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Annotation of OpenXM/src/asir-contrib/packages/doc/plucker/plucker.oxw, Revision 1.1

1.1     ! takayama    1: @c $OpenXM$
        !             2: /*&C
        !             3: @node Plucker relations,,, Top
        !             4: */
        !             5: /*&ja
        !             6: @chapter Plucker $B4X78<0(B
        !             7:
        !             8: */
        !             9:
        !            10: /*&en
        !            11: @chapter Plucker Relations
        !            12:
        !            13: */
        !            14:
        !            15: /*&C
        !            16: @menu
        !            17: * plucker::
        !            18: * plucker_y::
        !            19: * plucker_relation::
        !            20: * plucker_index::
        !            21: @end menu
        !            22: */
        !            23:
        !            24: /*&ja
        !            25: @node plucker,,, Plucker relations
        !            26: @subsection plucker
        !            27: @findex plucker
        !            28: @tex
        !            29: $(m+1) \times n$ $B9TNs$r9M$($k(B.
        !            30: $i_1, \ldots, i_m, j_k$ $BNs$r$J$i$Y$F$D$/$C$?@5J}9TNs<0$r(B
        !            31: $p_{i_1 \cdots i_m j_k}$ $B$H=q$/$H$-(B,
        !            32: Pl\"ucker $B$N4X78<0$O(B
        !            33: $$ \sum_{k=0}^{m+1} (-1)^k
        !            34:   p_{i_1 \cdots i_m j_k}
        !            35:   p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0$$
        !            36: $B$H=q$1$k(B.
        !            37: $B$3$N%Q%C%1!<%8$G$O(B, $B$3$N(B Pl\"ucker $B$N4X78<0$r07$&$?$a$N(B
        !            38: $B4X?t$rDs6!$9$k(B.
        !            39: @end tex
        !            40: */
        !            41:
        !            42:
        !            43: /*&en
        !            44: @node plucker,,, Plucker relations
        !            45: @subsection plucker
        !            46: @findex plucker
        !            47: @tex
        !            48: Consider $(m+1) \times n$ matrix.
        !            49: The subsquare matrix consisting of $i_1, \ldots, i_m, j_k$
        !            50: columns is denoted by
        !            51: $p_{i_1 \cdots i_m j_k}$.
        !            52: The Plucker relation is
        !            53: $$ \sum_{k=0}^{m+1} (-1)^k
        !            54:   p_{i_1 \cdots i_m j_k}
        !            55:   p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0.$$
        !            56: This package provides functions for Plucker relations.
        !            57: @end tex
        !            58: */
        !            59:
        !            60: /*&ja
        !            61: @node plucker_relation,,, Plucker relations
        !            62: @subsection @code{plucker_relation}
        !            63: @findex plucker_relation
        !            64: @table @t
        !            65: @item plucker_relation(@var{L},@var{M})
        !            66: ::  Index $B=89g(B @var{L}, @var{M} $B$KBP1~$9$k(B Plucker $B4X78<0$rLa$9(B.
        !            67: @end table
        !            68: @table @var
        !            69: @item return
        !            70: quote
        !            71: @item L
        !            72: $B%j%9%H(B
        !            73: @item M
        !            74: $B%j%9%H(B
        !            75: @end table
        !            76: @itemize @bullet
        !            77: @item  @var{L} $B$K$O(B, Plucker $B4X78<0$N(B
        !            78: @tex
        !            79: $i_1, \ldots, i_m$
        !            80: @end tex
        !            81: $B$r(B,
        !            82: @var{M} $B$K$O(B, Plucker $B4X78<0$N(B
        !            83: @tex
        !            84: $j_0, \ldots, j_{m+1}$
        !            85: @end tex
        !            86: $B$rM?$($k(B.
        !            87: @end itemize
        !            88: @example
        !            89: [297] A = plucker_relation([1,2],[3,4,5,6]);
        !            90: quote(y_1_2_3*y_4_5_6-y_1_2_4*y_3_5_6+y_1_2_5*y_3_4_6-y_1_2_6*y_3_4_5)
        !            91: [298] eval_str(print_terminal_form(A));
        !            92: y_4_5_6*y_1_2_3-y_3_5_6*y_1_2_4+y_3_4_6*y_1_2_5-y_3_4_5*y_1_2_6
        !            93:
        !            94: @end example
        !            95: */
        !            96:
        !            97: /*&en
        !            98:
        !            99: @node plucker_relation,,, Plucker relations
        !           100: @subsection @code{plucker_relation}
        !           101: @findex plucker_relation
        !           102: @table @t
        !           103: @item plucker_relation(@var{L},@var{M})
        !           104: ::  Returns the plucker relation defined by the index sets @var{L}
        !           105:     and @var{M}.
        !           106: @end table
        !           107: @table @var
        !           108: @item return
        !           109: quote
        !           110: @item L
        !           111: List
        !           112: @item M
        !           113: List
        !           114: @end table
        !           115: @itemize @bullet
        !           116: @item  @var{L} is the index set
        !           117: @tex
        !           118: $i_1, \ldots, i_m$
        !           119: @end tex
        !           120: of the plucker relations and
        !           121: @var{M} is the index set
        !           122: @tex
        !           123: $j_0, \ldots, j_{m+1}$
        !           124: @end tex
        !           125: of the plucker relations.
        !           126: @end itemize
        !           127: @example
        !           128: [297] A = plucker_relation([1,2],[3,4,5,6]);
        !           129: quote(y_1_2_3*y_4_5_6-y_1_2_4*y_3_5_6+y_1_2_5*y_3_4_6-y_1_2_6*y_3_4_5)
        !           130: [298] eval_str(print_terminal_form(A));
        !           131: y_4_5_6*y_1_2_3-y_3_5_6*y_1_2_4+y_3_4_6*y_1_2_5-y_3_4_5*y_1_2_6
        !           132:
        !           133: @end example
        !           134:
        !           135: */
        !           136:
        !           137: /*&ja
        !           138: @node plucker_y,,, Plucker relations
        !           139: @subsection @code{plucker_y}
        !           140: @findex plucker_y
        !           141: @table @t
        !           142: @item plucker_y(@var{L})
        !           143: ::  Index $B=89g(B @var{L} $B$KBP1~$9$kJQ?t$rLa$9(B.
        !           144: @end table
        !           145: @table @var
        !           146: @item return
        !           147: $BJQ?t(B
        !           148: @item L
        !           149: $B%j%9%H(B
        !           150: @end table
        !           151: @itemize @bullet
        !           152: @item  Index $B=89g(B @var{L} $B$O>.$5$$=g$K%=!<%H$5$l$k(B.
        !           153: $B$3$N$H$-Id9f$b$H$b$K7W;;$5$l$k(B.
        !           154: @end itemize
        !           155: @example
        !           156: [297] plucker_y([1,2,3]);
        !           157: y_1_2_3
        !           158:
        !           159: [298] plucker_y([2,1,3]);
        !           160: -y_1_2_3
        !           161:
        !           162: @end example
        !           163: */
        !           164:
        !           165: /*&en
        !           166:
        !           167: @node plucker_y,,, Plucker relations
        !           168: @subsection @code{plucker_y}
        !           169: @findex plucker_y
        !           170: @table @t
        !           171: @item plucker_y(@var{L})
        !           172: ::  Returns the variable standing for the index  @var{L}.
        !           173: @end table
        !           174: @table @var
        !           175: @item return
        !           176: Variable
        !           177: @item L
        !           178: List
        !           179: @end table
        !           180: @itemize @bullet
        !           181: @item  Index set @var{L} is sorted and the sign is evaluated
        !           182: by the sorting.
        !           183: @end itemize
        !           184: @example
        !           185: [297] plucker_y([1,2,3]);
        !           186: y_1_2_3
        !           187:
        !           188: [298] plucker_y([2,1,3]);
        !           189: -y_1_2_3
        !           190:
        !           191: @end example
        !           192:
        !           193: */
        !           194: