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Revision 1.2, Thu Dec 13 09:27:44 2001 UTC (22 years, 9 months ago) by takayama
Syntax: list base_permutation(list L) : All permutations of L. Example: [771] base_permutation([1,2,3]); [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]] Syntax: list base_choose(list L,number M) : all subsets of L of size M. Example: [841] taka_base_choose([1,2,3,4],2); [[4,3],[3,2],[4,2],[2,1],[3,1],[4,1]] plucker_relation returns the plucker relations. |
@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker.oxweave,v 1.2 2001/12/13 09:27:44 takayama Exp $ /*&ja @node Plucker relations,,, Top @chapter Plucker $B4X78<0(B */ /*&en @node Plucker relations,,, Top @chapter Plucker Relations */ /*&C @menu * plucker:: * plucker_y:: * plucker_relation:: @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 Not yet written */ /*&ja @node plucker_relation,,, Plucker relation @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 Not yet written. */ /*&ja @node plucker_y,,, Plucker relation @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 Not yet written */