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Annotation of OpenXM/src/asir-contrib/packages/doc/hg21-ja.tex, Revision 1.1

1.1     ! takayama    1: % $OpenXM$
        !             2: \documentclass{jarticle}
        !             3:
        !             4: \begin{document}
        !             5:
        !             6: {\tt u1(a,b,c,z)} $B$NLa$99TNs$r(B $U_1$ $B$H$9$k$H$-(B
        !             7: (u $B$O(B ``up'' $B$N(B u $B$G$"$k(B),
        !             8: $$\pmatrix{
        !             9:      F'(a+1,b,c;z) \cr
        !            10:      F(a+1,b,c;z) \cr} = U_1
        !            11:   \pmatrix{
        !            12:      F'(a,b,c;z) \cr
        !            13:      F(a,b,c;z) \cr}
        !            14: $$
        !            15: $B$,$J$j$?$D(B.
        !            16:
        !            17: {\tt u2(a,b,c,z)} $B$NLa$99TNs$r(B $U_2$ $B$H$9$k$H$-(B
        !            18: (u $B$O(B ``up'' $B$N(B u $B$G$"$k(B),
        !            19: $$\pmatrix{
        !            20:      F'(a,b+1,c;z) \cr
        !            21:      F(a,b+1,c;z) \cr} = U_2
        !            22:   \pmatrix{
        !            23:      F'(a,b,c;z) \cr
        !            24:      F(a,b,c;z) \cr}
        !            25: $$
        !            26: $B$,$J$j$?$D(B.
        !            27:
        !            28: {\tt u3(a,b,c,z)} $B$NLa$99TNs$r(B $U_3$ $B$H$9$k$H$-(B
        !            29: (u $B$O(B ``up'' $B$N(B u $B$G$"$k(B),
        !            30: $$\pmatrix{
        !            31:      F'(a,b,c+1;z) \cr
        !            32:      F(a,b,c+1;z) \cr} = U_3
        !            33:   \pmatrix{
        !            34:      F'(a,b,c;z) \cr
        !            35:      F(a,b,c;z) \cr}
        !            36: $$
        !            37: $B$,$J$j$?$D(B.
        !            38:
        !            39: {\tt d1(a,b,c,z)} $B$NLa$99TNs$r(B $D_1$ $B$H$9$k$H$-(B
        !            40: (d $B$O(B ``down'' $B$N(B d $B$G$"$k(B),
        !            41: $$\pmatrix{
        !            42:      F'(a-1,b,c;z) \cr
        !            43:      F(a-1,b,c;z) \cr} = D_1
        !            44:   \pmatrix{
        !            45:      F'(a,b,c;z) \cr
        !            46:      F(a,b,c;z) \cr}
        !            47: $$
        !            48: $B$,$J$j$?$D(B.
        !            49:
        !            50: {\tt d2(a,b,c,z)} $B$NLa$99TNs$r(B $D_2$ $B$H$9$k$H$-(B
        !            51: (d $B$O(B ``down'' $B$N(B d $B$G$"$k(B),
        !            52: $$\pmatrix{
        !            53:      F'(a,b-1,c;z) \cr
        !            54:      F(a,b-1,c;z) \cr} = D_2
        !            55:   \pmatrix{
        !            56:      F'(a,b,c;z) \cr
        !            57:      F(a,b,c;z) \cr}
        !            58: $$
        !            59: $B$,$J$j$?$D(B.
        !            60:
        !            61: {\tt d3(a,b,c,z)} $B$NLa$99TNs$r(B $D_3$ $B$H$9$k$H$-(B
        !            62: (d $B$O(B ``down'' $B$N(B d $B$G$"$k(B),
        !            63: $$\pmatrix{
        !            64:      F'(a,b,c-1;z) \cr
        !            65:      F(a,b,c-1;z) \cr} = D_3
        !            66:   \pmatrix{
        !            67:      F'(a,b,c;z) \cr
        !            68:      F(a,b,c;z) \cr}
        !            69: $$
        !            70: $B$,$J$j$?$D(B.
        !            71:
        !            72: $B$3$l$i$O(B, $B%,%&%9$ND64v2?4X?t$N$h$/$7$i$l$?8x<0$G$"$k(B.\\
        !            73: $BNc(B:
        !            74: \begin{verbatim}
        !            75: [377] load("hg21")$
        !            76: [378] u1(a,b,c,z);
        !            77: [ (b*z-c+a+1)/(-a*z+a) (b)/(-z+1) ]
        !            78: [ (z)/(a) 1 ]
        !            79: \end{verbatim}
        !            80:
        !            81:
        !            82: {\tt hg21\_check()} $B$G$O$3$l$i$NJQ498x<0$,$?$@$7$$$+(B
        !            83: $B$I$&$+$r(B,
        !            84: $B$?$H$($P(B,
        !            85: \verb@  R = d1(a+1,b,c,z)*u1(a,b,c,z); @
        !            86: $B$,C10L9TNs$+$I$&$+$r$_$k$3$H$K$h$j(B, $B%A%'%C%/$7$F$$$k(B.
        !            87:
        !            88: $p, q, r$ $B$r@0?t$H$9$k$H$-(B,
        !            89: $B$3$l$i$N9TNs$r$+$1;;$9$k$3$H$K$h$j(B,
        !            90: $B<!$N<0$r$_$?$9(B $T$ $B$rF@$k$3$H$,2DG=$G$"$k(B.
        !            91: $$\pmatrix{
        !            92:      F'(a+p,b+q,c+r;z) \cr
        !            93:      F(a+p,b+q,c+r;z) \cr} = T
        !            94:   \pmatrix{
        !            95:      F'(a,b,c;z) \cr
        !            96:      F(a,b,c;z) \cr}
        !            97: $$
        !            98: $B$?$@$7(B, $B9TNs(B $U_i, D_i$ $B$NJ,Jl$,(B $0$ $B$K$J$i$J$$(B
        !            99: $B$3$H$,I,MW$G$"$k(B.
        !           100:
        !           101: \noindent
        !           102: $BNc(B:
        !           103: \begin{verbatim}
        !           104: [379] tam(1/2,1/2,1,3/4);
        !           105: [Aplus,Bminus,Cplus]=[3,-3,6]
        !           106: [[ 9402863/1505280 170306533/752640 ]
        !           107: [ -8131157/430080 -147868387/215040 ],[7/2,-5/2,7]]
        !           108: [380]
        !           109: \end{verbatim}
        !           110: $B$3$N=PNO$O(B,
        !           111: $$\pmatrix{
        !           112:      F'(1/2,1/2,1;3/4) \cr
        !           113:      F(1/2,1/2,1;3/4) \cr} = T
        !           114:   \pmatrix{
        !           115:      F'(7/2,-5/2,7;3/4) \cr
        !           116:      F(7/2,-5/2,7;3/4) \cr}
        !           117: $$
        !           118: $B$G$"$k$3$H$r0UL#$9$k(B.
        !           119: $B$3$3$G(B,
        !           120: $$ T = \pmatrix{ 9402863/1505280 & 170306533/752640 \cr
        !           121:                  -8131157/430080 & -147868387/215040 \cr}
        !           122: $$
        !           123: $B$H$*$/(B.
        !           124: $B4X?t(B {\tt tam} $B$NLa$jCM$NBh0l@.J,$,(B $B9TNs(B $T$ $B$G$"$k(B.
        !           125: (cf. $BEDB<;a$N(B, HG function $B$N@:EYJ]>Z7W;;$N%W%m%0%i%`(B).
        !           126:
        !           127:
        !           128: $B$J$*(B,  $F'(a,b,c;z)$ $B$O(B $F(a,b,c;z)$ $B$H(B $F(a+1,b,c;z)$
        !           129: $B$GI=$9$3$H$,2DG=$G$"$k(B.
        !           130: $B$=$l$K$O<!$N$h$/$7$i$l$?D64v2?4X?t$N8x<0$r;H$($P$h$$(B:
        !           131: $$ \frac{1}{a} z F'(a,b,c;z) = - F(a,b,c;z) + F(a+1,b,c;z). $$
        !           132:
        !           133: \end{document}