N7W;;$rCfCG$7$F(B, $B:FEY3+;O$9$k$J$I$NI,MW$,$J$$(B.
        !           160: $\Rightarrow$ {\tt system} $B$N6/2=HG(B {\color{blue} oxshell}
        !           161: \newpage
        !           162:
        !           163: \pagetitle{ Oxshell $B$H$O(B }
        !           164: Oxshell $B$O>e5-$N$h$&$J%P%C%A=hM}BP1~%"%W%j%1!<%7%g%s$r%=!<%9%3!<%I$N2~JQ$J$/(B
        !           165: OX RFC 100 $B=`5r$K$9$k$?$a$N$$$o$f$k%i%C%Q!<7?$N(B OX $B%5!<%P$r=q$/$?$a$NJd=u5!G=$r(B
        !           166: $BDs6!$9$k(B sm1 $B$X$NAH$_9~$_4X?t$G$"$k(B.
        !           167:
        !           168: Oxshell $B$rMQ$$$F(B OX $B%5!<%P$r<B8=$9$k$N$,E,@Z$J?t3X%=%U%H%&%(%"$O0J2<$N$h$&$JFCD'$r$b$D$b$N$G$"$m$&(B. \\
        !           169: \nnn $B%P%C%A=hM}BP1~%"%W%j%1!<%7%g%s$G$"$k(B. \\
        !           170: \nnn $B%=!<%9%3!<%I$NJQ99$,$G$-$J$$$+:$Fq(B. \\
        !           171: \nnn $B%5!<%P$H$NDL?.$,IQHK$K$*$-$J$$(B. \\
        !           172: \nnn $B%5!<%P$N7W;;$rCfCG$7$F(B, $B:FEY3+;O$9$k$J$I$NI,MW$,$J$$(B. \\
        !           173: \nnn Windows $B$G$b(B unix $B$G$bF0$+$7$?$$(B.  \\
        !           174:
        !           175: \pagetitle{ OX RFC 100 $B$NI|=,(B}
        !           176:
        !           177: $B%/%i%$%"%s%H(B-$B%5!<%P%b%G%k(B.
        !           178: $B%5!<%P$O(B stackmachine.
        !           179: (1) $B%9%?%C%/%^%7%s$X$N%a%C%;!<%8$rAw$k$3$H$K$h$j7W;;$,?J9T$9$k(B.
        !           180: (2) $B7W;;$NCfCG$J$I$N%a%C%;!<%8$b$"$k(B.
        !           181: (3) $B%5!<%P$O%(%s%8%s$H%3%s%H%m!<%k%W%m%;%9$h$j$J$k(B.
        !           182:
        !           183: \newpage
        !           184:
        !           185: \noindent OX RFC 100 $B$K$O(B\underline{$B%U%!%$%k$N35G0$,$J$$(B}. $B$7$?$,$C$F(B, \\
        !           186: \verb@ polymake $B%U%!%$%kL>(B $BF0:n(B @ \\
        !           187: $B$_$?$$$J%W%m%0%i%`$O(B OX $B%9%?%C%/%^%7%s$N>e$N%G!<%?$r%U%!%$%k$K=q$-=P$7$F$+$i(B
        !           188: $B<B9T$7$F(B, $B$=$l$+$i$^$?%9%?%C%/%^%7%s$N>e$N%G!<%?$KJQ49$7$J$$$H$$$1$J$$(B.
        !           189: ($BC1=c;E;v(B, $B$7$+$7(B,  ZPG $B$N6KCW(B; unix $B$H(B windows $B0c$$(B,
        !           190: /bin/sh $B$NB8:_(B, $B%W%m%0%i%`$,BgJQFI$_$K$/$/J]<i$b$7$K$/$$(B)
        !           191:
        !           192: {\tt oxshell} $B$G$O$3$N;E;v$O<!$N(B 1 $B9T$G=q$/(B. \\
        !           193: {\color{red} \verb@[(polymake) (stringInOut://$B%9%?%C%/%^%7%sJQ?tL>(B.poly) $BF0:n(B] oxshell@}\\
        !           194: $B%9%?%C%/%^%7%s$NJQ?t$r%U%!%$%k$r$_$J$7$F$$$k(B.
        !           195:
        !           196: $B$3$N$h$&$J9M$(J}$O(B, $B$J$K$b?7$7$$$b$N$G$O$J$$(B. \\
        !           197: $BNc(B: Java $B$N(B io.StringReader ( io.InputStreamReader $B$NBe$o$j(B). \\
        !           198: $BNc(B: $B%9%/%j%W%H8@8l$G$"$k(B Python
        !           199:   \verb@ x=os.popen("abc","r").read(); @
        !           200:
        !           201: \noindent
        !           202: {\color{blue} $B?7$7$$ItJ,(B}:
        !           203: $B$3$N9M$($r?t3X%=%U%H%&%(%"$NE}9g2=$N$?$a$K;H$&$?$a$N<BAu$OB8:_$7$F$$$J$+$C$?(B.
        !           204: $B$3$l$,(B oxshell $B%3%^%s%I$NF3F~$K$h$C$F2r7h$5$l$kE@$N0l$D$G$"$k(B.
        !           205: $B9M$(J}$,@0M}$5$l%W%m%0%i%`$NJ]<i@-$,BgJQ$h$/$J$j(B, $B$^$??7$7$$%P%C%A7?%"%W%j%1!<%7%g%s$N(BOX $B%5!<%P2=$,3Z$K$J$C$?(B.
        !           206:
        !           207: \newpage
        !           208:
        !           209: \eee
        !           210: $BJ8;zNs(B {\tt S} $B$K3JG<$5$l$?C18l(B dog, cat, lion $B$r(B unix $B$N%D!<%k(B sort $B$G(B
        !           211: $BJB$YJQ$($k$K$O<!$N$h$&$K=q$/(B.
        !           212: $BF~NO$O(B oxshell $B$r<B9T$7$F$$$k%9%?%C%/%^%7%s$NJQ?t(B {\tt S} $B$K3JG<$5$l$F$$$k(B.
        !           213:
        !           214: \begin{verbatim}
        !           215: [1163]:= S="dog\ncat\nlion\n";
        !           216: [1164]:= oxshell.set_value("S",S);
        !           217: [1165]:= T=oxshell.oxshell(["sort","stringIn://S"]);
        !           218: [cat
        !           219: dog
        !           220: lion
        !           221: ,]
        !           222: \end{verbatim}
        !           223: \newpage
        !           224:
        !           225: \pagetitle{ oxshell.facets() $B$N<BAu(B, $B?t3X4X?t$N<BAuNc(B }
        !           226:
        !           227: \nnn $B%G!<%?JQ49$K$O(B tfb/2 ($BEDB<(B)format $B$rMxMQ(B, OpenMath $B%"!<%-%F%/%A%c$rMxMQ(B.
        !           228: {\color{blue}$B@.2L(B}: $B$=$NM-8z@-$r<B>Z$G$-$?(B.)
        !           229: %% $B$3$l$b?7$7$$E@$G$"$m$&(B.
        !           230: {\footnotesize \begin{verbatim}
        !           231: [ $polymake.data(polymake.POINTS([[1,0,0],[1,1,0],[1,0,1],[1,1,1]]),
        !           232:    polymake.FACETS([[0,0,1],[0,1,0],[1,0,-1],[1,-1,0]]),
        !           233:    polymake.AFFINE_HULL())$
        !           234:   CMO tree expression of the data above
        !           235:   Outputs to stdout and stderr ]
        !           236: \end{verbatim} }
        !           237:
        !           238:
        !           239: {\color{red} taka\_ahg.b(A,Idx)}(OpenXM/src/asir-contrib/packages/src/taka\_ahg.rr)
        !           240: oxshell $B$K$h$k(B polymake $B8F$S=P$75!G=$rMQ$$$??t3X4X?t(B.
        !           241: $B$3$N4X?t$O(B $B9TNs(B {\tt A} $B$KIU?o$7$?(B $BJ}8~(B {\tt Idx} $B$N$"$k(B $b$ $B4X?t$r7W;;$9$k(B.
        !           242: $B$3$l$O(B {\tt A} $B$NDj5A$9$k(B cone $B$N%U%!%;%C%H$r$"$i$o$90l<!<0$N@Q$GI=8=$5$l$k$3$H$,(B,
        !           243: $BCN$i$l$F$$$k(B
        !           244: (Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki; Hypergeometric polynomials and integer programming. Compositio Math. 115 (1999), no. 2, 185--204
        !           245: $B$*$h$S(B
        !           246: Saito, Mutsumi; Parameter shift in normal generalized hypergeometric systems. Tohoku Math. J. (2) 44 (1992), no. 4, 523--534
        !           247: $B$r$_$h(B.)
        !           248:
        !           249: \newpage
        !           250:
        !           251: {\footnotesize
        !           252: \begin{verbatim}
        !           253: [1163]:= load("oxshell.rr");
        !           254: [1164]:= load("taka_ahg.rr");
        !           255: [1165]:=  A=[[1,0,0],[1,1,0],[1,0,1],[1,1,1],[1,2,0]];
        !           256: [1166]:= fctr(taka_ahg.b(A,4,[s1,s2,s3]));
        !           257: [[1,1],[s1+2*s2,2],[s1+2*s2-1,1]]
        !           258: \end{verbatim}
        !           259:
        !           260: \begin{verbatim}
        !           261: def b(A,Idx,V) {
        !           262:   F = oxshell.facets(A);    /* Computing all the facets by polymake server.*/
        !           263:   F = F[1];                 /* F is the set of the facets */
        !           264:   P = A[Idx];
        !           265:   Nfacets = length(F);
        !           266:   F = toPrimitive2(P,F);   /* Translate into primitive supporting function */
        !           267:   Bf = 1;
        !           268:   for (I=0; I<Nfacets; I++) {
        !           269:     H = matrix_inner_product(P,F[I]);
        !           270:     if (H != 0) {
        !           271:       B = matrix_inner_product(P,V);
        !           272:       for (J=0; J<H; J++) {
        !           273:         Bf = Bf*(B-J);  /* See the papers above. */
        !           274:       }
        !           275:     }
        !           276:   }
        !           277:   return(Bf);
        !           278: }
        !           279: \end{verbatim}
        !           280: }
        !           281:
        !           282:
        !           283: \rightline{$B3+H/(B: $B9b;3(B}
        !           284: \newpage
        !           285:
        !           286:
        !           287: \noindent
        !           288: \pagetitle{3. {\color{blue} OX-RFC 103 ( 100, 101 $BJd0d(B)}}
        !           289:
        !           290: $B$3$N(B RFC $B$O(B OpenXM RFC 100 ($B$*$h$S(B 101) $B$N<BAu$K$h$jL@$i$+$K$J$C$?<o!9$NLdBjE@$r$b$H$K(B
        !           291: RFC 100 $B%W%m%H%3%k$X$N4v$D$+$NDI2C$rDs0F$9$k(B.
        !           292:
        !           293: \nnn $B%U%!%$%k$X$NFI$_=q$-(B \\
        !           294: \nnn $B?7$7$$(B CMO \\
        !           295: \nnn  $B%(%s%8%sG'>Z<jB3$-(B \\
        !           296: \nnn $BCfCG$*$h$SJQ?t$NEAGE(B \\
        !           297: 1. $B<+J,$N;R6!%W%m%;%9$r$9$Y$F%j%9%H$9$k(B
        !           298:   (asir$B$N>l9g(B:{\tt ox\_get\_serverinfo()}) \\
        !           299: 2. $B;R6!%W%m%;%9$K=gHV$K(B OpenXM-RFC 100 $B$NCfCG%a%C%;!<%8$rAw$k(B.
        !           300:
        !           301: \noindent
        !           302: {\color{red} ox103\_set\_shared\_variable(} CMO string {\tt Name}, CMO object {\tt
        !           303: value}{\tt )}
        !           304: $B%(%s%8%s%9%?%C%/%^%7%s$NJQ?t(B {\tt Name} $B$KCM(B
        !           305: {\tt value} $B$,@_Dj(B,
        !           306: $B$5$i$K;R$I$b$N%W%m%;%9$9$Y$F$N%(%s%8%s4X?t(B
        !           307:  {\tt ox103\_set\_shared\_variable}
        !           308: $B$r$h$V(B.
        !           309:
        !           310: \rightline{$B3+H/(B: $B9b;3(B}
        !           311: \newpage
        !           312:
        !           313: \noindent
        !           314: \pagetitle{4. {\color{blue} OX-RFC 102 --- $BK\3JE*$J%5!<%P4VDL?.$rMQ$$$?J,;67W;;(B}}
        !           315:
        !           316:
        !           317: \rightline{$B3+H/(B: $BLnO$(B}
        !           318: \newpage
        !           319:
        !           320: \end{document}
        !           321:
        !           322: %%$Id: rims-2003-12-16-ja-ohp.tex,v 1.4 2003/12/11 05:40:59 taka Exp $ at misc-2003/12/RIMS