% $OpenXM: OpenXM/doc/calc2000p/func2.tex,v 1.5 2000/07/22 00:31:06 takayama Exp $
\documentclass[twocolumn]{article}
\pagestyle{empty}
%\markright{ {\tt http://www.openxm.org} }
\usepackage{color}
\usepackage{epsfig}
\title{\huge \color{blue} 4252 functions are available
on our servers and libraries (continued)}
\author{} \date{}
\begin{document}
\maketitle

\noindent
\fbox{\huge {\color{green} $D$-modules}} ($D$ is the Weyl algebra)

\noindent
{\color{red} gb } (Gr\"obner basis),
{\color{red} syz} (syzygy),
{\color{red} annfs} (Annhilating ideal of $f^s$),
{\color{red} bfunction},
{\color{red} schreyer} (free resolution by the Schreyer method),
{\color{red} vMinRes} (V-minimal free resolution),
{\color{red} characteristic} (Characteristic variety),
{\color{red} restriction} in the derived category of $D$-modules,
{\color{red} integration} in the derived category,
{\color{red} tensor}  in the derived category,
{\color{red} dual} (Dual as a D-module),
{\color{red} slope}.

\medbreak
\noindent
\fbox{\huge {\color{green} Cohomology groups}} 

\noindent
{\color{red} deRham} (The de Rham cohomology groups of
${\bf C}^n \setminus V(f)$,
{\color{red} ext} (Ext modules for a holonomic $D$-module $M$
and the ring of formal power series).

\medbreak
\noindent
\fbox{\huge 
 {\color{green} Differential equations}}

\noindent
Helping to derive and prove {\color{red} combinatorial} and
{\color{red} special function identities},
{\color{red} gkz} (GKZ hypergeometric differential equations),
{\color{red} appell} (Appell's hypergeometric differential equations),
{\color{red} indicial} (indicial equations),
{\color{red} rank} (Holonomic rank),
{\color{red} rrank} (Holonomic rank of regular holonomic systems),
{\color{red} dsolv} (series solutions of holonomic systems).

\medbreak
\noindent
\fbox{\huge 
 {\color{green} OpenMATH support}}

\noindent
{\color{red} om\_xml} (CMO to OpenMATH XML),
{\color{red} om\_xml\_to\_cmo} (OpenMATH XML to CMO).

\medbreak
\noindent
\fbox{\huge 
 {\color{green} Homotopy Method}}

\noindent
{\color{red} phc} (Solving systems of algebraic equations by 
numerical and polyhedral homotopy methods).

\medbreak
\noindent
\fbox{\huge 
 {\color{green} Toric ideal}}

\noindent
{\color{red} tigers} (Enumerate all Gr\"obner basis of a toric ideal.
Finding test sets for integer program),
{\color{red} arithDeg} (Arithmetic degree of a monomial ideal),
{\color{red} stdPair} (Standard pair decomposition of a monomial ideal).

\medbreak
\noindent
\fbox{\huge {\color{green} Communications}}

\noindent
{\color{red} ox\_launch} (starting a server), 
{\color{red} ox\_launch\_nox}, 
{\color{red} ox\_shutdown},
{\color{red} ox\_launch\_generic}, 
{\color{red} generate\_port}, 
{\color{red} try\_bind\_listen}, 
{\color{red} try\_connect}, 
{\color{red} try\_accept}, 
{\color{red} register\_server}, 
{\color{red} ox\_rpc}, 
{\color{red} ox\_cmo\_rpc}, 
{\color{red} ox\_execute\_string}, 
{\color{red} ox\_reset} (reset the server),
{\color{red} ox\_intr},
{\color{red} register\_handler}, 
{\color{red} ox\_push\_cmo}, 
{\color{red} ox\_push\_local},
{\color{red} ox\_pop\_cmo}, 
{\color{red} ox\_pop\_local}, 
{\color{red} ox\_push\_cmd}, 
{\color{red} ox\_sync},
{\color{red} ox\_get}, 
{\color{red} ox\_pops}, 
{\color{red} ox\_select}, 
{\color{red} ox\_flush},
{\color{red} ox\_get\_serverinfo}

\medbreak
\noindent
In addition to these functions, {\color{green} Mathematica functions} 
can be called as server functions.
\medbreak
\noindent
\fbox{\huge {\color{green} Examples}}
{\footnotesize
\begin{verbatim}
[345] sm1_deRham([x^3-y^2*z^2,[x,y,z]]);
[1,1,0,0]
\end{verbatim}} 

\noindent
{\footnotesize \begin{verbatim}
[287] phc(katsura(7)); B=map(first,Phc)$
[291] gnuplot_plotDots(B,0)$
\end{verbatim} }

\epsfxsize=3cm
\begin{center}
\epsffile{../calc2000/katsura7.ps}
\end{center}
%%The first components of the solutions to the system of algebraic equations Katsura 7.

\noindent


\medbreak
\noindent
\fbox{ {\color{green} Authors}}
Castro-Jim\'enez, Doltman, Hubert, Murao, Noro, Oaku, Okutani, 
Shimoyama, Sturm, Takayama, Tamura, Verschelde, Yokoyama.

\medbreak
\vfill
\noindent
\rightline{ {\color{red} {\tt http://www.openxm.org} }}

\end{document}