CoCalc Public Fileswww / tables / fundomain / java-source / README
Author: William A. Stein
1FunDomain:
2
3FunDomain is a java program written by Helena A. Verrill
4for drawing fundamental domains of certain congruence
5subgroups of SL_2(Z) acting on the upper half complex plane.
6
7The program is covered by the GNU GPL license.
8
9To run the program, you will need to be able to
10run java programs, either from a browser such
11as netscape, or in an applet.
12
13You'll need to have "javac" installed to compile
14the program, and "java" to run it.
15You can get these from:
16http://java.sun.com/j2se/
17
18If you already have java, you can find the version
19by typing
20> java -version
21If it's  1.1.1 or higher this, program should work for you.
22(If you're using linux you might have to edit your
23font.properties file for it to not give error messages)
24
25Unpack the fundomain.tar.gz file by typing:
26> tar -zxvf fundomain.tar.gz
27This produces a fundomain directory containing the following files:
28
30 GNUGPL.txt
31 ArcSection.java
32 ConFrac.java
33 ConjClassRep.java
34 FunDomain.java
35 HypTriangle.java
36 IntMat.java
37 ModN.java
38 RepList.java
39
40
41To compile the program, type:
42> javac FunDomain.java
43
44To run the resulting program, type
45> java FunDomain
46
47A java applet should pop up.
48
49Instructions on using the program:
50
51General controls:
52-----------------
53
54Using the orange coloured buttons to:
55
56scale button:             Change scale (in pixels per unit)
57Expand Rectangle button:  Click on the screen and drag the mouse
58                          to form a rectangle.
59                          Then click on 'expand rectangle' and the scale
60                          changes so the height of the rectangle becomes
61                          the height of the screen.
62                          The center of the rectangle moves the the
63                          center of the screen (in vertical direction only).
64
65Colour choice buttons:    Change colour of triangles
66
67<-- <- 0 -> --> buttons:  Change position of the origin
68                          (Press "0" to put the origin in the center)
69
70
71
72Fundamental domain drawing mode:
73--------------------------------
74
75Draws Fundamental Domain for intersection of
76one of
77Gamma^0(N), Gamma^1(N), Gamma_0(N), Gamma_1(N), Gamma(N)
78with one of
79Gamma^0(M), Gamma^1(M), Gamma_0(M), Gamma_1(M), Gamma(M).
80
81
82Type of group:  There are choice buttons to choose which of the
83                above types of groups to use.
84
85Changing N:  Type in N, in the box provided, then click on "draw"
86             OR press the ">" and "<" buttons to increase N in steps.
87Changing M:  Type in M, in the box provided, then click on "draw"
88             OR press the ">" and "<" buttons to increase N in steps.
89
90Edit Mode:   Click on the "edit" button then you can move the triangles to give
91             a different fundamental domain by clicking on the yellow circles
92             on the boundaries of the triangles.
93
95
96Find matrix: Click on a triangle to find out what the corresponding
97             coset representative is, as a 2 by 2 matrix.
98
99
100Triangle Drawing mode:
101----------------------
102
103   Here you can draw a triangle corresponding
104   to transforming a standard domain by a given matrix.
105   Currently only matrices of determinant 1 are allowed.
106
107You can enter the matrix, by typing in the appropriate spaces on the right
108of the screen, and then click on "draw"
109OR use the buttons TM, RM, etc to transform the matrix M.
110Matrices are T=[1,1;0,1], T'=[1,-1;0,1], S=[0,-1;1,0], R = [0,-1;1,1].
111
112move/copy:  If move is selected, when the matrix is applied
113            (eg, T, R, etc) the triangle is moved by this matrix.
114            If copy is selected, a copy is made,
115            which is a translate by the applied matrix.
116
117Move to:    this moves the origin so that the triangle just drawn is
118            in the middle of the screen
119
120Scale to:   If you click on this, in addition to moving, it also scales,
121            so the triangle just drawn is in the middle of the screen,
122            AND at a reasonable size so you can see it.
123
124
125
126For more instructions for how to use the program see the web page at:
127http://hverrill.net/fundomain/index.html
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