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version 1.4, 2001/10/12 02:58:35 version 1.5, 2001/10/12 05:11:36
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 % $OpenXM: OpenXM/doc/Papers/dag-noro.tex,v 1.3 2001/10/12 02:22:17 noro Exp $  % $OpenXM: OpenXM/doc/Papers/dag-noro.tex,v 1.4 2001/10/12 02:58:35 noro Exp $
 \documentclass{slides}  \documentclass{slides}
 \usepackage{color}  \usepackage{color}
 \usepackage{rgb}  \usepackage{rgb}
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 \begin{slide}{}  \begin{slide}{}
 \fbox{\fbc A computer algebra system Risa/Asir}  \fbox{\fbc A computer algebra system Risa/Asir}
   
 ({\urlc \tt http://www.math.kobe-u.ac.jp/Asir/asir.html})  
   
 \begin{itemize}  \begin{itemize}
 \item {\itc Software mainly for polynomial computation}  \item {\itc Software mainly for polynomial computation}
   
   Polynomial factorization, Groebner basis computation
 \item {\itc User language with C-like syntax}  \item {\itc User language with C-like syntax}
   
 C language without type declaration, with list processing  C language without type declaration, with list processing
   
 \item {\itc Builtin {\tt gdb}-like debugger for user programs}  \item {\itc Builtin {\tt gdb}-like debugger for user programs}
   
 \item {\itc Open source}  \item {\itc Open source} ({\urlc \tt http://www.math.kobe-u.ac.jp/Asir/asir.html})
   
 Whole source tree is available via CVS  The source and binaries are available via ftp or CVS
   
 The latest version : see {\urlc \tt http://www.openxm.org}  See {\urlc \tt http://www.openxm.org} to get the latest version
   
 \item {\itc OpenXM interface}  \item {\itc OpenXM interface}
   
 \begin{itemize}  \begin{itemize}
 \item OpenXM  \item OpenXM ({\urlc \tt http://www.openxm.org})
   
 An infrastructure for exchanging mathematical data  An infrastructure for exchanging mathematical data
 \item Risa/Asir is a main client in OpenXM package.  \item Risa/Asir is a main client in OpenXM package
 \item An OpenXM server {\tt ox\_asir}  \item {\tt ox\_asir} is an OpenXM server
 \item A library with OpenXM library interface {\tt libasir.a}  \item {\tt libasir.a} provides OpenXM interface via function call
 \end{itemize}  \end{itemize}
 \end{itemize}  \end{itemize}
 \end{slide}  \end{slide}
Line 174  Univariate factorization over algebraic number fields
Line 173  Univariate factorization over algebraic number fields
   
 Intensive use of successive extension, non-squarefree norms  Intensive use of successive extension, non-squarefree norms
   
   Application to splitting field and Galois group computation
   
 \item {\itc 1996-1998}  \item {\itc 1996-1998}
   
 Univariate factorization over large finite fields  Univariate factorization over large finite fields
Line 226  Efficient $b$-function computation[OAKU97] by a modula
Line 227  Efficient $b$-function computation[OAKU97] by a modula
   
 \underline{\itc Univariate; over {\bf Q}}  \underline{\itc Univariate; over {\bf Q}}
   
 $N_i$ : a norm of a polynomial, $\deg(N_i) = i$  $N_{i,j}$ : a norm of a polynomial, $\deg(N_i) = i$ with $j$ modular factor
 \begin{center}  \begin{center}
 \begin{tabular}{|c||c|c|c|c|} \hline  \begin{tabular}{|c||c|c|c|c|} \hline
                 & $N_{105}$ & $N_{120}$ & $N_{168}$ & $N_{210}$ \\ \hline                  & $N_{105,23}$ & $N_{120,20}$ & $N_{168,24}$ & $N_{210,54}$ \\ \hline
 Asir    & 0.86  & 59 & 840 & hard \\ \hline  {\tc Asir}      & {\tc 0.86}    & {\tc 59} & {\tc 840} & {\tc hard} \\ \hline
 Asir NormFactor & 1.6   & 2.2& 6.1& hard \\ \hline  Asir NormFactor & 1.6   & 2.2& 6.1& hard \\ \hline
 %Singular& hard?        & hard?& hard? & hard? \\ \hline  %Singular& hard?        & hard?& hard? & hard? \\ \hline
 CoCoA 4 & 0.2   & 7.1   & 16 & 0.5 \\ \hline\hline  CoCoA 4 & 0.2   & 7.1   & 16 & 0.5 \\ \hline\hline
Line 244  $W_{i,j,k} = Wang[i]\cdot Wang[j]\cdot Wang[k]$ in {\t
Line 245  $W_{i,j,k} = Wang[i]\cdot Wang[j]\cdot Wang[k]$ in {\t
 \begin{center}  \begin{center}
 \begin{tabular}{|c||c|c|c|c|c|} \hline  \begin{tabular}{|c||c|c|c|c|c|} \hline
         & $W_{1,2,3}$ & $W_{4,5,6}$ & $W_{7,8,9}$ & $W_{10,11,12}$ & $W_{13,14,15}$ \\ \hline          & $W_{1,2,3}$ & $W_{4,5,6}$ & $W_{7,8,9}$ & $W_{10,11,12}$ & $W_{13,14,15}$ \\ \hline
 Asir    & 0.2 & 4.7 & 14 & 17 & 0.4 \\ \hline  variables & 3 & 5 & 5 & 5 & 4 \\ \hline
   monomials & 905 & 41369 & 51940 & 30988 & 3344 \\ \hline\hline
   {\tc Asir}      & {\tc 0.2} & {\tc 4.7} & {\tc 14} & {\tc 17} & {\tc 0.4} \\ \hline
 %Singular& $>$15min     & ---   & ---& ---& ---\\ \hline  %Singular& $>$15min     & ---   & ---& ---& ---\\ \hline
 CoCoA 4 & 5.2 & $>$15min        & $>$15min & $>$15min & 117 \\ \hline\hline  CoCoA 4 & 5.2 & $>$15min        & $>$15min & $>$15min & 117 \\ \hline\hline
 Mathematica 4& 0.2      & 16    & 23 & 36 & 1.1 \\ \hline  Mathematica 4& 0.2      & 16    & 23 & 36 & 1.1 \\ \hline
Line 262  Maple 7& 0.5  & 18  & 967  & 48 & 1.3 \\ \hline
Line 265  Maple 7& 0.5  & 18  & 967  & 48 & 1.3 \\ \hline
 \begin{center}  \begin{center}
 \begin{tabular}{|c||c|c|c|c|c|c|c|} \hline  \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                  & $C_7$ & $C_8$ & $K_7$ & $K_8$ & $K_9$ & $K_{10}$ & $K_{11}$ \\ \hline
 Asir $Buchberger$       & 31 & 1687  & 2.6  & 27 & 294  & 4309 & --- \\ \hline  {\tc Asir $Buchberger$} & {\tc 31} & {\tc 1687}  & {\tc 2.6}  & {\tc 27} & {\tc 294}  & {\tc 4309} & --- \\ \hline
 Singular & 8.7 & 278 & 0.6 & 5.6 & 54 & 508 & 5510 \\ \hline  Singular & 8.7 & 278 & 0.6 & 5.6 & 54 & 508 & 5510 \\ \hline
 CoCoA 4 & 241 & $>$ 5h & 3.8 & 35 & 402 &7021  & --- \\ \hline\hline  CoCoA 4 & 241 & $>$ 5h & 3.8 & 35 & 402 &7021  & --- \\ \hline\hline
 Asir $F_4$      & 5.3 & 129 & 0.5  & 4.5 & 31  & 273 & 2641 \\ \hline  {\tc Asir $F_4$}        & {\tc 5.3} & {\tc 129} & {\tc 0.5}  & {\tc 4.5} & {\tc 31}  & {\tc 273} & {\tc 2641} \\ \hline
 FGb(estimated)  & 0.9 & 23 & 0.1 & 0.8 & 6 & 51 & 366 \\ \hline  FGb(estimated)  & 0.9 & 23 & 0.1 & 0.8 & 6 & 51 & 366 \\ \hline
 \end{tabular}  \end{tabular}
 \end{center}  \end{center}
Line 275  FGb(estimated) & 0.9 & 23 & 0.1 & 0.8 & 6 & 51 & 366 \
Line 278  FGb(estimated) & 0.9 & 23 & 0.1 & 0.8 & 6 & 51 & 366 \
 \begin{center}  \begin{center}
 \begin{tabular}{|c||c|c|c|c|c|} \hline  \begin{tabular}{|c||c|c|c|c|c|} \hline
                 & $C_7$ & $Homog. C_7$ & $K_7$ & $K_8$ & $McKay$ \\ \hline                  & $C_7$ & $Homog. C_7$ & $K_7$ & $K_8$ & $McKay$ \\ \hline
 Asir $Buchberger$       & 389 & 594 & 29 & 299 & 34950 \\ \hline  {\tc Asir $Buchberger$}         & {\tc 389} & {\tc 594} & {\tc 29} & {\tc 299} & {\tc 34950} \\ \hline
 Singular & --- & 15247 & 7.6 & 79 & $>$ 20h \\ \hline  Singular & --- & 15247 & 7.6 & 79 & $>$ 20h \\ \hline
 CoCoA 4 & --- & 13227 & 57 & 709 & --- \\ \hline\hline  CoCoA 4 & --- & 13227 & 57 & 709 & --- \\ \hline\hline
 Asir $F_4$      &  989 & 456 & 90 & 991 & 4939 \\ \hline  {\tc Asir $F_4$}        &  {\tc 989} & {\tc 456} & {\tc 90} & {\tc 991} & {\tc 4939} \\ \hline
 FGb(estimated)  & 8 &11 & 0.6 & 5 & 10 \\ \hline  FGb(estimated)  & 8 &11 & 0.6 & 5 & 10 \\ \hline
 \end{tabular}  \end{tabular}
 \end{center}  \end{center}
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