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Added a manual for plucker.rr

@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker/plucker.oxw,v 1.1 2005/04/13 11:16:26 takayama Exp $
/*&C
@node Plucker relations,,, Top
*/
/*&ja
@chapter Plucker $B4X78<0(B 

*/

/*&en
@chapter Plucker Relations 

*/

/*&C
@menu
* plucker::
* plucker_y::
* plucker_relation::
* plucker_index::
@end menu
*/

/*&ja
@node plucker,,, Plucker relations 
@subsection plucker
@findex plucker
@tex
$(m+1) \times n$ $B9TNs$r9M$($k(B.
$i_1, \ldots, i_m, j_k$ $BNs$r$J$i$Y$F$D$/$C$?@5J}9TNs<0$r(B
$p_{i_1 \cdots i_m j_k}$ $B$H=q$/$H$-(B, 
Pl\"ucker $B$N4X78<0$O(B
$$ \sum_{k=0}^{m+1} (-1)^k
  p_{i_1 \cdots i_m j_k}
  p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0$$
$B$H=q$1$k(B.
$B$3$N%Q%C%1!<%8$G$O(B, $B$3$N(B Pl\"ucker $B$N4X78<0$r07$&$?$a$N(B
$B4X?t$rDs6!$9$k(B.
@end tex
*/


/*&en
@node plucker,,, Plucker relations 
@subsection plucker
@findex plucker
@tex
Consider $(m+1) \times n$ matrix.
The subsquare matrix consisting of $i_1, \ldots, i_m, j_k$ 
columns is denoted by 
$p_{i_1 \cdots i_m j_k}$.
The Plucker relation is
$$ \sum_{k=0}^{m+1} (-1)^k
  p_{i_1 \cdots i_m j_k}
  p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0.$$
This package provides functions for Plucker relations.
@end tex
*/

/*&ja
@node plucker_relation,,, Plucker relations
@subsection @code{plucker_relation}
@findex plucker_relation
@table @t
@item plucker_relation(@var{L},@var{M})
::  Index $B=89g(B @var{L}, @var{M} $B$KBP1~$9$k(B Plucker $B4X78<0$rLa$9(B.
@end table
@table @var
@item return
quote
@item L
$B%j%9%H(B
@item M
$B%j%9%H(B
@end table
@itemize @bullet
@item  @var{L} $B$K$O(B, Plucker $B4X78<0$N(B 
@tex 
$i_1, \ldots, i_m$ 
@end tex
$B$r(B, 
@var{M} $B$K$O(B, Plucker $B4X78<0$N(B 
@tex 
$j_0, \ldots, j_{m+1}$ 
@end tex
$B$rM?$($k(B.
@end itemize
@example
[297] A = plucker_relation([1,2],[3,4,5,6]);
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)
[298] eval_str(print_terminal_form(A));
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

@end example
*/

/*&en

@node plucker_relation,,, Plucker relations
@subsection @code{plucker_relation}
@findex plucker_relation
@table @t
@item plucker_relation(@var{L},@var{M})
::  Returns the plucker relation defined by the index sets @var{L} 
    and @var{M}.
@end table
@table @var
@item return
quote
@item L
List
@item M
List
@end table
@itemize @bullet
@item  @var{L} is the index set 
@tex 
$i_1, \ldots, i_m$ 
@end tex
of the plucker relations and 
@var{M} is the index set 
@tex 
$j_0, \ldots, j_{m+1}$ 
@end tex
of the plucker relations.
@end itemize
@example
[297] A = plucker_relation([1,2],[3,4,5,6]);
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)
[298] eval_str(print_terminal_form(A));
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

@end example

*/

/*&ja
@node plucker_y,,, Plucker relations
@subsection @code{plucker_y}
@findex plucker_y
@table @t
@item plucker_y(@var{L})
::  Index $B=89g(B @var{L} $B$KBP1~$9$kJQ?t$rLa$9(B.
@end table
@table @var
@item return
$BJQ?t(B
@item L
$B%j%9%H(B
@end table
@itemize @bullet
@item  Index $B=89g(B @var{L} $B$O>.$5$$=g$K%=!<%H$5$l$k(B.
$B$3$N$H$-Id9f$b$H$b$K7W;;$5$l$k(B.
@end itemize
@example
[297] plucker_y([1,2,3]);
y_1_2_3

[298] plucker_y([2,1,3]);
-y_1_2_3

@end example
*/

/*&en

@node plucker_y,,, Plucker relations
@subsection @code{plucker_y}
@findex plucker_y
@table @t
@item plucker_y(@var{L})
::  Returns the variable standing for the index  @var{L}.
@end table
@table @var
@item return
Variable
@item L
List
@end table
@itemize @bullet
@item  Index set @var{L} is sorted and the sign is evaluated
by the sorting.
@end itemize
@example
[297] plucker_y([1,2,3]);
y_1_2_3

[298] plucker_y([2,1,3]);
-y_1_2_3

@end example

*/