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Annotation of OpenXM/doc/calc2000p/func2.tex, Revision 1.5

1.5     ! takayama    1: % $OpenXM: OpenXM/doc/calc2000p/func2.tex,v 1.4 2000/07/21 01:34:53 takayama Exp $
1.1       takayama    2: \documentclass[twocolumn]{article}
1.4       takayama    3: \pagestyle{empty}
                      4: %\markright{ {\tt http://www.openxm.org} }
1.1       takayama    5: \usepackage{color}
1.2       takayama    6: \usepackage{epsfig}
1.1       takayama    7: \title{\huge \color{blue} 4252 functions are available
                      8: on our servers and libraries (continued)}
                      9: \author{} \date{}
                     10: \begin{document}
                     11: \maketitle
                     12:
                     13: \noindent
                     14: \fbox{\huge {\color{green} $D$-modules}} ($D$ is the Weyl algebra)
                     15:
                     16: \noindent
                     17: {\color{red} gb } (Gr\"obner basis),
                     18: {\color{red} syz} (syzygy),
                     19: {\color{red} annfs} (Annhilating ideal of $f^s$),
                     20: {\color{red} bfunction},
1.2       takayama   21: {\color{red} schreyer} (free resolution by the Schreyer method),
1.1       takayama   22: {\color{red} vMinRes} (V-minimal free resolution),
1.2       takayama   23: {\color{red} characteristic} (Characteristic variety),
1.1       takayama   24: {\color{red} restriction} in the derived category of $D$-modules,
                     25: {\color{red} integration} in the derived category,
                     26: {\color{red} tensor}  in the derived category,
1.2       takayama   27: {\color{red} dual} (Dual as a D-module),
1.1       takayama   28: {\color{red} slope}.
                     29:
                     30: \medbreak
                     31: \noindent
                     32: \fbox{\huge {\color{green} Cohomology groups}}
                     33:
                     34: \noindent
                     35: {\color{red} deRham} (The de Rham cohomology groups of
                     36: ${\bf C}^n \setminus V(f)$,
                     37: {\color{red} ext} (Ext modules for a holonomic $D$-module $M$
                     38: and the ring of formal power series).
                     39:
                     40: \medbreak
                     41: \noindent
                     42: \fbox{\huge
                     43:  {\color{green} Differential equations}}
                     44:
                     45: \noindent
                     46: Helping to derive and prove {\color{red} combinatorial} and
                     47: {\color{red} special function identities},
                     48: {\color{red} gkz} (GKZ hypergeometric differential equations),
1.2       takayama   49: {\color{red} appell} (Appell's hypergeometric differential equations),
1.1       takayama   50: {\color{red} indicial} (indicial equations),
1.2       takayama   51: {\color{red} rank} (Holonomic rank),
                     52: {\color{red} rrank} (Holonomic rank of regular holonomic systems),
1.1       takayama   53: {\color{red} dsolv} (series solutions of holonomic systems).
                     54:
1.2       takayama   55: \medbreak
                     56: \noindent
                     57: \fbox{\huge
                     58:  {\color{green} OpenMATH support}}
                     59:
                     60: \noindent
                     61: {\color{red} om\_xml} (CMO to OpenMATH XML),
                     62: {\color{red} om\_xml\_to\_cmo} (OpenMATH XML to CMO).
                     63:
                     64: \medbreak
                     65: \noindent
                     66: \fbox{\huge
                     67:  {\color{green} Homotopy Method}}
                     68:
                     69: \noindent
                     70: {\color{red} phc} (Solving systems of algebraic equations by
                     71: numerical and polyhedral homotopy methods).
                     72:
                     73: \medbreak
                     74: \noindent
                     75: \fbox{\huge
                     76:  {\color{green} Toric ideal}}
                     77:
                     78: \noindent
                     79: {\color{red} tigers} (Enumerate all Gr\"obner basis of a toric ideal.
                     80: Finding test sets for integer program),
1.4       takayama   81: {\color{red} arithDeg} (Arithmetic degree of a monomial ideal),
1.2       takayama   82: {\color{red} stdPair} (Standard pair decomposition of a monomial ideal).
                     83:
                     84: \medbreak
                     85: \noindent
                     86: \fbox{\huge {\color{green} Communications}}
                     87:
                     88: \noindent
                     89: {\color{red} ox\_launch} (starting a server),
                     90: {\color{red} ox\_launch\_nox},
                     91: {\color{red} ox\_shutdown},
                     92: {\color{red} ox\_launch\_generic},
                     93: {\color{red} generate\_port},
                     94: {\color{red} try\_bind\_listen},
                     95: {\color{red} try\_connect},
                     96: {\color{red} try\_accept},
                     97: {\color{red} register\_server},
                     98: {\color{red} ox\_rpc},
                     99: {\color{red} ox\_cmo\_rpc},
                    100: {\color{red} ox\_execute\_string},
                    101: {\color{red} ox\_reset} (reset the server),
                    102: {\color{red} ox\_intr},
                    103: {\color{red} register\_handler},
                    104: {\color{red} ox\_push\_cmo},
                    105: {\color{red} ox\_push\_local},
                    106: {\color{red} ox\_pop\_cmo},
                    107: {\color{red} ox\_pop\_local},
                    108: {\color{red} ox\_push\_cmd},
                    109: {\color{red} ox\_sync},
                    110: {\color{red} ox\_get},
                    111: {\color{red} ox\_pops},
                    112: {\color{red} ox\_select},
                    113: {\color{red} ox\_flush},
                    114: {\color{red} ox\_get\_serverinfo}
                    115:
                    116: \medbreak
                    117: \noindent
1.5     ! takayama  118: In addition to these functions, {\color{green} Mathematica functions}
        !           119: can be called as server functions.
        !           120: \medbreak
        !           121: \noindent
1.2       takayama  122: \fbox{\huge {\color{green} Examples}}
                    123: {\footnotesize
                    124: \begin{verbatim}
                    125: [345] sm1_deRham([x^3-y^2*z^2,[x,y,z]]);
                    126: [1,1,0,0]
                    127: \end{verbatim}}
                    128:
                    129: \noindent
                    130: {\footnotesize \begin{verbatim}
1.3       takayama  131: [287] phc(katsura(7)); B=map(first,Phc)$
                    132: [291] gnuplot_plotDots(B,0)$
1.2       takayama  133: \end{verbatim} }
                    134:
                    135: \epsfxsize=3cm
                    136: \begin{center}
                    137: \epsffile{../calc2000/katsura7.ps}
                    138: \end{center}
                    139: %%The first components of the solutions to the system of algebraic equations Katsura 7.
                    140:
                    141: \noindent
                    142:
                    143:
                    144: \medbreak
                    145: \noindent
                    146: \fbox{ {\color{green} Authors}}
1.3       takayama  147: Castro-Jim\'enez, Doltman, Hubert, Murao, Noro, Oaku, Okutani,
                    148: Shimoyama, Sturm, Takayama, Tamura, Verschelde, Yokoyama.
1.4       takayama  149:
                    150: \medbreak
1.5     ! takayama  151: \vfill
1.4       takayama  152: \noindent
                    153: \rightline{ {\color{red} {\tt http://www.openxm.org} }}
1.1       takayama  154:
                    155: \end{document}