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Annotation of OpenXM/doc/Papers/jsiamb-noro.tex, Revision 1.4

1.4     ! noro        1: % $OpenXM: OpenXM/doc/Papers/jsiamb-noro.tex,v 1.3 2001/10/04 08:30:17 noro Exp $
1.1       noro        2: \setlength{\parskip}{10pt}
                      3:
                      4: \begin{slide}{}
1.4     ! noro        5: \fbox{\bf $B7W;;5!Be?t%7%9%F%`(B Risa/Asir}
1.1       noro        6:
                      7: \begin{itemize}
                      8: \item $BB?9`<04D$K$*$1$kBg5,LO9bB.7W;;$rL\;X$7$F3+H/(B
                      9:
                     10: \begin{itemize}
                     11: \item C $B$G5-=R(B
1.4     ! noro       12: \item $B%a%b%j4IM}$O(B Boehm's conservative GC [Boehm] $B$K$h$k(B
1.1       noro       13: \end{itemize}
                     14:
                     15: \item C $B8@8l$K;w$?%f!<%68@8l%$%s%?%U%'!<%9$r$b$D(B.
                     16:
                     17: \begin{itemize}
                     18: \item $B7?@k8@$J$7(B
                     19: \item $B%f!<%68@8l%G%P%C%,$,AH$_9~$_(B
                     20: \end{itemize}
                     21:
                     22: \item $B%*!<%W%s%=!<%9(B
                     23:
                     24: \begin{itemize}
1.4     ! noro       25: \item 2000 $BG/$^$GIY;NDL8&$G3+H/(B
        !            26:
        !            27: $\Rightarrow$ 2001 $BG/$h$j(B Kobe branch [Risa/Asir]
1.1       noro       28: $B$,%9%?!<%H(B
                     29:
1.4     ! noro       30: \item CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B)
1.1       noro       31: \end{itemize}
                     32:
                     33: \item OpenXM ((Open message eXchange protocol for Mathematics) $B%$%s%?%U%'!<%9(B
                     34: \end{itemize}
                     35: \end{slide}
                     36:
                     37: \begin{slide}{}
1.4     ! noro       38: \fbox{\bf $B<g$J5!G=(B}
1.1       noro       39:
                     40: \begin{itemize}
                     41: \item $BB?9`<0$N4pK\1i;;(B
                     42:
                     43: \begin{itemize}
                     44: \item $B2C8:>h=|(B, GCD, $B=*7k<0(B etc.
                     45: \end{itemize}
                     46:
                     47: \item $BB?9`<00x?tJ,2r(B
                     48:
                     49: \begin{itemize}
                     50: \item $B0lJQ?tB?9`<0(B : $B78?tBN$OM-M}?tBN(B, $BBe?tBN(B, $B<o!9$NM-8BBN(B
                     51:
                     52: \item $BB?JQ?tB?9`<0(B : $B78?tBN$OM-M}?tBN(B
                     53: \end{itemize}
                     54:
                     55: \item $B%0%l%V%J4pDl7W;;(B
                     56:
                     57: \begin{itemize}
                     58: \item Buchberger $B%"%k%4%j%:%`(B, Fag\`ere $F_4$ [Faug\`ere] $B%"%k%4%j%:%`(B
                     59:
                     60: $BB?9`<04D$*$h$S(B Weyl $BBe?t(B
                     61:
                     62: \item 0 $B<!85%$%G%"%k$N(B change of ordering/RUR [Rouillier]
                     63:
1.4     ! noro       64: $BBe?tJ}Dx<0$N2r$r(B, $B0lJQ?tB?9`<0$N:,$GI=$9(B
        !            65:
        !            66: \item $B=`AG%$%G%"%kJ,2r(B [SY]
1.1       noro       67:
                     68: $BB?JQ?tBe?tJ}Dx<07O$N2r$NJ,2r$rM?$($k(B
                     69:
1.4     ! noro       70: \item $BB?9`<0$N(B $b$-$B4X?t(B (Bernstein-Sato polynomial) $B$N7W;;(B [Oaku]
1.1       noro       71:
                     72: $b$-$B4X?t(B : $BB?9`<0$NNmE@$G$"$kD66JLL$NITJQNL(B
                     73:
                     74: $D$-$B2C72$K$*$1$k7W;;$N(B, $BM-8B<!85$N@~7ABe?t$X$N5"Ce$KI,MW(B
                     75: \end{itemize}
                     76: \end{itemize}
                     77: \end{slide}
                     78:
                     79: \begin{slide}{}
1.4     ! noro       80: \fbox{\bf $B<g$J5!G=(B ($B$D$E$-(B)}
1.1       noro       81:
                     82: \begin{itemize}
                     83:
                     84: \item PARI [PARI] $B%i%$%V%i%j%$%s%?%U%'!<%9(B
                     85:
                     86: $B?tO@%i%$%V%i%j(B PARI $B$r%j%s%/$7$F$$$F<g$J4X?t$,8F$Y$k(B
                     87:
                     88: bigfloat $B7W;;(B, $BD61[4X?t$NI>2A$K$bMQ$$$i$l$k(B
                     89:
                     90: \item OpenXM $B$N85$G$NJ,;6JBNs7W;;(B
                     91:
                     92: OpenXM $B$K$h$kF1<o$^$?$O0[<o$N?t3X%=%U%H%&%'%"$N7k9g(B
                     93:
                     94: client-server $B7?J,;6JBNs7W;;$,MF0W$K<B83$G$-$k(B
                     95:
                     96: \item 2 $BJQ?t4X?t$NNmE@$N@:L)IA2h(B
                     97:
                     98: $BCf4VCM$NDjM}(B, Sturm $BNs$NMxMQ$K$h$k(B, 2 $BJQ?t4X?t$NNmE@$N@:L)IA2h(B
                     99:
                    100: OpenXM server $B$H$7$F<B8=(B
                    101: \end{itemize}
                    102: \end{slide}
                    103:
                    104: \begin{slide}{}
1.4     ! noro      105: \fbox{\bf $B3+H/$NNr;K(B : ---1994}
1.1       noro      106:
                    107: \begin{itemize}
                    108: \item --1989
                    109:
                    110: Prolog $B$N%5%V%k!<%A%s$H$7$F(B, $B$$$/$D$+$N5!G=$r3+H/(B
                    111:
                    112: \item 1989--1992
                    113:
                    114: \begin{itemize}
                    115: \item parser $B$*$h$S(B Boehm $B$N(B GC [Boehm] $B$H$H$b$K(B Risa/Asir $B$,%9%?!<%H(B
                    116:
                    117: \item $BM-M}?tBN>e0lJQ?t(B, $BB?JQ?tB?9`<0$N0x?tJ,2r$r3+H/(B
                    118: \end{itemize}
                    119:
                    120: \item 1992--1994
                    121:
                    122: \begin{itemize}
                    123: \item Buchberger $B%"%k%4%j%:%`$N<BAu3+;O(B
                    124:
                    125: $B%f!<%68@8l$G5-=R(B $\Rightarrow$ C $B$G=q$-D>$7(B (by $BB<Hx(B@$B8=:_EEDLBg(B)
                    126:
                    127: $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B
                    128:
                    129: \item $BBe?tBN>e$N0lJQ?tB?9`<0$N0x?tJ,2r(B
                    130:
                    131: $BC`<!3HBg$*$h$S(B, $B=EJ#0x;R$r$b$D%N%k%`$NAH?%E*MxMQ(B
                    132: \end{itemize}
                    133: \end{itemize}
                    134:
                    135: \end{slide}
                    136:
                    137: \begin{slide}{}
1.4     ! noro      138: \fbox{\bf $B3+H/$NNr;K(B : 1994-1996}
1.1       noro      139:
                    140: \begin{itemize}
                    141: \item $B%P%$%J%jHG$rIY;NDL$h$j8x3+(B
                    142:
                    143: \item $B=`AG%$%G%"%kJ,2r$N<BAu(B
                    144:
                    145: \begin{itemize}
                    146: \item $B2<;3(B-$B2#;3%"%k%4%j%:%`(B [SY]
                    147: \end{itemize}
                    148:
                    149: \item Buchberger $B%"%k%4%j%:%`$N2~NI(B
                    150:
                    151: \begin{itemize}
                    152: \item Trace lifting+$B@F<!2=(B
                    153:
                    154: \item compatible prime $B$K$h$k%0%l%V%J4pDl%A%'%C%/$N>JN,(B
                    155:
                    156: \item Modular change of ordering, Modular RUR
                    157:
                    158: $B2#;3$H$N6&F18&5f(B [NY]
                    159: \end{itemize}
                    160: \end{itemize}
                    161:
                    162: \end{slide}
                    163:
                    164: \begin{slide}{}
1.4     ! noro      165: \fbox{\bf $B3+H/$NNr;K(B : 1996-1998}
1.1       noro      166:
                    167: \begin{itemize}
                    168: \item $BJ,;67W;;5!G=$N<BAu(B
                    169:
                    170: \begin{itemize}
                    171: \item OpenXM $B$N%W%m%H%?%$%W(B
                    172: \end{itemize}
                    173:
                    174: \item Buchberger $B%"%k%4%j%:%`$N2~NI(B
                    175:
                    176: \begin{itemize}
                    177: \item $B@55,7A7W;;Cf$K$*$1$k78?t$N6&DL0x;R$N8zN(E*=|5n(B
                    178:
                    179: \item $B$=$NJBNs2=(B
                    180:
                    181: \item odd order replicable functions $B$N7W;;(B [Noro]
                    182:
                    183: Risa/Asir : DRL basis $B7W;;(B({\it McKay}) $B$K(B 5 $BF|$+$+$C$?(B
                    184:
                    185: Faug\`ere $B$N(B FGb : $B$3$N7W;;$r(B 53 $BIC$G<B9T(B
                    186: \end{itemize}
                    187:
                    188:
                    189: \item $BBg$-$JM-8BBN>e$N0lJQ?tB?9`<0$N0x?tJ,2r(B
                    190:
                    191: \begin{itemize}
                    192: \item Schoof-Elkies-Atkin $B%"%k%4%j%:%`$N<BAu$N$?$a(B
                    193:
                    194: $BM-8BBN>e$NBJ1_6J@~$NM-M}E@8D?t7W;;MQ(B
                    195:
1.2       noro      196: --- $B$3$N%W%m%0%i%`$O%U%j!<$G$O$J$$$,(B, $B4X78$9$k4X?t$O%U%j!<(B
1.1       noro      197: \end{itemize}
                    198: \end{itemize}
                    199:
                    200: \end{slide}
                    201:
                    202: \begin{slide}{}
1.4     ! noro      203: \fbox{\bf $B3+H/$NNr;K(B : 1998-2000}
1.1       noro      204: \begin{itemize}
                    205: \item OpenXM
                    206:
                    207: \begin{itemize}
                    208: \item OpenXM $B;EMM=q(B : $BLnO$(B, $B9b;3(B [OpenXM]
                    209:
                    210: enconding, phrasebook $B$K4X$9$k%"%$%G%#%"$O(B OpenMath [OpenMath] $B$+$i<ZMQ(B
                    211:
                    212: \item $BJ,;67W;;4X?t$O(B, OpenXM $B;EMM$K=q$-D>$7(B
                    213: \end{itemize}
                    214:
                    215: \item Risa/Asir on Windows
                    216:
                    217: \begin{itemize}
                    218: \item $B;E;v>eI,MW$K$J$C$?(B
                    219:
                    220: Visual C++ $B$G5-=R(B
                    221: \end{itemize}
                    222:
                    223: \item $F_4$ $B$N;n83<BAu(B
                    224:
                    225: \begin{itemize}
1.4     ! noro      226: \item $BO@J8(B [Faug\`ere] $B$K=`5r$7$F5-=R(B
1.1       noro      227:
                    228: \item $GF(p)$ $B>e(B : $B$J$+$J$+$h$$(B
                    229:
                    230: \item $BM-M}?tBN>e(B :{\it McKay} $B$r=|$$$F$@$a(B
                    231: \end{itemize}
                    232: \end{itemize}
                    233: \end{slide}
                    234:
                    235: \begin{slide}{}
1.4     ! noro      236: \fbox{\bf $B3+H/$NNr;K(B : 2000-current}
1.1       noro      237: \begin{itemize}
                    238: \item $B%*!<%W%s%=!<%92=(B
                    239:
                    240: \begin{itemize}
                    241: \item $BLnO$$,IY;NDL8&$h$j?@8MBg$K0\@R(B
                    242:
1.3       noro      243: Kobe branch $B$N%9%?!<%H(B
1.1       noro      244: \end{itemize}
                    245:
                    246: \item OpenXM
                    247:
                    248: \begin{itemize}
                    249: \item $B;EMM=q(B : OX-RFC100, 101, (102)
                    250:
                    251: \item OX-RFC102 ($BL$40@.(B) : MPI $B$rMQ$$$?%5!<%P4VDL?.(B
                    252: \end{itemize}
                    253:
                    254: \item Weyl $BBe?t(B
                    255:
                    256: \begin{itemize}
                    257: \item Buchberger $B%"%k%4%j%:%`(B [Takayama]
                    258:
                    259: \item $b$-$B4X?t(B
                    260:
                    261: $b$-$B4X?t$r:G>.B?9`<0$H$7$F%b%8%e%i7W;;(B
                    262: \end{itemize}
                    263: \end{itemize}
                    264:
                    265: \end{slide}
                    266:
                    267: \begin{slide}{}
1.4     ! noro      268: \fbox{\bf $B@-G=(B --- $B0x?tJ,2r(B}
1.1       noro      269:
                    270: \begin{itemize}
                    271: \item 10 $BG/A0(B
                    272:
                    273: REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
                    274:
                    275: \item 4 $BG/A0(B
                    276:
                    277: $B%N%k%`$+$i@8$8$kB?9`<0$N0x?tJ,2r$KBP$9$k%H%j%C%/$K(B
                    278: $B$h$j(B, $BBe?tBN>e$NJ,2r$O0MA3$H$7$FM%0L$@$C$?(B
                    279:
                    280: \item $B8=:_(B
                    281:
                    282: $BB?JQ?t(B : $B$^$:$^$:(B
                    283:
                    284: $BM-M}?tBN>e0lJQ?t(B : M. van Hoeij $B$N?7%"%k%4%j%:%`$K$h$j40A4$KIi$1(B
                    285: \end{itemize}
                    286:
                    287: \end{slide}
                    288:
                    289: \begin{slide}{}
1.4     ! noro      290: \fbox{\bf $B@-G=(B --- $B%0%l%V%J4pDl4XO"5!G=(B}
1.1       noro      291:
                    292: \begin{itemize}
                    293: \item 8 $BG/A0(B
                    294:
                    295: $B$H$j$"$($:F0$/DxEY$N@-G=(B
                    296:
                    297: \item 7 $BG/A0(B
                    298:
1.4     ! noro      299: Trace lifting $B$K$h$j9b@-G=$@$C$?$,(B, Faug\`ere $B$N(B Gb $B$K$O(B
1.1       noro      300: $BIi$1$F$$$?(B
                    301:
                    302: $B$7$+$7(B, $B@F<!2=$H$NAH9g$;$K$h$j(B, $B$h$j9-$$HO0O$NF~NO$KBP$7$F%0%l%V%J(B
                    303: $B4pDl$,7W;;$G$-$k$h$&$K$J$C$?(B
                    304:
                    305: \item 4 $BG/A0(B
                    306:
                    307: Modular RUR $B7W;;$O(B Rouillier $B$N<BAu$HHf3S$7$FF1Ey$"$k$$$OM%0L$@$C$?(B
                    308:
                    309: \item $B8=:_(B
                    310:
                    311: FGb $B$O(B Risa/Asir $B$N(B $F_4$ $B<BAu$h$j$:$$$V$s9bB.$N$h$&(B
                    312:
                    313: Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B, Risa/Asir $B$N?tG\9bB.(B
                    314: $B$N>l9g$b$"$k(B. ($B78?t$,Bg$-$/$J$k>l9g$O$^$@(B Risa/Asir $B$,M%0L(B)
                    315:
                    316: \end{itemize}
                    317: \end{slide}
                    318:
                    319: \begin{slide}{}
1.4     ! noro      320: \fbox{\bf $BBg5,LO7W;;$X$NBP1~(B}
1.1       noro      321:
                    322: \begin{itemize}
                    323: \item $B%0%l%V%J4pDl7W;;Cf$K@8@.$5$l$?4pDl$r%G%#%9%/$KJ]B8(B
                    324:
                    325: \begin{itemize}
                    326: \item $B<g5-21$NM-8zMxMQ(B
                    327:
                    328: \item $BESCf$+$i7W;;$r:F3+$G$-$k(B
                    329: \end{itemize}
                    330:
                    331: \item OpenXM $B$K$h$kJ,;67W;;(B
                    332:
                    333: \begin{itemize}
1.4     ! noro      334: \item $B$5$^$6$^$J%?%$%W$NJBNs7W;;$KBP1~(B
        !           335:
        !           336: OX-RFC100, 101 : client-server $B7?(B (OX-RFC100, 101)
        !           337:
        !           338: OX-RFC102 : server-server $BDL?.(B, collective operation
        !           339:
1.1       noro      340: \item $BJBNs2=$K$h$kBf?t8z2L(B
                    341:
                    342: \item $BJ#?t$N%"%k%4%j%:%`$N6%AhE*<B9T$,MF0W(B
1.4     ! noro      343:
        !           344: $B7W;;NL$K$h$k8zN($NDjNLE*Hf3S$,$G$-$J$$>l9g(B
        !           345:
        !           346: $B3d$j9~$_$K$h$kCfCG(B, $BI|5"$,MF0W(B
        !           347:
        !           348: $\Rightarrow$ $B%G!<%?$rJ];}$7$?$^$^7W;;$,B39T$G$-$k(B
1.1       noro      349: \end{itemize}
                    350:
                    351: \end{itemize}
                    352: \end{slide}
                    353:
                    354: \begin{slide}{}
1.4     ! noro      355: \fbox{\bf $B1~MQ;vNc(B}
1.1       noro      356:
                    357: \begin{itemize}
1.2       noro      358: \item $BBJ1_6J@~0E9f%Q%i%a%?@8@.(B [IKNY]
1.1       noro      359:
                    360: $BM-8BBN>e$NB?9`<00x?tJ,2r$N1~MQ(B
                    361:
                    362: \item $D$-$B2C72$K$*$1$k<o!9$N7W;;(B
                    363:
1.4     ! noro      364: de Rham $B%3%[%b%m%8!<(B, $BBe?tE*6I=j%3%[%b%m%8!<(B, $D$-$B2C72$N@)8B(B, $B%F%s%=%k@Q(B
1.1       noro      365: $B7W;;$K$*$$$F(B, $BB?9`<00x?tJ,2r(B, $B=`AGJ,2r(B, $b$-$B4X?t7W;;$rC4Ev(B (OpenXM $B7PM3(B)
                    366:
                    367: \item $BBe?tJ}Dx<07O$N5a2r(B
                    368:
                    369: $B;;K!(B, $B<BAuN>LL$+$iBg5,LO7W;;$KBP1~(B
                    370:
                    371: $BL$Dj78?tK!$K$h$k2D@QJ,7O$N7hDj(B
                    372:
1.4     ! noro      373: $BBPOCE*%7%9%F%`$N%P%C%/%(%s%I$GBe?tJ}Dx<05a2r(B($B%0%l%V%J4pDl7W;;(B)
1.1       noro      374:
                    375: \item $B%"%k%4%j%:%`<BAu<B83%D!<%k(B
                    376:
                    377: $BIbF0>.?t78?t%0%l%V%J4pDl7W;;(B, Wu $B$NJ}K!(B, $B6h4V1i;;(B
                    378: $B$J$I$N%"%k%4%j%:%`$N<BAu<B83(B. $B%=!<%9%l%Y%k$G$N(B
                    379: $B2~JQ$b2DG=(B
                    380:
                    381: \end{itemize}
1.4     ! noro      382: \end{slide}
1.1       noro      383:
                    384: \begin{slide}{}
1.4     ! noro      385: \fbox{\bf $B8=:_3+H/Cf(B($BM=Dj(B)$B$N5!G=(B}
1.1       noro      386:
                    387: \begin{itemize}
                    388: \item $BM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r(B, $BM-8BBN>e$N=`AGJ,2r(B
                    389:
                    390: \begin{itemize}
                    391: \item $BBe?t4v2?Id9f$X$N1~MQ$r8+9~$s$@M-8BBN>e$N=`AGJ,2r<BAu(B
                    392:
                    393: \item $BI8?t$,>.$5$$>l9gFCM-$N:$Fq$,$"$k(B
                    394:
                    395: \item $B4pAC$H$J$kM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r$r<BAuCf(B
                    396: \end{itemize}
                    397:
                    398: \item $B$h$j9-HO$J%G!<%?$NJ];}J}K!(B, $B5-=RG=NO$N8~>e(B
                    399:
                    400: \begin{itemize}
                    401: \item $B8=>u$G$O(B, $B2D49B?9`<04D0J30$N%G!<%?$N<+A3$J<h$j07$$$,:$Fq(B
                    402:
1.4     ! noro      403: \item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k(B flexible $B$J(B
        !           404: $B%G!<%?=hM}$,2DG=$J$h$&$KFbItI=8=$r3HD%Cf(B
1.1       noro      405: \end{itemize}
                    406:
1.4     ! noro      407: \item $B2C72BP1~(B
        !           408:
        !           409: \begin{itemize}
        !           410: \item $BEvA3$"$C$F$7$+$k$Y$-$J$N$K$J$+$C$?(B
        !           411:
        !           412: Buchberger $B%"%k%4%j%:%`$OMF0W(B, $B<+M3J,2r$OBgJQ(B
        !           413: \end{itemize}
        !           414:
        !           415: \item $B@~7ABe?t(B
        !           416: \begin{itemize}
        !           417: \item $B8=>u$O$"$^$j$KIO<e(B. $B$7$+$7(B, $B9-HO0O$NF~NO$KBP1~$9$k$N$OFq$7$$(B.
        !           418: \end{itemize}
1.1       noro      419: \end{itemize}
                    420: \end{slide}
                    421:
1.4     ! noro      422: \begin{slide}{}
        !           423: \fbox{\bf RUR $B7W;;$*$h$SAH$_9~$_%G%P%C%,;HMQK!$NNc(B }
        !           424:
        !           425: $BJ}Dx<0(B : $\{f_1(x_1,\ldots,x_n)=0, \ldots, f_m(x_1,\ldots,x_n)=0\}$
        !           426:
        !           427: lex $B=g=x%0%l%V%J4pDl(B : $\{g_1(x_1)=0, x_2 = h_2(x_1),\ldots,
        !           428: x_n=h_n(x_1)\}$
        !           429:
        !           430: RUR : $\{g_1(x_1)=0, x_2 = {g_2(x_1) \over g'_1(x_1)},\ldots,
        !           431: x_n={g_n(x_1) \over g'_1(x_1)}\}$
        !           432:
        !           433: $\Rightarrow$ $g_i$ $B$N78?t(B $<<$ $h_i$ $B$N78?t(B
        !           434:
        !           435: $B4JC1$JLdBj(B (Katsura-N) $B$G<B:]$KHf3S(B
        !           436:
        !           437: + $B7W;;ESCf$N3d$j9~$_$+$i%G%P%C%0%b!<%I$X$N0\9T(B, $BJQ?t$NFbMF(B
        !           438: $B$NI=<($N%G%b(B
1.1       noro      439: \end{slide}
                    440:
                    441: \begin{slide}{}
1.4     ! noro      442: \fbox{\bf $BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ }
1.1       noro      443:
                    444: \begin{verbatim}
                    445: /* competitive Gbase computation over GF(M) */
                    446: /* Cf. A.28 in SINGULAR Manual */
                    447: /* Process list is specified as an option : grvsf4(...|proc=P) */
                    448: def grvsf4(G,V,M,O)
                    449: {
                    450:   P = getopt(proc);
                    451:   if ( type(P) == -1 ) return dp_f4_mod_main(G,V,M,O);
                    452:   P0 = P[0]; P1 = P[1]; P = [P0,P1];
                    453:   map(ox_reset,P);
                    454:   ox_cmo_rpc(P0,"dp_f4_mod_main",G,V,M,O);
                    455:   ox_cmo_rpc(P1,"dp_gr_mod_main",G,V,0,M,O);
                    456:   map(ox_push_cmd,P,262); /* 262 = OX_popCMO */
                    457:   F = ox_select(P); R = ox_get(F[0]);
                    458:   if ( F[0] == P0 ) { Win = "F4"; Lose = P1;}
                    459:   else { Win = "Buchberger"; Lose = P0; }
                    460:   ox_reset(Lose); /* simply resets the loser */
                    461:   return [Win,R];
                    462: }
                    463: \end{verbatim}
                    464: \end{slide}
                    465:
                    466: \begin{slide}{}
1.4     ! noro      467: \fbox{\bf $BF~<jJ}K!(B : $BF?L>(B CVS}
        !           468:
        !           469: $B>r7o(B : CVS $B$,%$%s%9%H!<%k:Q(B ({\tt http://www.cvshome.org/} $B$+$iF~<j2DG=(B)
        !           470:
        !           471: $B:G=i$O%Q%9%o!<%IEPO?$,I,MW(B
        !           472:
        !           473: \begin{verbatim}
        !           474: % setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs
        !           475: % cvs login
        !           476: \end{verbatim}
        !           477:
        !           478: $B%Q%9%o!<%I(B : anoncvs $\Rightarrow$ {\tt \$HOME/.cvspass}
        !           479:
        !           480: \begin{verbatim}
        !           481: % setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs
        !           482: % cvs checkout OpenXM OpenXM_contrib OpenXM_contrib2
        !           483: \end{verbatim}
        !           484:
        !           485: $B$3$l$G(B, {\tt OpenXM}, {\tt OpenXM\_contrib}, {\tt OpenXM\_contrib2}
        !           486: $B$,$G$-$k(B
        !           487:
        !           488: \end{slide}
        !           489:
        !           490: \begin{slide}{}
        !           491: \fbox{\bf $B;29MJ88%(B}
1.1       noro      492:
                    493: [Bernardin] L. Bernardin, On square-free factorization of
                    494: multivariate polynomials over a finite field, Theoretical
                    495: Computer Science 187 (1997), 105-116.
                    496:
                    497: [Boehm] {\tt http://www.hpl.hp.com/personal/Hans\_Boehm/gc}
                    498:
                    499: [Faug\`ere] J.C. Faug\`ere,
                    500: A new efficient algorithm for computing Groebner bases  ($F_4$),
                    501: Journal of Pure and Applied Algebra (139) 1-3 (1999), 61-88.
                    502:
1.4     ! noro      503: [Hoeij] M. van Hoeij, Factoring polynomials and the knapsack problem,
1.1       noro      504: to appear in Journal of Number Theory (2000).
                    505:
1.2       noro      506: [IKNY] Izu et al. Efficient implementation of Schoof's algorithm, LNCS 1514
                    507: (Proc. of ASIACRYPT'98) (1998), 66-79.
                    508:
                    509: [Noro] M. Noro, J. McKay,
                    510: Computation of replicable functions on Risa/Asir.
                    511: Proc. of PASCO'97, ACM Press (1997), 130-138.
                    512:
1.1       noro      513: [NY] M. Noro, K. Yokoyama,
                    514: A Modular Method to Compute the Rational Univariate
                    515: Representation of Zero-Dimensional Ideals.
                    516: J. Symb. Comp. {\bf 28}/1 (1999), 243-263.
                    517:
1.2       noro      518: \end{slide}
                    519:
                    520: \begin{slide}{}
                    521:
1.1       noro      522: [Oaku] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic
                    523: local cohomology groups of $D$-modules.
                    524: Advancees in Applied Mathematics, 19 (1997), 61-105.
                    525:
                    526: [OpenMath] {\tt http://www.openmath.org}
                    527:
                    528: [OpenXM] {\tt http://www.openxm.org}
                    529:
                    530: [PARI] {\tt http://www.parigp-home.de}
                    531:
                    532: [Risa/Asir] {\tt http://www.math.kobe-u.ac.jp/Asir/asir.html}
                    533:
                    534: [Rouillier] F. Rouillier,
                    535: R\'esolution des syst\`emes z\'ero-dimensionnels.
                    536: Doctoral Thesis(1996), University of Rennes I, France.
                    537:
                    538: [SY] T. Shimoyama, K. Yokoyama, Localization and Primary Decomposition of Polynomial Ideals.  J. Symb. Comp. {\bf 22} (1996), 247-277.
                    539:
                    540: [Singular] {\tt http://www.singular.uni-kl.de}
                    541:
                    542: [Traverso] C. Traverso, \gr trace algorithms. Proc. ISSAC '88 (LNCS 358), 125-138.
                    543:
                    544: \end{slide}