Annotation of OpenXM/doc/Papers/jsiamb-noro.tex, Revision 1.1
1.1 ! noro 1: % $OpenXM$
! 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:
! 193: --- $B$3$N%W%m%0%i%`$O%U%j!<$G$O$J$$$,(B, $B4X78$9$k4X?t(B
! 194: $B$O%U%j!<(B
! 195: \end{itemize}
! 196: \end{itemize}
! 197:
! 198: \end{slide}
! 199:
! 200: \begin{slide}{}
! 201: \fbox{$B3+H/$NNr;K(B : 1998-2000}
! 202: \begin{itemize}
! 203: \item OpenXM
! 204:
! 205: \begin{itemize}
! 206: \item OpenXM $B;EMM=q(B : $BLnO$(B, $B9b;3(B [OpenXM]
! 207:
! 208: enconding, phrasebook $B$K4X$9$k%"%$%G%#%"$O(B OpenMath [OpenMath] $B$+$i<ZMQ(B
! 209:
! 210: \item $BJ,;67W;;4X?t$O(B, OpenXM $B;EMM$K=q$-D>$7(B
! 211: \end{itemize}
! 212:
! 213: \item Risa/Asir on Windows
! 214:
! 215: \begin{itemize}
! 216: \item $B;E;v>eI,MW$K$J$C$?(B
! 217:
! 218: Visual C++ $B$G5-=R(B
! 219: \end{itemize}
! 220:
! 221: \item $F_4$ $B$N;n83<BAu(B
! 222:
! 223: \begin{itemize}
! 224: \item [Faug\`ere]$B$K=`5r$7$F5-=R(B
! 225:
! 226: \item $GF(p)$ $B>e(B : $B$J$+$J$+$h$$(B
! 227:
! 228: \item $BM-M}?tBN>e(B :{\it McKay} $B$r=|$$$F$@$a(B
! 229: \end{itemize}
! 230: \end{itemize}
! 231: \end{slide}
! 232:
! 233: \begin{slide}{}
! 234: \fbox{$B3+H/$NNr;K(B : 2000-current}
! 235: \begin{itemize}
! 236: \item $B%*!<%W%s%=!<%92=(B
! 237:
! 238: \begin{itemize}
! 239: \item $BLnO$$,IY;NDL8&$h$j?@8MBg$K0\@R(B
! 240:
! 241: Started Kobe branch $B$N%9%?!<%H(B
! 242: \end{itemize}
! 243:
! 244: \item OpenXM
! 245:
! 246: \begin{itemize}
! 247: \item $B;EMM=q(B : OX-RFC100, 101, (102)
! 248:
! 249: \item OX-RFC102 ($BL$40@.(B) : MPI $B$rMQ$$$?%5!<%P4VDL?.(B
! 250: \end{itemize}
! 251:
! 252: \item Weyl $BBe?t(B
! 253:
! 254: \begin{itemize}
! 255: \item Buchberger $B%"%k%4%j%:%`(B [Takayama]
! 256:
! 257: \item $b$-$B4X?t(B
! 258:
! 259: $b$-$B4X?t$r:G>.B?9`<0$H$7$F%b%8%e%i7W;;(B
! 260: \end{itemize}
! 261: \end{itemize}
! 262:
! 263: \end{slide}
! 264:
! 265: \begin{slide}{}
! 266: \fbox{$B@-G=(B --- $B0x?tJ,2r(B}
! 267:
! 268: \begin{itemize}
! 269: \item 10 $BG/A0(B
! 270:
! 271: REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
! 272:
! 273: \item 4 $BG/A0(B
! 274:
! 275: $B%N%k%`$+$i@8$8$kB?9`<0$N0x?tJ,2r$KBP$9$k%H%j%C%/$K(B
! 276: $B$h$j(B, $BBe?tBN>e$NJ,2r$O0MA3$H$7$FM%0L$@$C$?(B
! 277:
! 278: \item $B8=:_(B
! 279:
! 280: $BB?JQ?t(B : $B$^$:$^$:(B
! 281:
! 282: $BM-M}?tBN>e0lJQ?t(B : M. van Hoeij $B$N?7%"%k%4%j%:%`$K$h$j40A4$KIi$1(B
! 283: \end{itemize}
! 284:
! 285: \end{slide}
! 286:
! 287: \begin{slide}{}
! 288: \fbox{$B@-G=(B --- $B%0%l%V%J4pDl4XO"5!G=(B}
! 289:
! 290: \begin{itemize}
! 291: \item 8 $BG/A0(B
! 292:
! 293: $B$H$j$"$($:F0$/DxEY$N@-G=(B
! 294:
! 295: \item 7 $BG/A0(B
! 296:
! 297: Rather trace lifting $B$K$h$j9b@-G=$@$C$?$,(B, Faug\`ere' $B$N(B Gb $B$K$O(B
! 298: $BIi$1$F$$$?(B
! 299:
! 300: $B$7$+$7(B, $B@F<!2=$H$NAH9g$;$K$h$j(B, $B$h$j9-$$HO0O$NF~NO$KBP$7$F%0%l%V%J(B
! 301: $B4pDl$,7W;;$G$-$k$h$&$K$J$C$?(B
! 302:
! 303: \item 4 $BG/A0(B
! 304:
! 305: Modular RUR $B7W;;$O(B Rouillier $B$N<BAu$HHf3S$7$FF1Ey$"$k$$$OM%0L$@$C$?(B
! 306:
! 307: \item $B8=:_(B
! 308:
! 309: FGb $B$O(B Risa/Asir $B$N(B $F_4$ $B<BAu$h$j$:$$$V$s9bB.$N$h$&(B
! 310:
! 311: Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B, Risa/Asir $B$N?tG\9bB.(B
! 312: $B$N>l9g$b$"$k(B. ($B78?t$,Bg$-$/$J$k>l9g$O$^$@(B Risa/Asir $B$,M%0L(B)
! 313:
! 314: \end{itemize}
! 315: \end{slide}
! 316:
! 317: \begin{slide}{}
! 318: \fbox{$BBg5,LO7W;;$X$NBP1~(B}
! 319:
! 320: \begin{itemize}
! 321: \item $B%0%l%V%J4pDl7W;;Cf$K@8@.$5$l$?4pDl$r%G%#%9%/$KJ]B8(B
! 322:
! 323: \begin{itemize}
! 324: \item $B<g5-21$NM-8zMxMQ(B
! 325:
! 326: \item $BESCf$+$i7W;;$r:F3+$G$-$k(B
! 327: \end{itemize}
! 328:
! 329: \item OpenXM $B$K$h$kJ,;67W;;(B
! 330:
! 331: \begin{itemize}
! 332: \item $BJBNs2=$K$h$kBf?t8z2L(B
! 333:
! 334: \item $BJ#?t$N%"%k%4%j%:%`$N6%AhE*<B9T$,MF0W(B
! 335: \end{itemize}
! 336:
! 337: \end{itemize}
! 338: \end{slide}
! 339:
! 340: \begin{slide}{}
! 341: \fbox{$B1~MQ;vNc(B}
! 342:
! 343: \begin{itemize}
! 344: \item $BBJ1_6J@~0E9f%Q%i%a%?@8@.(B
! 345:
! 346: $BM-8BBN>e$NB?9`<00x?tJ,2r$N1~MQ(B
! 347:
! 348: \item $D$-$B2C72$K$*$1$k<o!9$N7W;;(B
! 349:
! 350: de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, $D$-$B2C72$N@)8B(B, $B%F%s%=%k@Q(B
! 351: $B7W;;$K$*$$$F(B, $BB?9`<00x?tJ,2r(B, $B=`AGJ,2r(B, $b$-$B4X?t7W;;$rC4Ev(B (OpenXM $B7PM3(B)
! 352:
! 353: \item $BBe?tJ}Dx<07O$N5a2r(B
! 354:
! 355: $B;;K!(B, $B<BAuN>LL$+$iBg5,LO7W;;$KBP1~(B
! 356:
! 357: $BL$Dj78?tK!$K$h$k2D@QJ,7O$N7hDj(B
! 358:
! 359: $BBPOCE*%7%9%F%`$N%P%C%/%(%s%I$GBe?tJ}Dx<05a2r(B
! 360:
! 361: \item $B%"%k%4%j%:%`<BAu<B83%D!<%k(B
! 362:
! 363: $BIbF0>.?t78?t%0%l%V%J4pDl7W;;(B, Wu $B$NJ}K!(B, $B6h4V1i;;(B
! 364: $B$J$I$N%"%k%4%j%:%`$N<BAu<B83(B. $B%=!<%9%l%Y%k$G$N(B
! 365: $B2~JQ$b2DG=(B
! 366:
! 367: \end{itemize}
! 368:
! 369: \begin{slide}{}
! 370: \fbox{$B8=:_3+H/Cf$N5!G=(B}
! 371:
! 372: \begin{itemize}
! 373: \item $BM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r(B, $BM-8BBN>e$N=`AGJ,2r(B
! 374:
! 375: \begin{itemize}
! 376: \item $BBe?t4v2?Id9f$X$N1~MQ$r8+9~$s$@M-8BBN>e$N=`AGJ,2r<BAu(B
! 377:
! 378: \item $BI8?t$,>.$5$$>l9gFCM-$N:$Fq$,$"$k(B
! 379:
! 380: \item $B4pAC$H$J$kM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r$r<BAuCf(B
! 381: \end{itemize}
! 382:
! 383: \item $B$h$j9-HO$J%G!<%?$NJ];}J}K!(B, $B5-=RG=NO$N8~>e(B
! 384:
! 385: \begin{itemize}
! 386: \item $B8=>u$G$O(B, $B2D49B?9`<04D0J30$N%G!<%?$N<+A3$J<h$j07$$$,:$Fq(B
! 387:
! 388: \item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k%G!<%?=hM}$,2DG=$J$h$&$K(B
! 389: $BFbItI=8=$r3HD%Cf(B
! 390: \end{itemize}
! 391:
! 392: \end{itemize}
! 393: \end{slide}
! 394:
! 395: \end{slide}
! 396:
! 397: \begin{slide}{}
! 398: \fbox{$BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ }
! 399:
! 400: \begin{verbatim}
! 401: /* competitive Gbase computation over GF(M) */
! 402: /* Cf. A.28 in SINGULAR Manual */
! 403: /* Process list is specified as an option : grvsf4(...|proc=P) */
! 404: def grvsf4(G,V,M,O)
! 405: {
! 406: P = getopt(proc);
! 407: if ( type(P) == -1 ) return dp_f4_mod_main(G,V,M,O);
! 408: P0 = P[0]; P1 = P[1]; P = [P0,P1];
! 409: map(ox_reset,P);
! 410: ox_cmo_rpc(P0,"dp_f4_mod_main",G,V,M,O);
! 411: ox_cmo_rpc(P1,"dp_gr_mod_main",G,V,0,M,O);
! 412: map(ox_push_cmd,P,262); /* 262 = OX_popCMO */
! 413: F = ox_select(P); R = ox_get(F[0]);
! 414: if ( F[0] == P0 ) { Win = "F4"; Lose = P1;}
! 415: else { Win = "Buchberger"; Lose = P0; }
! 416: ox_reset(Lose); /* simply resets the loser */
! 417: return [Win,R];
! 418: }
! 419: \end{verbatim}
! 420: \end{slide}
! 421:
! 422: \begin{slide}{}
! 423: \fbox{$B;29MJ88%(B}
! 424:
! 425: [Bernardin] L. Bernardin, On square-free factorization of
! 426: multivariate polynomials over a finite field, Theoretical
! 427: Computer Science 187 (1997), 105-116.
! 428:
! 429: [Boehm] {\tt http://www.hpl.hp.com/personal/Hans\_Boehm/gc}
! 430:
! 431: [Faug\`ere] J.C. Faug\`ere,
! 432: A new efficient algorithm for computing Groebner bases ($F_4$),
! 433: Journal of Pure and Applied Algebra (139) 1-3 (1999), 61-88.
! 434:
! 435: [Hoeij] M. van Heoij, Factoring polynomials and the knapsack problem,
! 436: to appear in Journal of Number Theory (2000).
! 437:
! 438: [NY] M. Noro, K. Yokoyama,
! 439: A Modular Method to Compute the Rational Univariate
! 440: Representation of Zero-Dimensional Ideals.
! 441: J. Symb. Comp. {\bf 28}/1 (1999), 243-263.
! 442:
! 443: [Oaku] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic
! 444: local cohomology groups of $D$-modules.
! 445: Advancees in Applied Mathematics, 19 (1997), 61-105.
! 446:
! 447: \end{slide}
! 448:
! 449: \begin{slide}{}
! 450: [OpenMath] {\tt http://www.openmath.org}
! 451:
! 452: [OpenXM] {\tt http://www.openxm.org}
! 453:
! 454: [PARI] {\tt http://www.parigp-home.de}
! 455:
! 456: [Risa/Asir] {\tt http://www.math.kobe-u.ac.jp/Asir/asir.html}
! 457:
! 458: [Rouillier] F. Rouillier,
! 459: R\'esolution des syst\`emes z\'ero-dimensionnels.
! 460: Doctoral Thesis(1996), University of Rennes I, France.
! 461:
! 462: [SY] T. Shimoyama, K. Yokoyama, Localization and Primary Decomposition of Polynomial Ideals. J. Symb. Comp. {\bf 22} (1996), 247-277.
! 463:
! 464: [Singular] {\tt http://www.singular.uni-kl.de}
! 465:
! 466: [Traverso] C. Traverso, \gr trace algorithms. Proc. ISSAC '88 (LNCS 358), 125-138.
! 467:
! 468: \end{slide}
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