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