% $OpenXM: OpenXM/doc/calc2000p/func2.tex,v 1.3 2000/07/20 07:05:29 takayama Exp $ \documentclass[twocolumn]{article} \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} aDegree} (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 \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. \end{document}