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Annotation of OpenXM/doc/calc2000p/func2.tex, Revision 1.3

1.3     ! takayama    1: % $OpenXM: OpenXM/doc/calc2000p/func2.tex,v 1.2 2000/07/20 05:58:00 takayama Exp $
1.1       takayama    2: \documentclass[twocolumn]{article}
                      3: \usepackage{color}
1.2       takayama    4: \usepackage{epsfig}
1.1       takayama    5: \title{\huge \color{blue} 4252 functions are available
                      6: on our servers and libraries (continued)}
                      7: \author{} \date{}
                      8: \begin{document}
                      9: \maketitle
                     10:
                     11: \noindent
                     12: \fbox{\huge {\color{green} $D$-modules}} ($D$ is the Weyl algebra)
                     13:
                     14: \noindent
                     15: {\color{red} gb } (Gr\"obner basis),
                     16: {\color{red} syz} (syzygy),
                     17: {\color{red} annfs} (Annhilating ideal of $f^s$),
                     18: {\color{red} bfunction},
1.2       takayama   19: {\color{red} schreyer} (free resolution by the Schreyer method),
1.1       takayama   20: {\color{red} vMinRes} (V-minimal free resolution),
1.2       takayama   21: {\color{red} characteristic} (Characteristic variety),
1.1       takayama   22: {\color{red} restriction} in the derived category of $D$-modules,
                     23: {\color{red} integration} in the derived category,
                     24: {\color{red} tensor}  in the derived category,
1.2       takayama   25: {\color{red} dual} (Dual as a D-module),
1.1       takayama   26: {\color{red} slope}.
                     27:
                     28: \medbreak
                     29: \noindent
                     30: \fbox{\huge {\color{green} Cohomology groups}}
                     31:
                     32: \noindent
                     33: {\color{red} deRham} (The de Rham cohomology groups of
                     34: ${\bf C}^n \setminus V(f)$,
                     35: {\color{red} ext} (Ext modules for a holonomic $D$-module $M$
                     36: and the ring of formal power series).
                     37:
                     38: \medbreak
                     39: \noindent
                     40: \fbox{\huge
                     41:  {\color{green} Differential equations}}
                     42:
                     43: \noindent
                     44: Helping to derive and prove {\color{red} combinatorial} and
                     45: {\color{red} special function identities},
                     46: {\color{red} gkz} (GKZ hypergeometric differential equations),
1.2       takayama   47: {\color{red} appell} (Appell's hypergeometric differential equations),
1.1       takayama   48: {\color{red} indicial} (indicial equations),
1.2       takayama   49: {\color{red} rank} (Holonomic rank),
                     50: {\color{red} rrank} (Holonomic rank of regular holonomic systems),
1.1       takayama   51: {\color{red} dsolv} (series solutions of holonomic systems).
                     52:
1.2       takayama   53: \medbreak
                     54: \noindent
                     55: \fbox{\huge
                     56:  {\color{green} OpenMATH support}}
                     57:
                     58: \noindent
                     59: {\color{red} om\_xml} (CMO to OpenMATH XML),
                     60: {\color{red} om\_xml\_to\_cmo} (OpenMATH XML to CMO).
                     61:
                     62: \medbreak
                     63: \noindent
                     64: \fbox{\huge
                     65:  {\color{green} Homotopy Method}}
                     66:
                     67: \noindent
                     68: {\color{red} phc} (Solving systems of algebraic equations by
                     69: numerical and polyhedral homotopy methods).
                     70:
                     71: \medbreak
                     72: \noindent
                     73: \fbox{\huge
                     74:  {\color{green} Toric ideal}}
                     75:
                     76: \noindent
                     77: {\color{red} tigers} (Enumerate all Gr\"obner basis of a toric ideal.
                     78: Finding test sets for integer program),
                     79: {\color{red} aDegree} (Arithmetic degree of a monomial ideal),
                     80: {\color{red} stdPair} (Standard pair decomposition of a monomial ideal).
                     81:
                     82: \medbreak
                     83: \noindent
                     84: \fbox{\huge {\color{green} Communications}}
                     85:
                     86: \noindent
                     87: {\color{red} ox\_launch} (starting a server),
                     88: {\color{red} ox\_launch\_nox},
                     89: {\color{red} ox\_shutdown},
                     90: {\color{red} ox\_launch\_generic},
                     91: {\color{red} generate\_port},
                     92: {\color{red} try\_bind\_listen},
                     93: {\color{red} try\_connect},
                     94: {\color{red} try\_accept},
                     95: {\color{red} register\_server},
                     96: {\color{red} ox\_rpc},
                     97: {\color{red} ox\_cmo\_rpc},
                     98: {\color{red} ox\_execute\_string},
                     99: {\color{red} ox\_reset} (reset the server),
                    100: {\color{red} ox\_intr},
                    101: {\color{red} register\_handler},
                    102: {\color{red} ox\_push\_cmo},
                    103: {\color{red} ox\_push\_local},
                    104: {\color{red} ox\_pop\_cmo},
                    105: {\color{red} ox\_pop\_local},
                    106: {\color{red} ox\_push\_cmd},
                    107: {\color{red} ox\_sync},
                    108: {\color{red} ox\_get},
                    109: {\color{red} ox\_pops},
                    110: {\color{red} ox\_select},
                    111: {\color{red} ox\_flush},
                    112: {\color{red} ox\_get\_serverinfo}
                    113:
                    114: \medbreak
                    115: \noindent
                    116: \fbox{\huge {\color{green} Examples}}
                    117: {\footnotesize
                    118: \begin{verbatim}
                    119: [345] sm1_deRham([x^3-y^2*z^2,[x,y,z]]);
                    120: [1,1,0,0]
                    121: \end{verbatim}}
                    122:
                    123: \noindent
                    124: {\footnotesize \begin{verbatim}
1.3     ! takayama  125: [287] phc(katsura(7)); B=map(first,Phc)$
        !           126: [291] gnuplot_plotDots(B,0)$
1.2       takayama  127: \end{verbatim} }
                    128:
                    129: \epsfxsize=3cm
                    130: \begin{center}
                    131: \epsffile{../calc2000/katsura7.ps}
                    132: \end{center}
                    133: %%The first components of the solutions to the system of algebraic equations Katsura 7.
                    134:
                    135: \noindent
                    136:
                    137:
                    138: \medbreak
                    139: \noindent
                    140: \fbox{ {\color{green} Authors}}
1.3     ! takayama  141: Castro-Jim\'enez, Doltman, Hubert, Murao, Noro, Oaku, Okutani,
        !           142: Shimoyama, Sturm, Takayama, Tamura, Verschelde, Yokoyama.
1.1       takayama  143:
                    144: \end{document}