Return to dualgraph-manual.tex CVS log

Up to [local] / OpenXM / src / asir-contrib / packages / doc / fj_curve

Annotation of OpenXM/src/asir-contrib/packages/doc/fj_curve/dualgraph-manual.tex, Revision 1.1

1.1     ! fujimoto    1: %$OpenXM$
        !             2: \documentclass[a4paper,12pt]{article}
        !             3: \usepackage{amsmath,amssymb}
        !             4: \usepackage{graphicx,psfrag}
        !             5:
        !             6: \title{The usage of ``dualgraph" by examples}
        !             7: \begin{document}
        !             8: \maketitle
        !             9:
        !            10: \begin{enumerate}
        !            11: \item Download Risa/Asir from {\tt http://www.math.kobe-u.ac.jp/Asir/}\\
        !            12: \item Install Risa/Asir according to manual.\\
        !            13: \item Carry out Asir.
        !            14: \end{enumerate}
        !            15:
        !            16: The package is the file {\tt dualgraph.rr} in the directory 'asir-contrib/fj\_curve'.
        !            17:
        !            18: Attention: The file ``{\tt dualgraph.rr}" contains Japanese jis code.
        !            19:
        !            20: \begin{verbatim}
        !            21: This is Risa/Asir, Version 20051106 (Kobe Distribution).
        !            22: Copyright (C) 1994-2000, all rights reserved, FUJITSU LABORATORIES LIMITED.
        !            23: Copyright 2000-2005, Risa/Asir committers, http://www.openxm.org/.
        !            24: GC 6.5 Copyright 1988-2005, H-J. Boehm, A. J. Demers, Xerox, SGI, HP.
        !            25: PARI 2.0.17, copyright 1989-1999, C. Batut, K. Belabas, D. Bernardi,
        !            26:    H. Cohen and M. Olivier.
        !            27: Debug windows of ox servers will not be opened. Set Xm_noX=0 to open it.
        !            28: OpenXM/Risa/Asir-Contrib(20040302), Copyright 2000-2004, OpenXM.org committers
        !            29: ox_help(0); ox_help("keyword"); ox_grep("keyword");
        !            30:      for help messages (unix version only).
        !            31: http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html
        !            32: [1217] load("gr")$
        !            33: [1323] load("sp")$
        !            34: [1425] load("fj_curve/dualgraph.rr")$
        !            35: [1479] dual_graph((y^2-x^3)^2-y^7)$
        !            36: *** Newton Polygon ***
        !            37: [[0,4],[6,0]]
        !            38: [[0,2],[9,0]]
        !            39: ***** Dual Graph *****
        !            40: [3,[2,b1],2]
        !            41: b1:[2,2,2,3,[1,b2],2]
        !            42: b2:*
        !            43: [1480]
        !            44: \end{verbatim}
        !            45:
        !            46: This result means following dual graph.
        !            47:
        !            48:  \psfrag{-1}{$-1$}
        !            49:  \psfrag{-2}{$-2$}
        !            50:  \psfrag{-3}{$-3$}
        !            51:  \psfrag{-5}{$-5$}
        !            52:  \psfrag{*}{$*$}
        !            53:  \centerline{
        !            54:   \includegraphics*[height=5cm]{g-dual1.eps}
        !            55:  }
        !            56:
        !            57: \begin{verbatim}
        !            58: [194] F=((x^2-y^5)^2-x^5)*((-x^2+y^3)^2-y^9)
        !            59: *((x^2+y^3)^2-x^7)*(x^4+y^5)$
        !            60: [195] dual_graph(F)$
        !            61: *** Newton Polygon ***
        !            62: [[0,27],[4,17],[12,5],[16,0]]
        !            63: [[0,2],[5,0]]
        !            64: [[0,2],[6,0]]
        !            65: [[0,2],[9,0]]
        !            66: ***** Dual graph *****
        !            67: [2,[2,b1],4,[4,b2,b3],2,[1,b4],5]
        !            68: b1:[2,3,[1,b5],2]
        !            69: b5:*
        !            70: b2:[2,2,[1,b6,b7]]
        !            71: b6:*
        !            72: b7:*
        !            73: b3:[2,2,2,3,[1,b8],2]
        !            74: b8:*
        !            75: b4:*
        !            76: \end{verbatim}
        !            77:
        !            78: ``b1,b2,b3,b4" mean another branches from these verticies.
        !            79:
        !            80: \begin{center}
        !            81: {\large [2,[2,b1],4,[4,b2,b3],2,[1,b4],5]}
        !            82: \end{center}
        !            83: $$\big\Updownarrow$$
        !            84:  \psfrag{b1}{b1}
        !            85:  \psfrag{b2}{b2}
        !            86:  \psfrag{b3}{b3}
        !            87:  \psfrag{b4}{b4}
        !            88:  \centerline{
        !            89:   \includegraphics*[height=3.5cm]{ex2dual1.eps}
        !            90:  }
        !            91: \vspace*{6pt}
        !            92:
        !            93: The list "b1:..." means the dual graph of the branch "b1".
        !            94:
        !            95: \begin{center}
        !            96: {\large b1:[2,3,[1,b5],2]}
        !            97: \end{center}
        !            98: $$\big\Updownarrow$$
        !            99:  \psfrag{b1}{b1}
        !           100:  \psfrag{b5}{b5}
        !           101:  \centerline{
        !           102:   \includegraphics*[height=4cm]{ex2dual2.eps}
        !           103:  }
        !           104:
        !           105: Therefor we get following dual graph.
        !           106:
        !           107:  \psfrag{1}{$-1$}
        !           108:  \psfrag{2}{$-2$}
        !           109:  \psfrag{3}{$-3$}
        !           110:  \psfrag{4}{$-4$}
        !           111:  \psfrag{5}{$-5$}
        !           112:  \centerline{
        !           113:   \includegraphics*[width=11cm]{dualex2.eps}
        !           114:  }
        !           115:
        !           116: \end{document}