-
Notifications
You must be signed in to change notification settings - Fork 1
/
arrow30.mp
99 lines (78 loc) · 2.78 KB
/
arrow30.mp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
% tex/conc/mp/arrow30.mp 2012-4-8 Alan U. Kennington.
% $Id: tex/conc/mp/arrow30.mp 7e9d058561 2012-04-08 12:52:11Z Alan U. Kennington $
% Mixed tensor product space definition.
input mapmax.mp
verbatimtex
\input akmath
etex
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
beginfig(1);
path pat[];
pair w[];
aa := 3.3cm;
bb := 1.2cm;
cc := 0.68cm;
ddA := 0.4cm;
ddB := 0.3cm;
ee := 1.4cm;
ffA := 1.15cm;
ffB := 0.6cm;
qqa := 0.38cm;
qqb := 0.25cm;
qqc := 0.20cm;
da := 3.5cm;
penA := 0.5bp; % Pen scale for markings.
penB := 0.5bp; % Pen scale for boxes.
sizeA := 3pt;
de := 12pt;
df := de + 12pt;
dg := 13pt;
w0 := (0,0);
w1 := w0 + (0,bb);
w2 := w0 + (da,0);
w3 := w2 + (0,bb);
w10 := 0.5[w0+(cc,-ddA),w1+(cc,ddB)]; % Right of left box.
w11 := 0.5[w2+(-cc,-ddA),w3+(-cc,ddB)]; % Left of right box.
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% Multilinear maps from the V-spaces to K.
label(btex
\strut$\displaystyle\mathop{\times}\limits_{\alpha\in A}V_\alpha$ etex, w0);
label(btex \strut$K$ etex, w1);
pickup pencircle scaled penA;
S_arrowspaces(w0, w1, qqa, qqb, 1, black);
S_erd(w0, w1, qqa, qqb, 3, 0, black, black, sizeA, sizeA, penA, penA);
label.bot(btex \strut$\mlin((V_\alpha)_{\alpha\in A};K)$ etex, w0+(0,-ddA));
% label.bot(btex \strut over a set etex, w1+(0,-df));
pickup pencircle scaled penB;
pat1 := (w0+(-cc,-ddA))--(w0+(cc,-ddA))--(w1+(cc,ddB))--(w1+(-cc,ddB))--cycle;
draw pat1;
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% Multilinear maps from the W-spaces to K.
label(btex
\strut$\displaystyle\mathop{\times}\limits_{\beta\in B}W_\beta$ etex, w2);
label(btex \strut$K$ etex, w3);
pickup pencircle scaled penA;
S_arrowspaces(w2, w3, qqa, qqb, 1, black);
S_erd(w2, w3, qqa, qqb, 3, 0, black, black, sizeA, sizeA, penA, penA);
label.bot(btex \strut$\mlin((W_\beta)_{\beta\in B};K)$ etex, w2+(0,-ddA));
% label.bot(btex \strut over a set etex, w1+(0,-df));
pickup pencircle scaled penB;
pat2 := (w2+(-cc,-ddA))--(w2+(cc,-ddA))--(w3+(cc,ddB))--(w3+(-cc,ddB))--cycle;
draw pat2;
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
pickup pencircle scaled penA;
S_arrowspaces(w10, w11, qqc, qqc, 1, black);
S_erd(w10, w11, qqc, qqc, 1, 0, black, black, sizeA, sizeA, penA, penA);
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
pickup pencircle scaled penB;
pat3 := (w0+(-ee,-ffA))--(w2+(ee,-ffA))--(w3+(ee,ffB))--(w1+(-ee,ffB))--cycle;
draw pat3;
label.bot(btex
\strut$\Lin(\mlin((V_\alpha)_{\alpha\in A};K),\mlin((W_\beta)_{\beta\in B};K))$
etex,
0.5[w0,w2]+(0,-ffA));
label.bot(btex
\strut$=\botimesr((V_\alpha)_{\alpha\in A};\,(W_\beta)_{\beta\in B})$ etex,
0.5[w0,w2]+(0,-ffA-dg));
endfig;
end