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Annotation of OpenXM/src/asir-contrib/packages/doc/plucker.oxweave, Revision 1.2

1.2     ! takayama    1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker.oxweave,v 1.1 2001/12/02 07:43:04 takayama Exp $
1.1       takayama    2:
                      3: /*&ja
                      4: @node Plucker relations,,, Top
1.2     ! takayama    5: @chapter Plucker $B4X78<0(B
1.1       takayama    6:
                      7: */
                      8:
                      9: /*&en
                     10: @node Plucker relations,,, Top
1.2     ! takayama   11: @chapter Plucker Relations
1.1       takayama   12:
                     13: */
                     14:
                     15: /*&C
                     16: @menu
                     17: * plucker::
                     18: * plucker_y::
1.2     ! takayama   19: * plucker_relation::
1.1       takayama   20: @end menu
                     21: */
                     22:
                     23: /*&ja
                     24: @node plucker,,, Plucker relations
                     25: @subsection plucker
                     26: @findex plucker
                     27: @tex
                     28: $(m+1) \times n$ $B9TNs$r9M$($k(B.
                     29: $i_1, \ldots, i_m, j_k$ $BNs$r$J$i$Y$F$D$/$C$?@5J}9TNs<0$r(B
                     30: $p_{i_1 \cdots i_m j_k}$ $B$H=q$/$H$-(B,
                     31: Pl\"ucker $B$N4X78<0$O(B
                     32: $$ \sum_{k=0}^{m+1} (-1)^k
                     33:   p_{i_1 \cdots i_m j_k}
                     34:   p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0$$
                     35: $B$H=q$1$k(B.
                     36: $B$3$N%Q%C%1!<%8$G$O(B, $B$3$N(B Pl\"ucker $B$N4X78<0$r07$&$?$a$N(B
                     37: $B4X?t$rDs6!$9$k(B.
                     38: @end tex
                     39: */
                     40:
                     41:
                     42: /*&en
                     43:
                     44: Not yet written
                     45:
                     46: */
                     47:
                     48: /*&ja
1.2     ! takayama   49: @node plucker_relation,,, Plucker relation
        !            50: @subsection @code{plucker_relation}
        !            51: @findex plucker_relation
        !            52: @table @t
        !            53: @item plucker_relation(@var{L},@var{M})
        !            54: ::  Index $B=89g(B @var{L}, @var{M} $B$KBP1~$9$k(B Plucker $B4X78<0$rLa$9(B.
        !            55: @end table
        !            56: @table @var
        !            57: @item return
        !            58: quote
        !            59: @item L
        !            60: $B%j%9%H(B
        !            61: @item M
        !            62: $B%j%9%H(B
        !            63: @end table
        !            64: @itemize @bullet
        !            65: @item  @var{L} $B$K$O(B, Plucker $B4X78<0$N(B @tex $i_1, \ldots, i_m$ @end tex
        !            66: $B$r(B,
        !            67: @var{M} $B$K$O(B, Plucker $B4X78<0$N(B @tex $j_0, \ldots, j_{m+1}$ @end tex
        !            68: $B$rM?$($k(B.
        !            69: @end itemize
        !            70: @example
        !            71: [297] A = plucker_relation([1,2],[3,4,5,6]);
        !            72: 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)
        !            73: [298] eval_str(print_terminal_form(A));
        !            74: 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
        !            75:
        !            76: @end example
        !            77: */
        !            78:
        !            79: /*&en
        !            80:
        !            81: Not yet written.
        !            82:
        !            83: */
        !            84:
        !            85: /*&ja
1.1       takayama   86: @node plucker_y,,, Plucker relation
                     87: @subsection @code{plucker_y}
                     88: @findex plucker_y
                     89: @table @t
                     90: @item plucker_y(@var{L})
                     91: ::  Index $B=89g(B @var{L} $B$KBP1~$9$kJQ?t$rLa$9(B.
                     92: @end table
                     93: @table @var
                     94: @item return
                     95: $BJQ?t(B
                     96: @item L
                     97: $B%j%9%H(B
                     98: @end table
                     99: @itemize @bullet
                    100: @item  Index $B=89g(B @var{L} $B$O>.$5$$=g$K%=!<%H$5$l$k(B.
                    101: $B$3$N$H$-Id9f$b$H$b$K7W;;$5$l$k(B.
                    102: @end itemize
                    103: @example
                    104: [297] plucker_y([1,2,3]);
                    105: y_1_2_3
                    106:
                    107: [298] plucker_y([2,1,3]);
                    108: -y_1_2_3
                    109:
                    110: @end example
1.2     ! takayama  111: */
        !           112:
        !           113: /*&en
        !           114:
        !           115: Not yet written
        !           116:
        !           117: */
        !           118: