OpenXM/doc/Papers/dagb-noro.tex - diff

Return to dagb-noro.tex CVS log

Up to [local] / OpenXM / doc / Papers

Diff for /OpenXM/doc/Papers/Attic/dagb-noro.tex between version 1.5 and 1.6

-version 1.5, 2001/10/09 01:44:21
+version 1.6, 2001/10/09 11:44:43
 Line 1
 Line 1
 Line 1
- % $OpenXM: OpenXM/doc/Papers/dagb-noro.tex,v 1.4 2001/10/04 08:22:20 noro Exp $
+ % $OpenXM: OpenXM/doc/Papers/dagb-noro.tex,v 1.5 2001/10/09 01:44:21 noro Exp $
  \setlength{\parskip}{10pt}
  \begin{slide}{}
 Line 99  Whole source tree is available via CVS
 Line 99  Whole source tree is available via CVS
 Line 99  Whole source tree is available via CVS
  Polynomial factorization, Groebner basis related computation
- $\Rightarrow$ serves as an OpenXM server/library
+ $\Rightarrow$ my main motivation
  \item Front-end of a general purpose math software
 Line 218  derived from norms.
 Line 218  derived from norms.
 Line 218  derived from norms.
  \item Current
- Multivariate : not so bad
+ Multivariate : moderate
  Univariate : completely obsolete by M. van Hoeij's new algorithm
  [Hoeij]
 Line 249  $F_4$ in FGb : much more efficient than $F_4$ in Risa/
 Line 249  $F_4$ in FGb : much more efficient than $F_4$ in Risa/
 Line 249  $F_4$ in FGb : much more efficient than $F_4$ in Risa/
  Buchberger in Singular [Singular] : faster than Risa/Asir
- $\Leftarrow$ efficient monomial and polynomial representation
+ $\Leftarrow$ efficient monomial and polynomial comutation
  \end{itemize}
  \end{slide}
  \begin{slide}{}
+ \fbox{Some timing data --- DRL Groebner basis computation}
+ \underline{Over $GF(32003)$}
+ \begin{center}
+ \begin{tabular}{|c||c|c|c|c|c|c|c|} \hline
+                 & $C_7$ & $C_8$ & $K_7$ & $K_8$ & $K_9$ & $K_{10}$ & $K_{11}$ \\ \hline
+ Asir $Buchberger$       & 31 & 1687  & 2.6  & 27 & 294  & 4309 & --- \\ \hline
+ Singular & 8.7 & 278 & 0.6 & 5.6 & 54 & 508 & 5510 \\ \hline
+ CoCoA 4 & 241 & & 3.8 & 35 & 402 & &  \\ \hline\hline
+ Asir $F_4$      & 5.3 & 129 & 0.5  & 4.5 & 31  & 273 & 2641 \\ \hline
+ FGb(estimated)  & 0.9 & 23 & 0.1 & 0.8 & 6 & 51 & 366 \\ \hline
+ \end{tabular}
+ \end{center}
+ \underline{Over {\bf Q}}
+ \begin{center}
+ \begin{tabular}{|c||c|c|c|c|c|} \hline
+                 & $C_7$ & $Homog. C_7$ & $K_7$ & $K_8$ & $McKay$ \\ \hline
+ Asir $Buchberger$       & 389 & 594 & 29 & 299 & 34950 \\ \hline
+ Singular & & 15247 & 7.6 & 79 & \\ \hline
+ CoCoA 4 & & & 57 & 709 & \\ \hline\hline
+ Asir $F_4$      &  989 & 456 & 90 & 991 & 4939 \\ \hline
+ FGb(estimated)  & 8 &11 & 0.6 & 5 & 10 \\ \hline
+ \end{tabular}
+ \end{center}
+ \end{slide}
+ \begin{slide}{}
  \fbox{How do we proceed?}
  \begin{itemize}
-Line 262  $\Leftarrow$ efficient monomial and polynomial represe
+Line 291  $\Leftarrow$ efficient monomial and polynomial represe
 Line 262  $\Leftarrow$ efficient monomial and polynomial represe
 Line 291  $\Leftarrow$ efficient monomial and polynomial represe
  {ox\_NTL} for univariate factorization,
- {ox\_FGb} for Groebner basis computation (is it possible?) etc.
+ {ox\_???} for Groebner basis computation, etc.
  $\Rightarrow$ Risa/Asir can be a front-end of efficient servers
  \item Trying to improve our implementation
+ This is very important as a motivation of further development
  Computation of $b$-function : still faster than any other system
  (Kan/sm1, Macaulay2) but not satisfactory
-Line 280  algebra should be improved
+Line 311  algebra should be improved
 Line 280  algebra should be improved
 Line 311  algebra should be improved
  \end{center}
  \end{slide}
- \begin{slide}{}
- \fbox{OpenXM server interface in Risa/Asir}
- \begin{itemize}
- \item TCP/IP stream
- \begin{itemize}
- \item Launcher
- A client executes a launcher on a host.
- The launcher launches a server on the same host.
- \item Server
- Reads from the descriptor 3
- Writes to the descriptor 4
- \end{itemize}
- \item Subroutine call
- In Risa/Asir subroutine library {\tt libasir.a}:
- OpenXM functionalities are implemented as functon calls
- pushing and popping data, executing stack commands etc.
- \end{itemize}
- \end{slide}
- \begin{slide}{}
- \fbox{OpenXM client interface in Risa/Asir}
- \begin{itemize}
- \item Primitive interface functions
- Pushing and popping data, sending commands etc.
- \item Convenient functions
- Launching servers,
- Calling remote functions,
- Resetting remote executions etc.
- \item Parallel distributed computation
- Simple parallelization is practically important
- Competitive computation is easily realized ($\Rightarrow$ demo)
- \end{itemize}
- \end{slide}
  %\begin{slide}{}
  %\fbox{CMO = Serialized representation of mathematical object}
  %
-Line 685  evaluated by {\tt eval()}
+Line 661  evaluated by {\tt eval()}
 Line 685  evaluated by {\tt eval()}
 Line 661  evaluated by {\tt eval()}
  The knapsack factorization is available via {\tt pari(factor,{\it poly})}
  \end{itemize}
+ \end{itemize}
+ \end{slide}
+ \begin{slide}{}
+ \fbox{OpenXM server interface in Risa/Asir}
+ \begin{itemize}
+ \item TCP/IP stream
+ \begin{itemize}
+ \item Launcher
+ A client executes a launcher on a host.
+ The launcher launches a server on the same host.
+ \item Server
+ Reads from the descriptor 3
+ Writes to the descriptor 4
+ \end{itemize}
+ \item Subroutine call
+ In Risa/Asir subroutine library {\tt libasir.a}:
+ OpenXM functionalities are implemented as functon calls
+ pushing and popping data, executing stack commands etc.
+ \end{itemize}
+ \end{slide}
+ \begin{slide}{}
+ \fbox{OpenXM client interface in Risa/Asir}
+ \begin{itemize}
+ \item Primitive interface functions
+ Pushing and popping data, sending commands etc.
+ \item Convenient functions
+ Launching servers,
+ Calling remote functions,
+ Resetting remote executions etc.
+ \item Parallel distributed computation
+ Simple parallelization is practically important
+ Competitive computation is easily realized ($\Rightarrow$ demo)
  \end{itemize}
  \end{slide}

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