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

1.1     ! noro        1: \documentclass[12pt]{jarticle}
        !             2: \IfFileExists{my.sty}{\usepackage{my}}{}
        !             3: \IfFileExists{graphicx.sty}{\usepackage{graphicx}}{}
        !             4: \IfFileExists{epsfig.sty}{\usepackage{epsfig}}{}
        !             5: \title{Risa/Asir $B$N?7$7$$J,;6I=8=B?9`<0%Q%C%1!<%8(B}
        !             6: \author{$BLnO$(B $B@59T(B \\ ($B?@8MBgM}(B)}
        !             7: \date{}
        !             8: \begin{document}
        !             9: \maketitle
        !            10: \def\gr{Gr\"obner $B4pDl(B}
        !            11: \def\st{\, s.t. \,}
        !            12: \def\noi{\noindent}
        !            13: \def\ve{\vfill\eject}
        !            14:
        !            15: \section{$B3+H/$N7P0^(B}
        !            16: Risa/Asir $B$K$*$$$F$O!"B?9`<0$O:F5"I=8=$^$?$OJ,;6I=8=$K$h$jJ];}$5$l$k!#(B
        !            17: $B8e<T$O%0%l%V%J!<4pDl4XO"7W;;$K$*$1$k4pK\E*$J%G!<%?7A<0$G$"$j!"(B
        !            18: $BC19`<0$rI=$99=B$BN(B {\tt oMP} $B$N(B linked list $B$G$"$k!#(B
        !            19:
        !            20: \vskip 5mm
        !            21: \begin{tabular}{cc}
        !            22: \begin{minipage}{.5\hsize}
        !            23: \begin{verbatim}
        !            24: typedef struct oMP {
        !            25:     struct oDL *dl;
        !            26:     P c;
        !            27:     struct oMP *next;
        !            28: } *MP;
        !            29: \end{verbatim}
        !            30: \end{minipage}
        !            31: &
        !            32: \begin{minipage}{.5\hsize}
        !            33: \begin{verbatim}
        !            34: typedef struct oDL {
        !            35:     int td;
        !            36:     int d[1];
        !            37: } *DL;
        !            38: \end{verbatim}
        !            39: \end{minipage}
        !            40: \end{tabular}
        !            41: \vskip 5mm
        !            42:
        !            43: {\tt oMP} $B$N78?t$O(B {\tt c} $B$G$"$k!#(B
        !            44: {\tt oDL} $B$N%a%s%P!<(B {\tt d}
        !            45: $B$OC19`<0$N;X?t%Y%/%H%k$rI=$7$F$*$j!"<B:]$K$OJQ?t$N8D?tJ,$ND9$5$N(B
        !            46: $BG[Ns$,%;%C%H$5$l$k!#:F5"I=8=$5$l$?B?9`<0$OJ,;6I=8=$KJQ49$5$l!"(B
        !            47: Buchberger, $F_4$, $B$"$k$$$O(B change of ordering $B$J$I$N%"%k%4%j%:%`(B
        !            48: $B%I%i%$%P$K$h$j=hM}$5$l$k!#(B
        !            49:
        !            50: Risa/Asir $B$N%0%l%V%J!<4pDl7W;;$K$*$$$F$O!"%Z%"$NA*Br@oN,!"@F<!2=!"%b%8%e(B
        !            51: $B%i7W;;!"8zN(E*MFNL=|5n$J$I$5$^$6$^$J8zN(2=$N9)IW$r:N$jF~$l$k$3$H$K$h$j!"(B
        !            52: $BM-M}?tBN>e$G$N7W;;8zN($K4X$7$F$O0lDj$NI>2A$rF@$F$-$?$,!"M-8BBN>e(B
        !            53: $B$G$N7W;;$K$*$$$F$O!"(BSingular $B$N:G6a$NHG$HHf3S$9$k$HBg$-$/@-G=$,Nt$C$F$$$?!#(B
        !            54: $B$^$?!"M-M}?tBN>e$K$*$$$F$b!"B?G\D91i;;$K(B {\tt gmp} $B$r;HMQ$7$F$$$k(B
        !            55: Singular $B$J$I$N%7%9%F%`$G$O!"6aG/$H$_$K9bB.2=$7$?(B
        !            56: {\tt gmp} $B$N@-G=$H!"(BRisa/Asir $B$G(B
        !            57: $B;HMQ$7$F$k<+<g3+H/$NB?G\D91i;;5!G=$H$N@-G=:9$K$h$j!"I,$:$7$b(B Risa/Asir $B$N(B
        !            58: $BM%0L@-$,<gD%$G$-$J$/$J$C$F$-$?!#(B
        !            59: $B0lJ}$G!"(BPC $B$KEk:\$G$-$k%a%b%jNL$b?t(B GB $B$KC#$7!"(BCPU $B$b$I$s$I$s9bB.2=$7!"(B
        !            60: $B%0%l%V%J!<4pDl7W;;$N1~MQHO0O$O$I$s$I$sBg$-$/$J$C$F$$$k!#$=$3$G!"(B
        !            61: $B$3$l$^$G$N$5$^$6$^$J7P83$*$h$S!"<BAu$K4X$9$k:G6a$NCN8+$r$b$H$K!"(B
        !            62: $B$G$-$k8B$j9bB.$JJ,;6I=8=B?9`<07W;;$*$h$S%0%l%V%J!<4pDl7W;;$r<B8=$9$k(B
        !            63: $B%Q%C%1!<%8$r?75,$K=q$/$3$H$K$7$?!#(B
        !            64:
        !            65: \section{$B9bB.2=$N9)IW(B}
        !            66:
        !            67: Buchberger $B%"%k%4%j%:%`$K4X$7$F$O!"(B
        !            68: Gebauer-Moeller $B$N(B useless pair detection$B!"(Bsugar strategy $B$J$I$K(B
        !            69: $B$h$j!"%"%k%4%j%:%`E*$K$O$"$kDxEY8G$^$C$?$,!":G6a$K$J$C$F$$$/$D$+(B
        !            70: $B<BAu$K4X$9$kDs0F$,$J$5$l$?!#:#2s$N<BAu$K:N$jF~$l$?$b$N$K$D$$$F(B
        !            71: $B@bL@$9$k!#(B
        !            72:
        !            73: \begin{itemize}
        !            74: \item geobucket
        !            75:
        !            76: $B$3$l$O!"B?9`<0$N2C;;$r8zN(2=$9$k$?$a$NJ}K!$G$"$k!#(B
        !            77: $B@55,2=7W;;$G$O(B, $B?tB?$/$NB?9`<0$N2C;;$,9T$o$l$k$,(B, $BHs>o$K(B
        !            78: $B9`?t$NB?$$B?9`<0$K(B, $B9`?t$NHf3SE*>/$J$$B?9`<0$r7+$jJV$7B-$9$h$&$J>l9g(B,
        !            79: $B9`$I$&$7$NHf3S1i;;$N%3%9%H$,BgJQBg$-$/$J$k(B. geobucket $B$H$O(B, $BB?9`<0$r(B
        !            80: $BMWAG$H$9$kG[Ns(B $g$ $B$G$"$C$F(B, $BE,Ev$J@0?t(B $b$ ($BNc$($P(B 2) $B$KBP$7(B, $g[i]$
        !            81: $B$NB?9`<0$,9b!9(B $b^i$ $B$N9`?t$r;}$D$h$&$J$b$N$G$"$k(B. $g$ $B$K(B, $B9`?t(B $l$
        !            82: ($b^{i-1} < l \le b^i$) $B$NB?9`<0(B $p$ $B$rB-$9>l9g(B, $B$^$:(B $g[i]+p$ $B$r(B
        !            83: $B7W;;$9$k(B. $B$3$l$N9`?t$,(B $b^i$ $B0J2<$J$i$=$N$^$^(B $g[i]$ $B$rCV$-49$((B,
        !            84: $b^i$ $B$h$jBg$-$1$l$P(B $g[i+1]$ $B$K2C$($k(B, $B$H$$$&A`:n$r(B geobucket $B$N(B
        !            85: $B>r7o$,K~$?$5$l$k$^$GB3$1$k(B. $B$3$l$K$h$j(B, $BOB$K8=$o$l$kB?9`<0$N9`$NAm?t$r(B
        !            86: $N$ $B$H$9$k$H$-(B, $O(N\log N)$ $B$N%3%9%H$GB?9`<0$NOB$,7W;;$G$-$k(B.
        !            87:
        !            88: \item $B2DJQD9;X?t%Y%/%H%k(B
        !            89:
        !            90: {\tt oDL} $B$N%a%s%P!<$G$O(B, $BC19`<0$NJQ?t$N3F;X?t$r(B 32 bit $B8GDj$GI=8=$7$F(B
        !            91: $B$$$?$,(B, $BB?$/$N>l9g$3$l$O2aJ,$G$"$j(B, $B7k2L$H$7$F(B, $BB?9`<0$N$b$D>pJsNL(B
        !            92: $B$h$j$bM>J,$K%a%b%j$,I,MW$H$J$C$F$$$?(B. $B$3$l$KBP$7$F(B, $BI,MW:G>.8B$N(B
        !            93: bit $BD9$r;X?t$K3d$jEv$F$F$*$-(B, $B$"$U$l$,@8$8$k:]$K(B, $B%5%$%:$rJQ99$7$F(B
        !            94: $BB?9`<0$r:n$j$J$*$9$H$$$&$N$,$3$NJ}K!$G$"$k(B.
        !            95:
        !            96: \item $BG[Ns$K$h$kB?9`<0$NJ];}(B
        !            97:
        !            98: Buchberger $B%"%k%4%j%:%`$K$*$1$k4pK\A`:n$O(B, $f-mg$ ($f$, $g$ $B$OB?9`<0(B,
        !            99: $m$ $B$OC19`<0(B) $B$G$"$k(B. $B$3$l$r$5$i$K(B $mg$ $B$r:n$kA`:n$H(B, $BB?9`<0$NOB$r(B
        !           100: $B:n$kA`:n$KJ,2r$7$F9M$($k(B. $B8e<T$O(B geobucket $B$K$h$j9bB.2=$,2DG=$G$"$k(B.
        !           101: $BA0<T$K4X$7$F$O(B, $B$I$&$7$h$&$b$J$5$=$&$K$b;W$($k$,(B, $B$3$N1i;;$O(B, $g$ $B$N(B
        !           102: $BI=8=J}K!$K$h$j7W;;8zN($,Bg$-$/0[$J$k(B. $B7kO@$r8@$($P(B,
        !           103: $g$ $B$,(B $BC19`<0$N(B linked list $B$GI=8=$5$l$F$$$k$h$j(B, $BC19`<0(B ($B$3$l<+?H(B
        !           104: $BG[Ns$G$"$k(B) $B$NG[Ns$H$7$FI=8=$5$l$F$$$k$[$&$,(B, $mg$ $B$N7W;;$,9bB.(B
        !           105: $B$G$"$k(B. $g$ $B$O(B, $B$9$G$K7W;;$5$l$?Cf4V4pDl$J$N$G(B, $BG[Ns$H$7$FJ];}$9$k$3$H(B
        !           106: $B$KLdBj$O$J$$(B. $B$?$@$7(B, $mg$ $B$O(B, $BB?9`<02C;;$K$^$o$k$N$G(B, linked list
        !           107: $B$H$7$FI=<($5$l$F$$$J$$$HET9g$,0-$$(B. $B0J>e$K$h$j(B, $BB?9`<0$O>u67$K1~$8$F(B
        !           108: linked list $B$HG[Ns$N(B 2 $B$D$NI=8=$r$H$k$3$H$K$J$C$?(B.
        !           109:
        !           110: \item $B4X?t$N%$%s%i%$%s2=(B, unrolling
        !           111:
        !           112: $B3+H/$,?J$`$K$D$$$F(B, $B%\%H%k%M%C%/$H$J$kItJ,$,<!Bh$KDc%l%Y%k$JItJ,$K(B
        !           113: $B$J$C$F$$$C$?(B. $BFC$KLdBj$H$J$k$N$,(B, $BC19`<0$N;X?t%Y%/%H%k$KBP$9$kA`:n(B
        !           114: $B$G$"$k(B. $B$9$J$o$A(B, $B;X?t%Y%/%H%k$NOB(B, $B:9(B, $BHf3S(B, divisibility $B$J$I$G$"$k(B.
        !           115: $B$3$l$i$NItJ,$K4X$7$F$O(B, $B%$%s%i%$%s2=(B, $B$*$h$S(B unrolling $B$N@'Hs$r(B
        !           116: $B8DJL$K<B83$K$h$jH=CG$7$?(B.
        !           117:
        !           118: \item reducer $B$N%5!<%A$N%O%C%7%e2=(B
        !           119:
        !           120: $B9`(B $t$ $B$r3d$j@Z$kF,9`$r$b$DCf4V4pDl(B (reducer) $g_i$ $B$N%5!<%A$b(B,
        !           121: $BB>ItJ,$N8zN(2=$,?J$`$K$D$l(B, $B$=$N%3%9%H$,LdBj$K$J$C$F$-$?(B.
        !           122: reducer $B$H$7$F$O(B, $B7P83>e(B,
        !           123: $i$ $B$N>.$5$$=g$+$iC5$7$F(B, $t$ $B$r3d$j@Z$k:G=i$N$b$N$rMQ$$$k$N$,(B
        !           124: $B$h$$$H$5$l$k(B ($BNc30$b$"$k$,(B). $B$3$N$?$a(B, $t$ $B$N(B reducer $B$O$"$l$P0l0U(B
        !           125: $B$K$-$^$k(B.
        !           126: $t$ $B$N(B reducer $g_t$ $B$,8+$D$+$C$?$i(B,
        !           127: $t$ $B$N%O%C%7%eCM(B $h_t$ $B$r7W;;$7$F(B, $B$"$k%F!<%V%k$N(B $h_t$ $B$N0LCV$K(B,
        !           128: $(t,g_t)$ $B$rEPO?$9$k(B. $t$ $B$N(B reducer $B$rC5$9:]$K$O(B, $h_t$ $B$N0LCV(B
        !           129: $B$KEPO?$5$l$?%G!<%?$+$i(B, $t$ $B$N(B reducer $B$rC5$7$F(B, $B$b$7$"$l$P$=$l$r(B
        !           130: $BMQ$$$l$P$h$$(B.
        !           131:
        !           132: \item $B%a%b%j4IM}(B
        !           133:
        !           134: $B7W;;ESCf(B, $B$5$^$6$^$JBg$-$5$NNN0h$,7+$jJV$7I,MW$H$J$k(B. $BFC$KB?$/I,MW$H$5(B
        !           135: $B$l$k$$$/$D$+$N9=B$BNMQNN0h$O(B, garbage collector (GC) $B$GF@$?$b$N$r<+A0(B
        !           136: $B$G%U%j!<%j%9%H4IM}$7$F$$$k(B. $B$3$l$O(B, GC $B$K$h$k(B allocation, collection
        !           137: $B$,0lDj$N%3%9%H$rH<$&$?$a$G$"$k(B.  $B$3$N4IM}$O(B nd $B%Q%C%1!<%8Fb$GJD$8$F$*(B
        !           138: $B$j(B, $B$+$D%U%j!<%j%9%H$N(B root $B$r(B 0 $B$K$7$F$*$1$P(B, $B$$$:$l(B GC $B$K$h$j2s<}$5(B
        !           139: $B$l$k(B.
        !           140: \end{itemize}
        !           141:
        !           142: \section{$B4pK\%G!<%?9=B$(B}
        !           143:
        !           144: \vskip 5mm
        !           145: \begin{tabular}{cc}
        !           146: \begin{minipage}{.5\hsize}
        !           147: \begin{verbatim}
        !           148: typedef struct oND {
        !           149:     struct oNM *body;
        !           150:     int nv;
        !           151:     int len;
        !           152:     int sugar;
        !           153: } *ND;
        !           154: \end{verbatim}
        !           155: \end{minipage}
        !           156: &
        !           157: \begin{minipage}{.5\hsize}
        !           158: \begin{verbatim}
        !           159: typedef struct oNDV {
        !           160:     struct oNMV *body;
        !           161:     int nv;
        !           162:     int len;
        !           163:     int sugar;
        !           164: } *NDV;
        !           165: \end{verbatim}
        !           166: \end{minipage}
        !           167: \end{tabular}
        !           168: \vskip 5mm
        !           169:
        !           170: $B$3$l$i$O(B, $B$$$:$l$bJ,;6I=8=B?9`<0$rJ];}$9$k$?$a$N9=B$BN$G$"$k(B.
        !           171: {\tt ND} $B$O(B linked list $B7A<0$N(B, {\tt NDV} $B$OG[Ns7A<0$NB?9`<0(B
        !           172: $B$rI=$9(B.
        !           173:
        !           174: \vskip 5mm
        !           175: \begin{tabular}{cc}
        !           176: \begin{minipage}{.5\hsize}
        !           177: \begin{verbatim}
        !           178: typedef struct oNM {
        !           179:     struct oNM *next;
        !           180:     union oNDC c;
        !           181:     UINT dl[1];
        !           182: } *NM;
        !           183: \end{verbatim}
        !           184: \end{minipage}
        !           185: &
        !           186: \begin{minipage}{.5\hsize}
        !           187: \begin{verbatim}
        !           188: typedef struct oNMV {
        !           189:     union oNDC c;
        !           190:     UINT dl[1];
        !           191: } *NMV;
        !           192: \end{verbatim}
        !           193: \end{minipage}
        !           194: \end{tabular}
        !           195: \vskip 5mm
        !           196:
        !           197: $B$3$l$i$O(B, $BC19`<0$rI=$9$?$a$N9=B$BN$G$"$k(B.  {\tt dl} $B$OC19`<0$N;X?t%Y%/(B
        !           198: $B%H%k$rI=$7$F$*$j!"<B:]$K$OJQ?t$N8D?tJ,$ND9$5$NG[Ns$,%;%C%H$5$l$k(B.
        !           199: {\tt NM} $B$O(B linked list $B7A<0$N(B, {\tt NMV} $B$OG[Ns7A<0$NB?9`<0$K$*$1$k(B
        !           200: $BC19`<0$rI=$9(B. {\tt NDV} $B$O(B, {oNMV} $B$9$J$o$A9=B$BN$=$N$b$N$N(B
        !           201: $BG[Ns$X$N%]%$%s%?$r;}$D(B. {\tt NDC} $B$O78?t$rJ];}$9$k$?$a$NHFMQ$N6&MQBN(B
        !           202: $B$G$"$k(B.
        !           203: \begin{verbatim}
        !           204: typedef union oNDC {
        !           205:     int m;
        !           206:     Q z;
        !           207:     P p;
        !           208: } *NDC;
        !           209: \end{verbatim}
        !           210: {\tt m} $B$O(B, $B0L?t$,(B 1 $B%o!<%I$G<}$^$kM-8BBN$N85$rJ];}$9$k$?$a$N(B
        !           211: $B%a%s%P!<$G$"$k(B.
        !           212:
        !           213: \begin{tabular}{cc}
        !           214: \begin{minipage}{.5\hsize}
        !           215: \begin{verbatim}
        !           216: typedef struct oRHist {
        !           217:     struct oRHist *next;
        !           218:     int index;
        !           219:     int sugar;
        !           220:     UINT dl[1];
        !           221: } *RHist;
        !           222: \end{verbatim}
        !           223: \end{minipage}
        !           224: &
        !           225: \begin{minipage}{.5\hsize}
        !           226: \begin{verbatim}
        !           227: typedef struct oND_pairs {
        !           228:     struct oND_pairs *next;
        !           229:     int i1,i2;
        !           230:     int sugar;
        !           231:     UINT lcm[1];
        !           232: } *ND_pairs;
        !           233: \end{verbatim}
        !           234: \end{minipage}
        !           235: \end{tabular}
        !           236:
        !           237: {\tt RHist} $B$O(B reducer $B$NMzNr$r%O%C%7%e%F!<%V%k$KEPO?$9$k$?$a$N9=B$BN$G$"$k(B.
        !           238: $B3F%(%s%H%j$O(B, {\tt RHist} $B$N%j%9%H$H$7$FEPO?$5$l$k(B. $B$^$?(B {\tt ND\_pairs}
        !           239: $B$O(B S-pair $B$rJ];}$9$k$?$a$N9=B$BN$G$"$j(B, $B$d$O$j%j%9%H$G$"$k(B.
        !           240: \section{$B3FIt$N>\:Y(B}
        !           241:
        !           242: \subsection{$B%I%i%$%P(B}
        !           243:
        !           244: Buchberger $B%"%k%4%j%:%`$N%I%i%$%P$O(B, {\tt nd\_gb} $B$H(B {\tt nd\_gb\_trace}
        !           245: $B$NFs$D$,$"$k(B. {\tt nd\_gb} $B$O(B, $BG$0U$N78?tBN>e$G(B, sugar $B%9%H%i%F%8!<$D$-$N(B
        !           246: Buchberger $B%"%k%4%j%:%`$r<B9T$9$k$?$a$N$b$N$G$"$k(B.
        !           247: $B$3$3$G$O(B,
        !           248:
        !           249: \begin{enumerate}
        !           250: \item S-pair $B%j%9%H$N%a%s%F%J%s%9(B
        !           251: \item S-pair $B$N<h$j=P$7(B, $B@55,2=7W;;$N8F$S=P$7(B
        !           252: \item $B@55,7A$N(B, content $B=|5n(B, {\tt NDV} $B$X$NJQ49(B
        !           253: \item $B;X?t$K$"$U$l$,=P$?>l9g$N(B, $BCf4V4pDl$N:n$j$J$*$7(B
        !           254: \end{enumerate}
        !           255:
        !           256: $B$J$I$,9T$o$l$k(B. {\tt nd\_gb\_trace} $B$O(B, $BM-M}?tBN(B, $BM-M}4X?tBN>e$N%0%l%V%J!<(B
        !           257: $B4pDl7W;;$r(B trace $B%"%k%4%j%:%`$K$h$j9T$&$?$a$N$b$N$G$"$j(B, $B>e5-$N;E;v$K(B
        !           258: $B2C$((B, $B7k2L$r%A%'%C%/$9$k4X?t$N8F$S=P$7(B, homogenization, dehomogenization
        !           259: $B$b9T$o$l$k(B.
        !           260:
        !           261: $B$5$i$K(B, $B8=>u$G$OM-8BBN>e$N$_$G$"$k$,(B, $F_4$ $B%I%i%$%P(B {\tt nd\_f4} $B$b(B
        !           262: $B<BAu$7$?(B. S-pair, $BCf4V4pDl$N07$$$K4X$7$F$O(B {\tt nd\_gb} $B$HF1MM$G$"$k(B.
        !           263: symbolic preprocessing $B$O(B, $B@lMQ$N(B geobucket $B$,<BAu$5$l$F$$$k(B.
        !           264: $F_4$ $B$N3K?4$G$"$k(B, $BJ#?t$N(B S-pair $B$+$i(B, reducer $B$r$^$H$a$F(B
        !           265: $B9TNs$H$7$FA]$-=P$9:n6H$r9T$&$^$($K(B, $B3F(B reducer $B$K$h$j(B S-poly $B$r(B
        !           266: $B@55,2=$7$F$$$k(B. $B$3$NA`:n$r9T$&$?$a$K(B, $B3F(B reducer $B$r(B, $B05=L%Y%/%H%k(B
        !           267: $B7A<0$KJQ49$7$F$*$-(B, $B@55,2=$5$l$kB&$N(B S-poly $B$OHs05=L$N%Y%/%H%k(B
        !           268: $B7A<0$H$7$F@55,2=$r9T$&(B. $B:G8e$K(B, $B;D$C$?ItJ,$r=8$a$F9TNs$H$7(B,
        !           269: $BA]$-=P$7$r9T$C$F$$$k(B. $B$3$l$i$K$h$j(B, $B$G$-$k8B$j;HMQ%a%b%jNL$r2!$($F(B
        !           270: $B$$$k(B.
        !           271:
        !           272: \subsection{$B;X?t%Y%/%H%k$NJQ99(B}
        !           273:
        !           274: $B;X?t%Y%/%H%k$NJQ99$O(B, $B;X?t$NOB$G$"$U$l$,@8$8$?$H$-$KI,MW$H$J$k(B.
        !           275: $B$3$l$,5/$3$jF@$k$N$O(B, S-poly $B$N7W;;$H(B, $B@55,7A$N7W;;$K$*$1$k(B,
        !           276: $BC19`<0$HB?9`<0$N@Q$N7W;;$K$*$$$F$G$"$k(B. $B$3$NCf$G$N(B, $BC19`<0(B
        !           277: $B$I$&$7$N@Q$N7W;;$N$?$S$K%A%'%C%/$9$k$N$OHs8zN(E*$J$N$G(B,
        !           278: $B3FCf4V4pDl$KBP$7(B, $B3FJQ?t$KBP$9$k;X?t$N:GBgCM$r5-O?$7$F$*$-(B,
        !           279: $B$=$N%Y%/%H%k$H$NOB$,$"$U$l$r5/$3$9>l9g$K:n$j$J$*$7$r$7$F$$$k(B.
        !           280:
        !           281: \subsection{$BCf4V4pDl$N(B demand loading}
        !           282:
        !           283: {\tt dp} $B7O$GDs6!$5$l$F$$$k$N$HF1MM$K(B,
        !           284: nd $B$K$*$$$F$b(B, $BCf4V4pDl$r%G%#%9%/>e$N;XDj$5$l$?%G%#%l%/%H%j$K(B
        !           285: $BCV$/$3$H$,$G$-$k(B. $B;XDjJ}K!$O(B {\tt dp} $B7O$HF1MM(B {\tt dp\_gr\_flags()}
        !           286: $B$G;XDj$9$k(B. $B%U%!%$%k$O(B {\tt dp} $B7O$HF1MM$N7A<0$J$N$G(B, {\tt bload()}
        !           287: $B$GFI$`$3$H$,$G$-$k(B.
        !           288:
        !           289: \subsection{$BM-M}?tBN>e$G$N(B content $B=|5n(B}
        !           290:
        !           291: $B@55,2=7W;;ESCf$G$N(B content $B=|5n$O(B, $B>o$K9T$o$l$k(B. $B8=>u$G$O(B
        !           292: $BF,78?t$,(B 2 $BG\(B ($B8GDj(B) $B$K$J$C$?$H$-$K=|5n$,9T$o$l$k!#(B
        !           293:
        !           294: \section{$B@-G=(B}
        !           295:
        !           296: $B0lHL$K(B, $BM-8BBN>e$N7W;;$N>l9g(B, {\tt nd\_gr} $B$O(B {\tt dp\_gr\_mod\_main}
        !           297: $B$h$j?tG\$+$i==?tG\9bB.$G$"$k(B. $B$^$?(B, $BLdBj$K$b$h$k$,(B, {\tt nd\_f4} $B$O(B
        !           298: {\tt nd\_gr} $B$N?tG\DxEY9bB.$J>l9g$,$"$k(B. $B$*$J$8$_$N(B cyclic-$n$ $B$G(B
        !           299: $BHf3S$9$k$HI=(B \ref{tab:cyclic}$B$N$h$&$J7k2L$rF@$k(B.
        !           300:
        !           301: \begin{table}[hbtp]
        !           302: \begin{center}
        !           303: \begin{tabular}{c||c|c|c|c} \hline
        !           304:  $n$        & {\tt nd\_gr} & {\tt nd\_f4} & Singular & {\tt dp\_gr\_mod\_main} \\ \hline
        !           305:   7         &              &              &          &                         \\ \hline
        !           306:   8         &              &              &          &                         \\ \hline
        !           307:   9         &              &              &          &                         \\ \hline
        !           308: \end{tabular}
        !           309: \end{center}
        !           310: \caption{$GF(31991)$ $B>e$G$N(B DRL $B=g=x%0%l%V%J!<4pDl7W;;(B}
        !           311: \label{tab:cyclic}
        !           312: \end{table}
        !           313: $B$3$N$h$&$K(B, $B>/$J$/$H$b(B cyclic-$n$ $B$G$O(B, nd $B$N<BAu$N8z2L$,==J,$K8=$o$l$F$$$k(B.
        !           314: $BI=(B \ref{tab:janet} $B$O(B, $B<o!9$N%Y%s%A%^!<%/LdBj$N7W;;;~4V$r<($9(B.
        !           315:
        !           316: $BM-M}?tBN>e$N7W;;$N>l9g(B, $BB?9`<0$d(B, $B;X?t%Y%/%H%k$NI=8=J}K!0J30$K(B, $BESCf$"$i$o$l$k(B
        !           317: $B78?t$NKDD%$NJ}$,(B, $B7W;;;~4V$KBg$-$/1F6A$rM?$($k>l9g$,B?$$(B. $B$3$NE@$G$O(B
        !           318: {\tt nd\_gr\_trace} $B$H(B {\tt dp\_gr\_main} $B$H$G$OBg:9$J$$$N$G3d0&$9$k$,(B,
        !           319: $B$h$j0-$/$J$k$3$H$O$J$$(B.
        !           320:
        !           321: \section{$B:#8e$NM=Dj(B}
        !           322:
        !           323: {\tt dp} $B7O$K$"$C$F(B nd $B$K$J$$5!G=$H$7$F(B, $BM-M}4X?tBN78?t$N%0%l%V%J!<4pDl(B
        !           324: $B7W;;$H(B, $BM-M}?tBN>e$N(B $F_4$ $B7W;;$,$"$k(B. $B$J$k$Y$/Aa$$$&$A$K$3$l$i$r<BAu(B
        !           325: $B$7$?$$$H9M$($F$$$k(B.
        !           326:
        !           327: \end{document}