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Annotation of OpenXM/doc/Papers/rims2003-noro-ohp.tex, Revision 1.1

1.1     ! noro        1: \documentclass{slides}
        !             2: %\documentclass[pdf,distiller,slideColor,colorBG,azure]{prosper}
        !             3: \usepackage{color}
        !             4: \usepackage{rgb}
        !             5: \usepackage{graphicx}
        !             6: \usepackage{epsfig}
        !             7: \newcommand{\qed}{$\Box$}
        !             8: \newcommand{\mred}[1]{\smash{\mathop{\hbox{\rightarrowfill}}\limits_{\scriptstyle #1}}}
        !             9: \newcommand{\tmred}[1]{\smash{\mathop{\hbox{\rightarrowfill}}\limits_{\scriptstyle #1}\limits^{\scriptstyle *}}}
        !            10: \newtheorem{prop}{\redc $BL?Bj(B}
        !            11: \def\gr{Gr\"obner basis }
        !            12: \def\st{\, s.t. \,}
        !            13: \def\ni{\noindent}
        !            14: \def\init{{\rm in}}
        !            15: \def\Q{{\bf Q}}
        !            16: \def\Spoly{{\rm Spoly}}
        !            17: \def\Span{{\rm Span}}
        !            18: \def\Supp{{\rm Supp}}
        !            19: \def\StdMono{{\rm StdMono}}
        !            20: \def\Im{{\rm Im}}
        !            21: \def\Ker{{\rm Ker}}
        !            22: \def\NF{{\rm NF}}
        !            23: \def\HT{{\rm HT}}
        !            24: \def\LT{{\rm LT}}
        !            25: \def\ini{{\rm in}}
        !            26: \def\Id#1{\langle #1 \rangle}
        !            27: \def\ve{\vfill\eject}
        !            28: \textwidth 9.2in
        !            29: \textheight 7.2in
        !            30: \columnsep 0.33in
        !            31: \topmargin -1in
        !            32: \def\tc{\color{orange}}
        !            33: \def\fbc{\bf\color{orange}}
        !            34: \def\itc{\color{LimeGreen}}
        !            35: %\def\itc{\color{DarkGreen}}
        !            36: %\def\urlc{\bf\color{DarkGreen}}
        !            37: \def\urlc{\bf\color{LimeGreen}}
        !            38: \def\goldc{\color{goldenrod3}}
        !            39: \def\redc{\color{orange}}
        !            40: \def\vs{\vskip 1cm}
        !            41: \def\vsh{\vskip 0.5cm}
        !            42:
        !            43: \title{\bf Risa/Asir $B>e$N?7%0%l%V%J!<4pDl7W;;%Q%C%1!<%8$K$D$$$F(B}
        !            44:
        !            45: %\slideCaption{Risa/Asir $B>e$N?7%0%l%V%J!<4pDl7W;;%Q%C%1!<%8$K$D$$$F(B}
        !            46: \author{{\bf\Large $BLnO$(B $B@59T(B\\ $B?@8MBg3XM}3XIt?t3X2J(B}}
        !            47: %\date{\bf\Large June 21, 2002}
        !            48: %\date{\bf\Large Nov. 26, 2003}
        !            49: \date{\bf\Large Dec. 18, 2003}
        !            50: \begin{document}
        !            51: \setlength{\parskip}{10pt}
        !            52: \maketitle
        !            53:
        !            54: %\itc: item color
        !            55: %\fbc: fbox color
        !            56: %\urlc: URL color
        !            57: %\goldc: bold color a
        !            58: %\redc: bold color b
        !            59:
        !            60: \Large
        !            61: \bf
        !            62: \setlength{\parskip}{0pt}
        !            63:
        !            64: \begin{slide}{$B?7%Q%C%1!<%83+H/$N7P0^(B}
        !            65:
        !            66: $B%0%l%V%J!<4pDl7W;;$N8zN((B : $B%"%k%4%j%:%`$HF1;~$K(B, $B<BAu(B, $B%G!<%?9=B$$K$bBg$-$/(B
        !            67: $B0MB8(B
        !            68:
        !            69: $BJ,;6I=8=B?9`<0(B {\tt DP} : $BC19`<0(B {\tt MP} $B$N(B linked list
        !            70:
        !            71: {\tt MP} : $B;X?t%Y%/%H%k(B {\tt DL} $B$r%]%$%s%?$G$b$D(B
        !            72:
        !            73: {\tt DL} : 32bit $B@0?tG[Ns(B (1 $BMWAG(B 32bit $B$G8GDj(B)
        !            74:
        !            75: \vskip 1cm
        !            76: \begin{tabular}{cc}
        !            77: \begin{minipage}{.5\hsize}
        !            78: \baselineskip 0.5in
        !            79: \begin{verbatim}
        !            80: typedef struct oMP {
        !            81:     struct oDL *dl;
        !            82:     P c;
        !            83:     struct oMP *next;
        !            84: } *MP;
        !            85: \end{verbatim}
        !            86: \end{minipage}
        !            87: &
        !            88: \begin{minipage}{.5\hsize}
        !            89: \baselineskip 0.5in
        !            90: \begin{verbatim}
        !            91: typedef struct oDL {
        !            92:     int td;
        !            93:     int d[1];
        !            94: } *DL;
        !            95: \end{verbatim}
        !            96: \end{minipage}
        !            97: \end{tabular}
        !            98:
        !            99: \end{slide}
        !           100:
        !           101: \begin{slide}{Singular $B$H$NHf3S(B}
        !           102:
        !           103: Singular 2-0-4
        !           104:
        !           105: \begin{itemize}
        !           106: \item $BM-8BBN>e$G9bB.(B
        !           107:
        !           108: $B4pK\E*%"%k%4%j%:%`$O(B Asir $B$HF1$8(B.
        !           109:
        !           110: $BO@J8$K$h$k$H(B, geobucket, $B2DJQD9;X?t%Y%/%H%k(B, $B8zN($h$$(B
        !           111: $B%a%b%j4IM}(B etc. $B$r<BAu(B
        !           112:
        !           113: \item $BM-M}?tBN>e$G$b9bB.(B
        !           114:
        !           115: gmp $B$r@0?t1i;;$K;HMQ(B $\Rightarrow$ Asir $B$N(B bignum $B$h$j(B,
        !           116: $BBg$-$$?t$G$OB.$$(B
        !           117: \end{itemize}
        !           118: \end{slide}
        !           119:
        !           120: \begin{slide}{$BIi$1$C$Q$J$7$O$/$d$7$$(B$\ldots$}
        !           121:
        !           122: $B$[$\40A4$K(B 0 $B$+$i=q$/(B
        !           123:
        !           124: ($B$G$-$l$P(B) $B%*%j%8%J%k$J9)IW$rF~$l$?$$(B
        !           125:
        !           126: $\Rightarrow$ ($B;n9T:x8m$r$5$s$6$s$d$C$?(B)$B7k2L$H$7$F(B,
        !           127: geobucket, $B2DJQD9;X?t%Y%/%H%k$O<BAu(B
        !           128:
        !           129: $B>u67$K1~$8$?(B 2 $B<oN`$NB?9`<0I=8=(B ($B%j%9%H(B or $BG[Ns(B) $B$N@ZBX$((B
        !           130:
        !           131: $B@55,2=7W;;$K$*$1$k(B reducer $BC5$7$K%O%C%7%e$rMxMQ(B
        !           132:
        !           133: $B4X?t$N%$%s%i%$%s(B, unrolling $B$NB?MQ(B
        !           134: \end{slide}
        !           135:
        !           136: \begin{slide}{$B8zN(2=$N9)IW(B --- geobucket}
        !           137:
        !           138: $BB?9`<0$r(B, $BG[Ns(B $g$$B$G;}$D(B
        !           139:
        !           140: $g[i]$ $B$K$O(B, $B9`?t$,(B, $B9b!9(B $b^i$ $B$NB?9`<0$,F~$k(B
        !           141:
        !           142: $BB?9`<0$O(B, $g[i]$ $BA4It$NOB(B
        !           143:
        !           144: $B9`?t$,(B $l$ ($b^(i-1) < l \le b^i$) $B$NB?9`<0(B $p$ $B$r(B $g$ $B$K(B
        !           145: $BB-$9>l9g(B
        !           146:
        !           147: \begin{enumerate}
        !           148: \item $p \leftarrow g[i]+p$
        !           149: \item $B$b$7(B $p$ $B$ND9$5$,(B $b^i$ $B$h$jBg$J$i(B, $g[i]=0$, $i\leftarrow i+1$, 1. $B$X(B.
        !           150: $B$5$b$J$/$P(B, $g[i] \leftarrow p$ $B$H$7$F=*N;(B
        !           151: \end{enumerate}
        !           152:
        !           153: $B8z2L(B : $BB??t$NOB$N7W;;$K$*$$$F(B, $BHf3S1i;;$r8:$i$9(B
        !           154:
        !           155: \end{slide}
        !           156:
        !           157: \begin{slide}{$B8zN(2=$N9)IW(B --- $B2DJQD9;X?t%Y%/%H%k(B}
        !           158:
        !           159: $BNc$($P(B, $f(x_1,x_2,x_3,x_4)$ $B$N3FJQ?t$N;X?t$,(B 256 $B0J2<$J$i(B, $B;X?t%Y%/%H%k$O(B
        !           160: 32 bit $B$K(B 4 $B$DF~$k(B.
        !           161:
        !           162: \begin{tabular}{|c|c|c|c|} \hline
        !           163: $e_1$ & $e_2$ & $e_3$ & $e_4$ \\ \hline
        !           164: \end{tabular}
        !           165:
        !           166: $B;X?t$NOB(B : 32bit $B@0?t$NOB(B
        !           167:
        !           168: $B;X?t$NHf3S(B : $B<-=q<0$J$i(B, 32bit $B@0?t$NBg$-$5$NHf3S(B
        !           169: $B5U<-=q<0$J$i(B, $B$"$i$+$8$a5U=g$K5M$a$k(B.
        !           170:
        !           171: \end{slide}
        !           172:
        !           173: \begin{slide}{$B8zN(2=$N9)IW(B --- $BG[Ns$K$h$kB?9`<0$NJ];}(B}
        !           174:
        !           175: $B4pK\A`:n(B : $f-mg$ ($m$ $B$OC19`<0(B)
        !           176:
        !           177: $f-(mg)$ : geobucket
        !           178:
        !           179: $mg$ : $g$ $B$NI=8=$K$h$j(B, $B8zN($,0[$J$k(B
        !           180:
        !           181: $B;n9T:x8m$N7k2L(B : $g$ $B$,(B, $B%a%b%j>e$K0l<!85E*$KI=8=$5$l$F$$$k$H9bB.(B
        !           182:
        !           183: $g$ $B$OCf4V4pDl(B $\Rightarrow$ $BCf4V4pDl$N$_(B, $BG[NsI=8=(B
        !           184:
        !           185: $mg$ $B<+?H$O(B, $B2C;;$K$^$o$k$N$G(B, linked list $B$,$h$$(B
        !           186:
        !           187: \end{slide}
        !           188:
        !           189: \begin{slide}{$B8zN(2=$N9)IW(B --- $B4X?t$N%$%s%i%$%s2=(B, unrolling}
        !           190:
        !           191: $BBgJ*$rJRIU$1$k$H(B, $B>.J*$,L\$K$D$/(B
        !           192:
        !           193: $B>.J*(B : $B;X?t%Y%/%H%k$NA`:n(B ($BOB(B, $B:9(B, $BHf3S(B, divisibility)
        !           194:
        !           195: $B<B83$GHf3S$7$J$,$i(B, $B$7$?$[$&$,$h$$$b$N$r%$%s%i%$%s(B, unrolling
        !           196: \end{slide}
        !           197:
        !           198: \begin{slide}{$B8zN(2=$N9)IW(B --- reducer $B%5!<%A$N%O%C%7%e2=(B}
        !           199:
        !           200: $B9`(B t $B$r3d$j@Z$kCf4V4pDl(B $g_t$ $B$N%5!<%A$bLdBj$H$J$C$?(B
        !           201:
        !           202: $g_t$ $B$O(B, $B8E$$4pDl$+$i=g$KC5$9(B $\Rightarrow$ $B$"$l$P0l0UE*(B
        !           203:
        !           204: $\Rightarrow$ $B%O%C%7%eI=(B $H$ $B$O(B, $t$ $B$N%O%C%7%eCM(B $h(t)$ $B$KBP$7(B,
        !           205: $H[h(t)]$ $B$K(B $(t,g_t)$ $B$rEPO?$9$k(B.
        !           206:
        !           207: $t$ $B$,M?$($i$l$?$i(B, $H[h(t)]$ $B$rC5$7(B, $B$_$D$+$C$?$i(B $g_t$ $B$r;H$&(B.
        !           208:
        !           209: $B$J$1$l$P(B $g_t$ $B$rDL>o$NJ}K!$G$5$,$7(B, $B$"$l$P(B $H[h(t)]$ $B$K(B
        !           210: $BEPO?(B
        !           211: \end{slide}
        !           212:
        !           213: \begin{slide}{$B8zN(2=$N9)IW(B --- $B@F<!$N>l9g$N8zN(2=(B}
        !           214:
        !           215: \begin{itemize}
        !           216: \item $B0lHL$N>l9g(B : $BESCf$G(B interreduction $B$7$J$$(B
        !           217:
        !           218: \item $B@F<!$N>l9g(B : $B$7$F$h$$(B
        !           219:
        !           220: $BF,9`$OJQ2=$7$J$$(B
        !           221:
        !           222: $BF@$i$l$?Cf4V4pDl$O<B$O4JLs%0%l%V%J!<4pDl$N$&$A(B, $B8=<!?t$^$G$N$9$Y$F(B
        !           223:
        !           224: $\Rightarrow$ 0 $B$K@55,2=$5$l$?(B S-poly $B$O(B, interreduction $B8e$b(B 0 $B$K9T$/(B
        !           225: \end{itemize}
        !           226: \end{slide}
        !           227:
        !           228: \begin{slide}{$B8zN(2=$N9)IW(B --- $B%a%b%j4IM}(B}
        !           229:
        !           230: $BHf3SE*>.$5$$%a%b%jNN0h$,7+$jJV$7I,MW$H$J$k(B
        !           231:
        !           232: $\Rightarrow$ $BKh2s(B {\tt GC\_malloc()} $B$O=E$9$.(B
        !           233:
        !           234: $\Rightarrow$ GC $B$+$i$b$i$C$?%a%b%j$r(B, $B<+A0$G(B
        !           235: $B%U%j!<%j%9%H4IM}(B
        !           236: \end{slide}
        !           237:
        !           238: \begin{slide}{$B3FIt$N>\:Y(B --- $B%I%i%$%P(B}
        !           239:
        !           240: \begin{itemize}
        !           241: \item {\tt nd\_gr}
        !           242:
        !           243: $BM-8BBN(B, $BM-M}?tBN78?t$J$I(B, $B$9$Y$F$KBP1~$9$k(B.
        !           244:
        !           245: \item {\tt nd\_gr\_trace}
        !           246:
        !           247: $BM-M}?tBN@lMQ(B. trace $B%"%k%4%j%:%`$r<B9T$9$k(B.
        !           248:
        !           249: $B@F<!2=$rMxMQ$9$k$h$&;XDj$,2DG=(B
        !           250:
        !           251: \item {\tt nd\_f4}
        !           252:
        !           253: $BM-8BBN@lMQ(B $F_4$ $B<BAu(B. $B;~4V(B, $B6u4VAPJ}$K4X$9$k8zN(2=(B
        !           254: $B$rL\;X$7$?<BAu(B
        !           255:
        !           256: \end{itemize}
        !           257: \end{slide}
        !           258:
        !           259: \begin{slide}{$B3FIt$N>\:Y(B --- $B;X?t%Y%/%H%k$ND9$5JQ99(B}
        !           260:
        !           261: \begin{itemize}
        !           262: \item $B$"$U$l(B
        !           263:
        !           264: $BB?9`<0(B $f$  $\Rightarrow$ $B:GBg;X?t%Y%/%H%k(B $M_f$ $B$rBP1~(B
        !           265:
        !           266: \item $x^E f$
        !           267:
        !           268: $E+M_f$ $B$,$"$U$l$r$*$3$9$+$I$&$+D4$Y$k(B
        !           269:
        !           270: \item $B%A%'%C%/$,I,MW$J>l=j(B
        !           271:
        !           272: S-poly $B7W;;(B, $B@55,2=$K$*$1$k(B, $BC19`<0(B $\times$ reducer $B$N7W;;(B
        !           273: \end{itemize}
        !           274:
        !           275: \end{slide}
        !           276:
        !           277: \begin{slide}{$B3FIt$N>\:Y(B --- $B$=$NB>(B}
        !           278:
        !           279: \begin{itemize}
        !           280: \item $BCf4V4pDl$r%G%#%9%/>e$KCV$-(B, demand loading
        !           281:
        !           282: $B4{B85!G=$HF1$8%9%$%C%A$r;H$&(B. ({\tt dp\_gr\_flags()}).
        !           283:
        !           284: \item content $B=|5n(B
        !           285:
        !           286: default $B$G9T$&(B. $BF,78?t$,(B 2 $BG\$N(B bit $BD9$K$J$C$?$i(B
        !           287: content $B=|5n(B
        !           288: \end{itemize}
        !           289:
        !           290: \end{slide}
        !           291:
        !           292: \begin{slide}{$B@-G=(B --- $BM-8BBN>e$G$N(B cyclic-$n$ }
        !           293:
        !           294: \vskip 1cm
        !           295:
        !           296: \begin{tabular}{c||c|c|c|c}
        !           297:  $n$        & {\tt nd\_gr} & Singular & {\tt nd\_f4} & {\tt dp\_gr\_mod\_main} \\ \hline
        !           298:   7         &   5.1        &  5.0         & 1.8      & 17                      \\
        !           299:   8         &   124        &  135         & 34       & 564                     \\
        !           300:   9         &   27810      &  29725       & 3951     &    ---                  \\
        !           301: \end{tabular}
        !           302: \end{slide}
        !           303:
        !           304: \begin{slide}{$B@-G=(B --- $BM-8BBN>e$G$N%Y%s%A%^!<%/(B }
        !           305:
        !           306: \vskip 1cm
        !           307: \begin{tabular}{c||c|c|c}
        !           308:        & {\tt nd\_gr} & Singular & {\tt nd\_f4} \\ \hline
        !           309: dl & 5.9 & 4.9 &4.0 \\
        !           310: eco10 & 7.1 & 10 &3.1 \\
        !           311: eco11 & 63 & 106 &23 \\
        !           312: eco12 & 507 & 1012 &198 \\
        !           313: extcyc6 & 11 & 9.4 &4.1 \\
        !           314: extcyc7 & 1813 & 1283 &447 \\
        !           315: f855 & 3.6 & 3.4 &2.5 \\
        !           316: filter9 & 0.28 & 0.80 &3.2 \\
        !           317: hairer2 & 5.9 & 3.8 &4.5 \\
        !           318: hairer3 & 11 & 35 &*
        !           319: \end{tabular}
        !           320: \end{slide}
        !           321:
        !           322: \begin{slide}{$B@-G=(B --- $BM-8BBN>e$G$N%Y%s%A%^!<%/(B }
        !           323:
        !           324: \vskip 1cm
        !           325: \begin{tabular}{c||c|c|c}
        !           326:        & {\tt nd\_gr} & Singular & {\tt nd\_f4} \\ \hline
        !           327: hcyclic7 & 6.5 & 4.8 &3.1 \\
        !           328: hcyclic8 & 213 & 163 &82 \\
        !           329: hf744 & 1.1 & 1.1 &1.6 \\
        !           330: hf855 & 25 & 25 &17 \\
        !           331: ilias13 & 11 & 8.4 &6.0\\
        !           332: ilias\_k\_2 & 3.1 & 2.7 &1.1\\
        !           333: ilias\_k\_3 & 4.4 & 2.9 &1.2 \\
        !           334: katsura10 & 285 & 218 &80 \\
        !           335: katsura8 & 4.1 & 3.3 &1.3 \\
        !           336: katsura9 & 35 & 29 &11 \\
        !           337: \end{tabular}
        !           338: \end{slide}
        !           339:
        !           340: \begin{slide}{$B@-G=(B --- $BM-8BBN>e$G$N%Y%s%A%^!<%/(B }
        !           341:
        !           342: \vskip 1cm
        !           343: \begin{tabular}{c||c|c|c}
        !           344:        & {\tt nd\_gr} & Singular & {\tt nd\_f4} \\ \hline
        !           345: noon7 & 4.4 & 1.8 &13 \\
        !           346: noon8 & 35 & 18 &220 \\
        !           347: pinchon1 & 3.6 & 1.0 &7.6 \\
        !           348: rbpl & 1.0 & 0.89 &1.2 \\
        !           349: redcyc7 & 3.5 & 3.3 &1.2 \\
        !           350: redeco10 & 2.8 & 2.3 &1.3 \\
        !           351: redeco11 & 24 & 18 &12 \\
        !           352: redeco12 & 177 & 134 &74 \\
        !           353: reimer6 & 11 & 32 &10 \\
        !           354: reimer7 & 4000 & 4108 & 956 \\
        !           355: virasoro & 1.8 & 1.4 & 0.65
        !           356: \end{tabular}
        !           357: \end{slide}
        !           358:
        !           359: \begin{slide}{$B:#8e$NM=Dj(B}
        !           360:
        !           361: \begin{itemize}
        !           362: \item $BM-M}4X?tBN>e$N%0%l%V%J!<4pDl7W;;(B
        !           363:
        !           364: \item $BM-M}?tBN>e$N(B $F_4$ $B7W;;(B
        !           365:
        !           366: \item tangent cone $B%"%k%4%j%:%`(B, $BI8=`4pDl(B
        !           367:
        !           368: \end{itemize}
        !           369: \end{slide}
        !           370:
        !           371: %\begin{slide}{}
        !           372: %\end{slide}
        !           373: \end{document}