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Annotation of OpenXM/src/asir-contrib/packages/doc/plucker.oxweave, Revision 1.4

1.4     ! takayama    1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker.oxweave,v 1.3 2002/08/11 08:39:47 takayama Exp $
        !             2: /*&C
        !             3: @node Plucker relations,,, Top
        !             4: */
1.1       takayama    5: /*&ja
1.2       takayama    6: @chapter Plucker $B4X78<0(B
1.1       takayama    7:
                      8: */
                      9:
                     10: /*&en
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
1.4     ! takayama   49: @node plucker_relation,,, Plucker relations
1.2       takayama   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:
1.4     ! takayama   81: @node plucker_relation,,, Plucker relations
1.3       takayama   82: @subsection @code{plucker_relation}
                     83: @findex plucker_relation
                     84: @table @t
                     85: @item plucker_relation(@var{L},@var{M})
                     86: ::  Returns the plucker relation defined by the index sets @var{L}
                     87:     and @var{M}.
                     88: @end table
                     89: @table @var
                     90: @item return
                     91: quote
                     92: @item L
                     93: List
                     94: @item M
                     95: List
                     96: @end table
                     97: @itemize @bullet
                     98: @item  @var{L} is the index set @tex $i_1, \ldots, i_m$ @end tex
                     99: of the plucker relations and
                    100: @var{M} is the index set @tex $j_0, \ldots, j_{m+1}$ @end tex
                    101: of the plucker relations.
                    102: @end itemize
                    103: @example
                    104: [297] A = plucker_relation([1,2],[3,4,5,6]);
                    105: 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)
                    106: [298] eval_str(print_terminal_form(A));
                    107: 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
                    108:
                    109: @end example
1.2       takayama  110:
                    111: */
                    112:
                    113: /*&ja
1.4     ! takayama  114: @node plucker_y,,, Plucker relations
1.1       takayama  115: @subsection @code{plucker_y}
                    116: @findex plucker_y
                    117: @table @t
                    118: @item plucker_y(@var{L})
                    119: ::  Index $B=89g(B @var{L} $B$KBP1~$9$kJQ?t$rLa$9(B.
                    120: @end table
                    121: @table @var
                    122: @item return
                    123: $BJQ?t(B
                    124: @item L
                    125: $B%j%9%H(B
                    126: @end table
                    127: @itemize @bullet
                    128: @item  Index $B=89g(B @var{L} $B$O>.$5$$=g$K%=!<%H$5$l$k(B.
                    129: $B$3$N$H$-Id9f$b$H$b$K7W;;$5$l$k(B.
                    130: @end itemize
                    131: @example
                    132: [297] plucker_y([1,2,3]);
                    133: y_1_2_3
                    134:
                    135: [298] plucker_y([2,1,3]);
                    136: -y_1_2_3
                    137:
                    138: @end example
1.2       takayama  139: */
                    140:
                    141: /*&en
                    142:
1.4     ! takayama  143: @node plucker_y,,, Plucker relations
1.3       takayama  144: @subsection @code{plucker_y}
                    145: @findex plucker_y
                    146: @table @t
                    147: @item plucker_y(@var{L})
                    148: ::  Returns the variable standing for the index  @var{L}.
                    149: @end table
                    150: @table @var
                    151: @item return
                    152: Variable
                    153: @item L
                    154: List
                    155: @end table
                    156: @itemize @bullet
                    157: @item  Index set @var{L} is sorted and the sign is evaluated
                    158: by the sorting.
                    159: @end itemize
                    160: @example
                    161: [297] plucker_y([1,2,3]);
                    162: y_1_2_3
                    163:
                    164: [298] plucker_y([2,1,3]);
                    165: -y_1_2_3
                    166:
                    167: @end example
                    168:
                    169: */
                    170:
                    171: /*&ja
                    172:
                    173: @include plucker-auto-ja.texi
1.2       takayama  174:
                    175: */
                    176:
1.3       takayama  177: /*&en
                    178:
                    179: @include plucker-auto-en.texi
                    180:
                    181: */