version 1.3, 2002/08/11 08:39:47 |
version 1.7, 2004/03/05 19:05:11 |
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@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker.oxweave,v 1.2 2001/12/13 09:27:44 takayama Exp $ |
@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker.oxweave,v 1.6 2003/07/27 13:18:46 takayama Exp $ |
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/*&C |
/*&ja |
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@node Plucker relations,,, Top |
@node Plucker relations,,, Top |
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*/ |
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/*&ja |
@chapter Plucker $B4X78<0(B |
@chapter Plucker $B4X78<0(B |
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*/ |
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/*&en |
/*&en |
@node Plucker relations,,, Top |
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@chapter Plucker Relations |
@chapter Plucker Relations |
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*/ |
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* plucker:: |
* plucker:: |
* plucker_y:: |
* plucker_y:: |
* plucker_relation:: |
* plucker_relation:: |
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* plucker_index:: |
@end menu |
@end menu |
*/ |
*/ |
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Line 40 $$ \sum_{k=0}^{m+1} (-1)^k |
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Line 41 $$ \sum_{k=0}^{m+1} (-1)^k |
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/*&en |
/*&en |
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@node plucker,,, Plucker relations |
Not yet written |
@subsection plucker |
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@findex plucker |
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@tex |
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Consider $(m+1) \times n$ matrix. |
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The subsquare matrix consisting of $i_1, \ldots, i_m, j_k$ |
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columns is denoted by |
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$p_{i_1 \cdots i_m j_k}$. |
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The Plucker relation is |
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$$ \sum_{k=0}^{m+1} (-1)^k |
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p_{i_1 \cdots i_m j_k} |
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p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0.$$ |
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This package provides functions for Plucker relations. |
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@end tex |
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*/ |
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/*&ja |
/*&ja |
@node plucker_relation,,, Plucker relation |
@node plucker_relation,,, Plucker relations |
@subsection @code{plucker_relation} |
@subsection @code{plucker_relation} |
@findex plucker_relation |
@findex plucker_relation |
@table @t |
@table @t |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @var{L} $B$K$O(B, Plucker $B4X78<0$N(B @tex $i_1, \ldots, i_m$ @end tex |
@item @var{L} $B$K$O(B, Plucker $B4X78<0$N(B |
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@tex |
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$i_1, \ldots, i_m$ |
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@end tex |
$B$r(B, |
$B$r(B, |
@var{M} $B$K$O(B, Plucker $B4X78<0$N(B @tex $j_0, \ldots, j_{m+1}$ @end tex |
@var{M} $B$K$O(B, Plucker $B4X78<0$N(B |
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@tex |
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$j_0, \ldots, j_{m+1}$ |
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@end tex |
$B$rM?$($k(B. |
$B$rM?$($k(B. |
@end itemize |
@end itemize |
@example |
@example |
Line 78 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_ |
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Line 96 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_ |
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/*&en |
/*&en |
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@node plucker_relation,,, Plucker relation |
@node plucker_relation,,, Plucker relations |
@subsection @code{plucker_relation} |
@subsection @code{plucker_relation} |
@findex plucker_relation |
@findex plucker_relation |
@table @t |
@table @t |
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List |
List |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @var{L} is the index set @tex $i_1, \ldots, i_m$ @end tex |
@item @var{L} is the index set |
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@tex |
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$i_1, \ldots, i_m$ |
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@end tex |
of the plucker relations and |
of the plucker relations and |
@var{M} is the index set @tex $j_0, \ldots, j_{m+1}$ @end tex |
@var{M} is the index set |
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@tex |
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$j_0, \ldots, j_{m+1}$ |
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@end tex |
of the plucker relations. |
of the plucker relations. |
@end itemize |
@end itemize |
@example |
@example |
Line 111 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_ |
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Line 135 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_ |
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*/ |
*/ |
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/*&ja |
/*&ja |
@node plucker_y,,, Plucker relation |
@node plucker_y,,, Plucker relations |
@subsection @code{plucker_y} |
@subsection @code{plucker_y} |
@findex plucker_y |
@findex plucker_y |
@table @t |
@table @t |
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/*&en |
/*&en |
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@node plucker_y,,, Plucker relation |
@node plucker_y,,, Plucker relations |
@subsection @code{plucker_y} |
@subsection @code{plucker_y} |
@findex plucker_y |
@findex plucker_y |
@table @t |
@table @t |
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/*&ja |
/*&ja |
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@include plucker-auto-ja.texi |
@include plucker-auto.ja |
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*/ |
*/ |
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/*&en |
/*&en |
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@include plucker-auto-en.texi |
@include plucker-auto.en |
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*/ |
*/ |