Annotation of OpenXM/src/asir-contrib/packages/doc/plucker.oxweave, Revision 1.5
1.5 ! takayama 1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker.oxweave,v 1.4 2002/08/23 08:16:13 takayama Exp $
1.4 takayama 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
1.5 ! takayama 43: @node plucker,,, Plucker relations
! 44: @subsection plucker
! 45: @findex plucker
! 46: @tex
! 47: Consider $(m+1) \times n$ matrix.
! 48: The subsquare matrix consisting of $i_1, \ldots, i_m, j_k$
! 49: columns is denoted by
! 50: $p_{i_1 \cdots i_m j_k}$.
! 51: The Plucker relation is
! 52: $$ \sum_{k=0}^{m+1} (-1)^k
! 53: p_{i_1 \cdots i_m j_k}
! 54: p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0.$$
! 55: This package provides functions for Plucker relations.
! 56: @end tex
1.1 takayama 57: */
58:
59: /*&ja
1.4 takayama 60: @node plucker_relation,,, Plucker relations
1.2 takayama 61: @subsection @code{plucker_relation}
62: @findex plucker_relation
63: @table @t
64: @item plucker_relation(@var{L},@var{M})
65: :: Index $B=89g(B @var{L}, @var{M} $B$KBP1~$9$k(B Plucker $B4X78<0$rLa$9(B.
66: @end table
67: @table @var
68: @item return
69: quote
70: @item L
71: $B%j%9%H(B
72: @item M
73: $B%j%9%H(B
74: @end table
75: @itemize @bullet
76: @item @var{L} $B$K$O(B, Plucker $B4X78<0$N(B @tex $i_1, \ldots, i_m$ @end tex
77: $B$r(B,
78: @var{M} $B$K$O(B, Plucker $B4X78<0$N(B @tex $j_0, \ldots, j_{m+1}$ @end tex
79: $B$rM?$($k(B.
80: @end itemize
81: @example
82: [297] A = plucker_relation([1,2],[3,4,5,6]);
83: 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)
84: [298] eval_str(print_terminal_form(A));
85: 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
86:
87: @end example
88: */
89:
90: /*&en
91:
1.4 takayama 92: @node plucker_relation,,, Plucker relations
1.3 takayama 93: @subsection @code{plucker_relation}
94: @findex plucker_relation
95: @table @t
96: @item plucker_relation(@var{L},@var{M})
97: :: Returns the plucker relation defined by the index sets @var{L}
98: and @var{M}.
99: @end table
100: @table @var
101: @item return
102: quote
103: @item L
104: List
105: @item M
106: List
107: @end table
108: @itemize @bullet
109: @item @var{L} is the index set @tex $i_1, \ldots, i_m$ @end tex
110: of the plucker relations and
111: @var{M} is the index set @tex $j_0, \ldots, j_{m+1}$ @end tex
112: of the plucker relations.
113: @end itemize
114: @example
115: [297] A = plucker_relation([1,2],[3,4,5,6]);
116: 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)
117: [298] eval_str(print_terminal_form(A));
118: 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
119:
120: @end example
1.2 takayama 121:
122: */
123:
124: /*&ja
1.4 takayama 125: @node plucker_y,,, Plucker relations
1.1 takayama 126: @subsection @code{plucker_y}
127: @findex plucker_y
128: @table @t
129: @item plucker_y(@var{L})
130: :: Index $B=89g(B @var{L} $B$KBP1~$9$kJQ?t$rLa$9(B.
131: @end table
132: @table @var
133: @item return
134: $BJQ?t(B
135: @item L
136: $B%j%9%H(B
137: @end table
138: @itemize @bullet
139: @item Index $B=89g(B @var{L} $B$O>.$5$$=g$K%=!<%H$5$l$k(B.
140: $B$3$N$H$-Id9f$b$H$b$K7W;;$5$l$k(B.
141: @end itemize
142: @example
143: [297] plucker_y([1,2,3]);
144: y_1_2_3
145:
146: [298] plucker_y([2,1,3]);
147: -y_1_2_3
148:
149: @end example
1.2 takayama 150: */
151:
152: /*&en
153:
1.4 takayama 154: @node plucker_y,,, Plucker relations
1.3 takayama 155: @subsection @code{plucker_y}
156: @findex plucker_y
157: @table @t
158: @item plucker_y(@var{L})
159: :: Returns the variable standing for the index @var{L}.
160: @end table
161: @table @var
162: @item return
163: Variable
164: @item L
165: List
166: @end table
167: @itemize @bullet
168: @item Index set @var{L} is sorted and the sign is evaluated
169: by the sorting.
170: @end itemize
171: @example
172: [297] plucker_y([1,2,3]);
173: y_1_2_3
174:
175: [298] plucker_y([2,1,3]);
176: -y_1_2_3
177:
178: @end example
179:
180: */
181:
182: /*&ja
183:
184: @include plucker-auto-ja.texi
1.2 takayama 185:
186: */
187:
1.3 takayama 188: /*&en
189:
190: @include plucker-auto-en.texi
191:
192: */
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