Annotation of OpenXM/src/asir-contrib/packages/doc/plucker.oxweave, Revision 1.7
1.7 ! ohara 1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/plucker.oxweave,v 1.6 2003/07/27 13:18:46 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::
1.6 takayama 20: * plucker_index::
1.1 takayama 21: @end menu
22: */
23:
24: /*&ja
25: @node plucker,,, Plucker relations
26: @subsection plucker
27: @findex plucker
28: @tex
29: $(m+1) \times n$ $B9TNs$r9M$($k(B.
30: $i_1, \ldots, i_m, j_k$ $BNs$r$J$i$Y$F$D$/$C$?@5J}9TNs<0$r(B
31: $p_{i_1 \cdots i_m j_k}$ $B$H=q$/$H$-(B,
32: Pl\"ucker $B$N4X78<0$O(B
33: $$ \sum_{k=0}^{m+1} (-1)^k
34: p_{i_1 \cdots i_m j_k}
35: p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0$$
36: $B$H=q$1$k(B.
37: $B$3$N%Q%C%1!<%8$G$O(B, $B$3$N(B Pl\"ucker $B$N4X78<0$r07$&$?$a$N(B
38: $B4X?t$rDs6!$9$k(B.
39: @end tex
40: */
41:
42:
43: /*&en
1.5 takayama 44: @node plucker,,, Plucker relations
45: @subsection plucker
46: @findex plucker
47: @tex
48: Consider $(m+1) \times n$ matrix.
49: The subsquare matrix consisting of $i_1, \ldots, i_m, j_k$
50: columns is denoted by
51: $p_{i_1 \cdots i_m j_k}$.
52: The Plucker relation is
53: $$ \sum_{k=0}^{m+1} (-1)^k
54: p_{i_1 \cdots i_m j_k}
55: p_{j_0 \cdots {\hat j}_k \cdots j_{m+1}} = 0.$$
56: This package provides functions for Plucker relations.
57: @end tex
1.1 takayama 58: */
59:
60: /*&ja
1.4 takayama 61: @node plucker_relation,,, Plucker relations
1.2 takayama 62: @subsection @code{plucker_relation}
63: @findex plucker_relation
64: @table @t
65: @item plucker_relation(@var{L},@var{M})
66: :: Index $B=89g(B @var{L}, @var{M} $B$KBP1~$9$k(B Plucker $B4X78<0$rLa$9(B.
67: @end table
68: @table @var
69: @item return
70: quote
71: @item L
72: $B%j%9%H(B
73: @item M
74: $B%j%9%H(B
75: @end table
76: @itemize @bullet
1.6 takayama 77: @item @var{L} $B$K$O(B, Plucker $B4X78<0$N(B
78: @tex
79: $i_1, \ldots, i_m$
80: @end tex
1.2 takayama 81: $B$r(B,
1.6 takayama 82: @var{M} $B$K$O(B, Plucker $B4X78<0$N(B
83: @tex
84: $j_0, \ldots, j_{m+1}$
85: @end tex
1.2 takayama 86: $B$rM?$($k(B.
87: @end itemize
88: @example
89: [297] A = plucker_relation([1,2],[3,4,5,6]);
90: 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)
91: [298] eval_str(print_terminal_form(A));
92: 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
93:
94: @end example
95: */
96:
97: /*&en
98:
1.4 takayama 99: @node plucker_relation,,, Plucker relations
1.3 takayama 100: @subsection @code{plucker_relation}
101: @findex plucker_relation
102: @table @t
103: @item plucker_relation(@var{L},@var{M})
104: :: Returns the plucker relation defined by the index sets @var{L}
105: and @var{M}.
106: @end table
107: @table @var
108: @item return
109: quote
110: @item L
111: List
112: @item M
113: List
114: @end table
115: @itemize @bullet
1.6 takayama 116: @item @var{L} is the index set
117: @tex
118: $i_1, \ldots, i_m$
119: @end tex
1.3 takayama 120: of the plucker relations and
1.6 takayama 121: @var{M} is the index set
122: @tex
123: $j_0, \ldots, j_{m+1}$
124: @end tex
1.3 takayama 125: of the plucker relations.
126: @end itemize
127: @example
128: [297] A = plucker_relation([1,2],[3,4,5,6]);
129: 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)
130: [298] eval_str(print_terminal_form(A));
131: 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
132:
133: @end example
1.2 takayama 134:
135: */
136:
137: /*&ja
1.4 takayama 138: @node plucker_y,,, Plucker relations
1.1 takayama 139: @subsection @code{plucker_y}
140: @findex plucker_y
141: @table @t
142: @item plucker_y(@var{L})
143: :: Index $B=89g(B @var{L} $B$KBP1~$9$kJQ?t$rLa$9(B.
144: @end table
145: @table @var
146: @item return
147: $BJQ?t(B
148: @item L
149: $B%j%9%H(B
150: @end table
151: @itemize @bullet
152: @item Index $B=89g(B @var{L} $B$O>.$5$$=g$K%=!<%H$5$l$k(B.
153: $B$3$N$H$-Id9f$b$H$b$K7W;;$5$l$k(B.
154: @end itemize
155: @example
156: [297] plucker_y([1,2,3]);
157: y_1_2_3
158:
159: [298] plucker_y([2,1,3]);
160: -y_1_2_3
161:
162: @end example
1.2 takayama 163: */
164:
165: /*&en
166:
1.4 takayama 167: @node plucker_y,,, Plucker relations
1.3 takayama 168: @subsection @code{plucker_y}
169: @findex plucker_y
170: @table @t
171: @item plucker_y(@var{L})
172: :: Returns the variable standing for the index @var{L}.
173: @end table
174: @table @var
175: @item return
176: Variable
177: @item L
178: List
179: @end table
180: @itemize @bullet
181: @item Index set @var{L} is sorted and the sign is evaluated
182: by the sorting.
183: @end itemize
184: @example
185: [297] plucker_y([1,2,3]);
186: y_1_2_3
187:
188: [298] plucker_y([2,1,3]);
189: -y_1_2_3
190:
191: @end example
192:
193: */
194:
195: /*&ja
196:
1.7 ! ohara 197: @include plucker-auto.ja
1.2 takayama 198:
199: */
200:
1.3 takayama 201: /*&en
202:
1.7 ! ohara 203: @include plucker-auto.en
1.3 takayama 204:
205: */
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