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}
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>