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version 1.1, 2001/10/04 08:16:27 version 1.4, 2001/10/09 01:44:21
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 % $OpenXM$  % $OpenXM: OpenXM/doc/Papers/jsiamb-noro.tex,v 1.3 2001/10/04 08:30:17 noro Exp $
 \setlength{\parskip}{10pt}  \setlength{\parskip}{10pt}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B7W;;5!Be?t%7%9%F%`(B Risa/Asir}  \fbox{\bf $B7W;;5!Be?t%7%9%F%`(B Risa/Asir}
   
 \begin{itemize}  \begin{itemize}
 \item $BB?9`<04D$K$*$1$kBg5,LO9bB.7W;;$rL\;X$7$F3+H/(B  \item $BB?9`<04D$K$*$1$kBg5,LO9bB.7W;;$rL\;X$7$F3+H/(B
   
 \begin{itemize}  \begin{itemize}
 \item C $B$G5-=R(B  \item C $B$G5-=R(B
 \item $B%a%b%j4IM}$O(B Boehm's conservative GC $B$K$h$k(B  \item $B%a%b%j4IM}$O(B Boehm's conservative GC [Boehm] $B$K$h$k(B
 \end{itemize}  \end{itemize}
   
 \item C $B8@8l$K;w$?%f!<%68@8l%$%s%?%U%'!<%9$r$b$D(B.  \item C $B8@8l$K;w$?%f!<%68@8l%$%s%?%U%'!<%9$r$b$D(B.
Line 22 
Line 22 
 \item $B%*!<%W%s%=!<%9(B  \item $B%*!<%W%s%=!<%9(B
   
 \begin{itemize}  \begin{itemize}
 \item 2000 $BG/$^$GIY;NDL8&$G3+H/(B $\Rightarrow$ $B?@8M(B branch [Risa/Asir]  \item 2000 $BG/$^$GIY;NDL8&$G3+H/(B
   
   $\Rightarrow$ 2001 $BG/$h$j(B Kobe branch [Risa/Asir]
 $B$,%9%?!<%H(B  $B$,%9%?!<%H(B
   
 CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B)  \item CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B)
 \end{itemize}  \end{itemize}
   
 \item OpenXM ((Open message eXchange protocol for Mathematics) $B%$%s%?%U%'!<%9(B  \item OpenXM ((Open message eXchange protocol for Mathematics) $B%$%s%?%U%'!<%9(B
Line 33  CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B)
Line 35  CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B)
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B<g$J5!G=(B}  \fbox{\bf $B<g$J5!G=(B}
   
 \begin{itemize}  \begin{itemize}
 \item $BB?9`<0$N4pK\1i;;(B  \item $BB?9`<0$N4pK\1i;;(B
   
 \begin{itemize}  \begin{itemize}
 \item $B2C8:>h=|(B, GCD, $B=*7k<0(B etc.  \item $B2C8:>h=|(B, GCD, $B=*7k<0(B etc.
 representation  
 \end{itemize}  \end{itemize}
   
 \item $BB?9`<00x?tJ,2r(B  \item $BB?9`<00x?tJ,2r(B
Line 60  representation
Line 61  representation
   
 \item 0 $B<!85%$%G%"%k$N(B change of ordering/RUR [Rouillier]  \item 0 $B<!85%$%G%"%k$N(B change of ordering/RUR [Rouillier]
   
 \item $B=`AG%$%G%"%kJ,2r(B  $BBe?tJ}Dx<0$N2r$r(B, $B0lJQ?tB?9`<0$N:,$GI=$9(B
   
   \item $B=`AG%$%G%"%kJ,2r(B [SY]
   
 $BB?JQ?tBe?tJ}Dx<07O$N2r$NJ,2r$rM?$($k(B  $BB?JQ?tBe?tJ}Dx<07O$N2r$NJ,2r$rM?$($k(B
   
 \item $BB?9`<0$N(B $b$-$B4X?t$N7W;;(B [Oaku]  \item $BB?9`<0$N(B $b$-$B4X?t(B (Bernstein-Sato polynomial) $B$N7W;;(B [Oaku]
   
 $b$-$B4X?t(B : $BB?9`<0$NNmE@$G$"$kD66JLL$NITJQNL(B  $b$-$B4X?t(B : $BB?9`<0$NNmE@$G$"$kD66JLL$NITJQNL(B
   
Line 74  $D$-$B2C72$K$*$1$k7W;;$N(B, $BM-8B<!85$N@~7ABe?t$X$
Line 77  $D$-$B2C72$K$*$1$k7W;;$N(B, $BM-8B<!85$N@~7ABe?t$X$
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B<g$J5!G=(B ($B$D$E$-(B)}  \fbox{\bf $B<g$J5!G=(B ($B$D$E$-(B)}
   
 \begin{itemize}  \begin{itemize}
   
Line 99  OpenXM server $B$H$7$F<B8=(B
Line 102  OpenXM server $B$H$7$F<B8=(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B3+H/$NNr;K(B : ---1994}  \fbox{\bf $B3+H/$NNr;K(B : ---1994}
   
 \begin{itemize}  \begin{itemize}
 \item --1989  \item --1989
Line 132  $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B
Line 135  $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B3+H/$NNr;K(B : 1994-1996}  \fbox{\bf $B3+H/$NNr;K(B : 1994-1996}
   
 \begin{itemize}  \begin{itemize}
 \item $B%P%$%J%jHG$rIY;NDL$h$j8x3+(B  \item $B%P%$%J%jHG$rIY;NDL$h$j8x3+(B
Line 159  $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B
Line 162  $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B3+H/$NNr;K(B : 1996-1998}  \fbox{\bf $B3+H/$NNr;K(B : 1996-1998}
   
 \begin{itemize}  \begin{itemize}
 \item $BJ,;67W;;5!G=$N<BAu(B  \item $BJ,;67W;;5!G=$N<BAu(B
Line 190  Faug\`ere $B$N(B FGb : $B$3$N7W;;$r(B 53 $BIC$G<B
Line 193  Faug\`ere $B$N(B FGb : $B$3$N7W;;$r(B 53 $BIC$G<B
   
 $BM-8BBN>e$NBJ1_6J@~$NM-M}E@8D?t7W;;MQ(B  $BM-8BBN>e$NBJ1_6J@~$NM-M}E@8D?t7W;;MQ(B
   
 --- $B$3$N%W%m%0%i%`$O%U%j!<$G$O$J$$$,(B, $B4X78$9$k4X?t(B  --- $B$3$N%W%m%0%i%`$O%U%j!<$G$O$J$$$,(B, $B4X78$9$k4X?t$O%U%j!<(B
 $B$O%U%j!<(B  
 \end{itemize}  \end{itemize}
 \end{itemize}  \end{itemize}
   
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B3+H/$NNr;K(B : 1998-2000}  \fbox{\bf $B3+H/$NNr;K(B : 1998-2000}
 \begin{itemize}  \begin{itemize}
 \item OpenXM  \item OpenXM
   
Line 221  Visual C++ $B$G5-=R(B
Line 223  Visual C++ $B$G5-=R(B
 \item $F_4$ $B$N;n83<BAu(B  \item $F_4$ $B$N;n83<BAu(B
   
 \begin{itemize}  \begin{itemize}
 \item [Faug\`ere]$B$K=`5r$7$F5-=R(B  \item $BO@J8(B [Faug\`ere] $B$K=`5r$7$F5-=R(B
   
 \item $GF(p)$ $B>e(B : $B$J$+$J$+$h$$(B  \item $GF(p)$ $B>e(B : $B$J$+$J$+$h$$(B
   
Line 231  Visual C++ $B$G5-=R(B
Line 233  Visual C++ $B$G5-=R(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B3+H/$NNr;K(B : 2000-current}  \fbox{\bf $B3+H/$NNr;K(B : 2000-current}
 \begin{itemize}  \begin{itemize}
 \item $B%*!<%W%s%=!<%92=(B  \item $B%*!<%W%s%=!<%92=(B
   
 \begin{itemize}  \begin{itemize}
 \item $BLnO$$,IY;NDL8&$h$j?@8MBg$K0\@R(B  \item $BLnO$$,IY;NDL8&$h$j?@8MBg$K0\@R(B
   
 Started Kobe branch $B$N%9%?!<%H(B  Kobe branch $B$N%9%?!<%H(B
 \end{itemize}  \end{itemize}
   
 \item OpenXM  \item OpenXM
Line 263  $b$-$B4X?t$r:G>.B?9`<0$H$7$F%b%8%e%i7W;;(B
Line 265  $b$-$B4X?t$r:G>.B?9`<0$H$7$F%b%8%e%i7W;;(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B@-G=(B --- $B0x?tJ,2r(B}  \fbox{\bf $B@-G=(B --- $B0x?tJ,2r(B}
   
 \begin{itemize}  \begin{itemize}
 \item 10 $BG/A0(B  \item 10 $BG/A0(B
Line 285  REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
Line 287  REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B@-G=(B --- $B%0%l%V%J4pDl4XO"5!G=(B}  \fbox{\bf $B@-G=(B --- $B%0%l%V%J4pDl4XO"5!G=(B}
   
 \begin{itemize}  \begin{itemize}
 \item 8 $BG/A0(B  \item 8 $BG/A0(B
Line 294  REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
Line 296  REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
   
 \item 7 $BG/A0(B  \item 7 $BG/A0(B
   
 Rather trace lifting $B$K$h$j9b@-G=$@$C$?$,(B, Faug\`ere' $B$N(B Gb $B$K$O(B  Trace lifting $B$K$h$j9b@-G=$@$C$?$,(B, Faug\`ere $B$N(B Gb $B$K$O(B
 $BIi$1$F$$$?(B  $BIi$1$F$$$?(B
   
 $B$7$+$7(B, $B@F<!2=$H$NAH9g$;$K$h$j(B, $B$h$j9-$$HO0O$NF~NO$KBP$7$F%0%l%V%J(B  $B$7$+$7(B, $B@F<!2=$H$NAH9g$;$K$h$j(B, $B$h$j9-$$HO0O$NF~NO$KBP$7$F%0%l%V%J(B
Line 315  Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B
Line 317  Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$BBg5,LO7W;;$X$NBP1~(B}  \fbox{\bf $BBg5,LO7W;;$X$NBP1~(B}
   
 \begin{itemize}  \begin{itemize}
 \item $B%0%l%V%J4pDl7W;;Cf$K@8@.$5$l$?4pDl$r%G%#%9%/$KJ]B8(B  \item $B%0%l%V%J4pDl7W;;Cf$K@8@.$5$l$?4pDl$r%G%#%9%/$KJ]B8(B
Line 329  Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B
Line 331  Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B
 \item OpenXM $B$K$h$kJ,;67W;;(B  \item OpenXM $B$K$h$kJ,;67W;;(B
   
 \begin{itemize}  \begin{itemize}
   \item $B$5$^$6$^$J%?%$%W$NJBNs7W;;$KBP1~(B
   
   OX-RFC100, 101 : client-server $B7?(B (OX-RFC100, 101)
   
   OX-RFC102 : server-server $BDL?.(B, collective operation
   
 \item $BJBNs2=$K$h$kBf?t8z2L(B  \item $BJBNs2=$K$h$kBf?t8z2L(B
   
 \item $BJ#?t$N%"%k%4%j%:%`$N6%AhE*<B9T$,MF0W(B  \item $BJ#?t$N%"%k%4%j%:%`$N6%AhE*<B9T$,MF0W(B
   
   $B7W;;NL$K$h$k8zN($NDjNLE*Hf3S$,$G$-$J$$>l9g(B
   
   $B3d$j9~$_$K$h$kCfCG(B, $BI|5"$,MF0W(B
   
   $\Rightarrow$ $B%G!<%?$rJ];}$7$?$^$^7W;;$,B39T$G$-$k(B
 \end{itemize}  \end{itemize}
   
 \end{itemize}  \end{itemize}
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B1~MQ;vNc(B}  \fbox{\bf $B1~MQ;vNc(B}
   
 \begin{itemize}  \begin{itemize}
 \item $BBJ1_6J@~0E9f%Q%i%a%?@8@.(B  \item $BBJ1_6J@~0E9f%Q%i%a%?@8@.(B [IKNY]
   
 $BM-8BBN>e$NB?9`<00x?tJ,2r$N1~MQ(B  $BM-8BBN>e$NB?9`<00x?tJ,2r$N1~MQ(B
   
 \item $D$-$B2C72$K$*$1$k<o!9$N7W;;(B  \item $D$-$B2C72$K$*$1$k<o!9$N7W;;(B
   
 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  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
 $B7W;;$K$*$$$F(B, $BB?9`<00x?tJ,2r(B, $B=`AGJ,2r(B, $b$-$B4X?t7W;;$rC4Ev(B (OpenXM $B7PM3(B)  $B7W;;$K$*$$$F(B, $BB?9`<00x?tJ,2r(B, $B=`AGJ,2r(B, $b$-$B4X?t7W;;$rC4Ev(B (OpenXM $B7PM3(B)
   
 \item $BBe?tJ}Dx<07O$N5a2r(B  \item $BBe?tJ}Dx<07O$N5a2r(B
Line 356  de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
Line 370  de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
   
 $BL$Dj78?tK!$K$h$k2D@QJ,7O$N7hDj(B  $BL$Dj78?tK!$K$h$k2D@QJ,7O$N7hDj(B
   
 $BBPOCE*%7%9%F%`$N%P%C%/%(%s%I$GBe?tJ}Dx<05a2r(B  $BBPOCE*%7%9%F%`$N%P%C%/%(%s%I$GBe?tJ}Dx<05a2r(B($B%0%l%V%J4pDl7W;;(B)
   
 \item $B%"%k%4%j%:%`<BAu<B83%D!<%k(B  \item $B%"%k%4%j%:%`<BAu<B83%D!<%k(B
   
Line 365  de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
Line 379  de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
 $B2~JQ$b2DG=(B  $B2~JQ$b2DG=(B
   
 \end{itemize}  \end{itemize}
   \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B8=:_3+H/Cf$N5!G=(B}  \fbox{\bf $B8=:_3+H/Cf(B($BM=Dj(B)$B$N5!G=(B}
   
 \begin{itemize}  \begin{itemize}
 \item $BM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r(B, $BM-8BBN>e$N=`AGJ,2r(B  \item $BM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r(B, $BM-8BBN>e$N=`AGJ,2r(B
Line 385  de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
Line 400  de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
 \begin{itemize}  \begin{itemize}
 \item $B8=>u$G$O(B, $B2D49B?9`<04D0J30$N%G!<%?$N<+A3$J<h$j07$$$,:$Fq(B  \item $B8=>u$G$O(B, $B2D49B?9`<04D0J30$N%G!<%?$N<+A3$J<h$j07$$$,:$Fq(B
   
 \item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k%G!<%?=hM}$,2DG=$J$h$&$K(B  \item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k(B flexible $B$J(B
 $BFbItI=8=$r3HD%Cf(B  $B%G!<%?=hM}$,2DG=$J$h$&$KFbItI=8=$r3HD%Cf(B
 \end{itemize}  \end{itemize}
   
   \item $B2C72BP1~(B
   
   \begin{itemize}
   \item $BEvA3$"$C$F$7$+$k$Y$-$J$N$K$J$+$C$?(B
   
   Buchberger $B%"%k%4%j%:%`$OMF0W(B, $B<+M3J,2r$OBgJQ(B
 \end{itemize}  \end{itemize}
   
   \item $B@~7ABe?t(B
   \begin{itemize}
   \item $B8=>u$O$"$^$j$KIO<e(B. $B$7$+$7(B, $B9-HO0O$NF~NO$KBP1~$9$k$N$OFq$7$$(B.
   \end{itemize}
   \end{itemize}
 \end{slide}  \end{slide}
   
   \begin{slide}{}
   \fbox{\bf RUR $B7W;;$*$h$SAH$_9~$_%G%P%C%,;HMQK!$NNc(B }
   
   $BJ}Dx<0(B : $\{f_1(x_1,\ldots,x_n)=0, \ldots, f_m(x_1,\ldots,x_n)=0\}$
   
   lex $B=g=x%0%l%V%J4pDl(B : $\{g_1(x_1)=0, x_2 = h_2(x_1),\ldots,
   x_n=h_n(x_1)\}$
   
   RUR : $\{g_1(x_1)=0, x_2 = {g_2(x_1) \over g'_1(x_1)},\ldots,
   x_n={g_n(x_1) \over g'_1(x_1)}\}$
   
   $\Rightarrow$ $g_i$ $B$N78?t(B $<<$ $h_i$ $B$N78?t(B
   
   $B4JC1$JLdBj(B (Katsura-N) $B$G<B:]$KHf3S(B
   
   + $B7W;;ESCf$N3d$j9~$_$+$i%G%P%C%0%b!<%I$X$N0\9T(B, $BJQ?t$NFbMF(B
   $B$NI=<($N%G%b(B
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ }  \fbox{\bf $BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ }
   
 \begin{verbatim}  \begin{verbatim}
 /* competitive Gbase computation over GF(M) */  /* competitive Gbase computation over GF(M) */
Line 420  def grvsf4(G,V,M,O)
Line 464  def grvsf4(G,V,M,O)
 \end{slide}  \end{slide}
   
 \begin{slide}{}  \begin{slide}{}
 \fbox{$B;29MJ88%(B}  \fbox{\bf $BF~<jJ}K!(B : $BF?L>(B CVS}
   
   $B>r7o(B : CVS $B$,%$%s%9%H!<%k:Q(B ({\tt http://www.cvshome.org/} $B$+$iF~<j2DG=(B)
   
   $B:G=i$O%Q%9%o!<%IEPO?$,I,MW(B
   
   \begin{verbatim}
   % setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs
   % cvs login
   \end{verbatim}
   
   $B%Q%9%o!<%I(B : anoncvs $\Rightarrow$ {\tt \$HOME/.cvspass}
   
   \begin{verbatim}
   % setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs
   % cvs checkout OpenXM OpenXM_contrib OpenXM_contrib2
   \end{verbatim}
   
   $B$3$l$G(B, {\tt OpenXM}, {\tt OpenXM\_contrib}, {\tt OpenXM\_contrib2}
   $B$,$G$-$k(B
   
   \end{slide}
   
   \begin{slide}{}
   \fbox{\bf $B;29MJ88%(B}
   
 [Bernardin] L. Bernardin, On square-free factorization of  [Bernardin] L. Bernardin, On square-free factorization of
 multivariate polynomials over a finite field, Theoretical  multivariate polynomials over a finite field, Theoretical
 Computer Science 187 (1997), 105-116.  Computer Science 187 (1997), 105-116.
Line 432  Computer Science 187 (1997), 105-116.
Line 500  Computer Science 187 (1997), 105-116.
 A new efficient algorithm for computing Groebner bases  ($F_4$),  A new efficient algorithm for computing Groebner bases  ($F_4$),
 Journal of Pure and Applied Algebra (139) 1-3 (1999), 61-88.  Journal of Pure and Applied Algebra (139) 1-3 (1999), 61-88.
   
 [Hoeij] M. van Heoij, Factoring polynomials and the knapsack problem,  [Hoeij] M. van Hoeij, Factoring polynomials and the knapsack problem,
 to appear in Journal of Number Theory (2000).  to appear in Journal of Number Theory (2000).
   
   [IKNY] Izu et al. Efficient implementation of Schoof's algorithm, LNCS 1514
   (Proc. of ASIACRYPT'98) (1998), 66-79.
   
   [Noro] M. Noro, J. McKay,
   Computation of replicable functions on Risa/Asir.
   Proc. of PASCO'97, ACM Press (1997), 130-138.
   
 [NY] M. Noro, K. Yokoyama,  [NY] M. Noro, K. Yokoyama,
 A Modular Method to Compute the Rational Univariate  A Modular Method to Compute the Rational Univariate
 Representation of Zero-Dimensional Ideals.  Representation of Zero-Dimensional Ideals.
 J. Symb. Comp. {\bf 28}/1 (1999), 243-263.  J. Symb. Comp. {\bf 28}/1 (1999), 243-263.
   
   \end{slide}
   
   \begin{slide}{}
   
 [Oaku] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic  [Oaku] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic
 local cohomology groups of $D$-modules.  local cohomology groups of $D$-modules.
 Advancees in Applied Mathematics, 19 (1997), 61-105.  Advancees in Applied Mathematics, 19 (1997), 61-105.
   
 \end{slide}  
   
 \begin{slide}{}  
 [OpenMath] {\tt http://www.openmath.org}  [OpenMath] {\tt http://www.openmath.org}
   
 [OpenXM] {\tt http://www.openxm.org}  [OpenXM] {\tt http://www.openxm.org}

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