CoCalc Public Fileswww / tables / fundomain / java-source / READMEOpen with one click!
Author: William A. Stein
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FunDomain:
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FunDomain is a java program written by Helena A. Verrill
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for drawing fundamental domains of certain congruence
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subgroups of SL_2(Z) acting on the upper half complex plane.
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The program is covered by the GNU GPL license.
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To run the program, you will need to be able to
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run java programs, either from a browser such
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as netscape, or in an applet.
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You'll need to have "javac" installed to compile
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the program, and "java" to run it.
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You can get these from:
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http://java.sun.com/j2se/
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If you already have java, you can find the version
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by typing
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> java -version
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If it's 1.1.1 or higher this, program should work for you.
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(If you're using linux you might have to edit your
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font.properties file for it to not give error messages)
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Unpack the fundomain.tar.gz file by typing:
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> tar -zxvf fundomain.tar.gz
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This produces a fundomain directory containing the following files:
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README
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GNUGPL.txt
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ArcSection.java
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ConFrac.java
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ConjClassRep.java
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FunDomain.java
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HypTriangle.java
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IntMat.java
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ModN.java
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RepList.java
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To compile the program, type:
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> javac FunDomain.java
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To run the resulting program, type
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> java FunDomain
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A java applet should pop up.
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Instructions on using the program:
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General controls:
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-----------------
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Using the orange coloured buttons to:
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scale button: Change scale (in pixels per unit)
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Expand Rectangle button: Click on the screen and drag the mouse
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to form a rectangle.
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Then click on 'expand rectangle' and the scale
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changes so the height of the rectangle becomes
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the height of the screen.
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The center of the rectangle moves the the
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center of the screen (in vertical direction only).
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Colour choice buttons: Change colour of triangles
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<-- <- 0 -> --> buttons: Change position of the origin
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(Press "0" to put the origin in the center)
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Fundamental domain drawing mode:
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Draws Fundamental Domain for intersection of
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one of
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Gamma^0(N), Gamma^1(N), Gamma_0(N), Gamma_1(N), Gamma(N)
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with one of
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Gamma^0(M), Gamma^1(M), Gamma_0(M), Gamma_1(M), Gamma(M).
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Type of group: There are choice buttons to choose which of the
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above types of groups to use.
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Changing N: Type in N, in the box provided, then click on "draw"
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OR press the ">" and "<" buttons to increase N in steps.
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Changing M: Type in M, in the box provided, then click on "draw"
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OR press the ">" and "<" buttons to increase N in steps.
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Edit Mode: Click on the "edit" button then you can move the triangles to give
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a different fundamental domain by clicking on the yellow circles
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on the boundaries of the triangles.
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Links Mode: Click on the "link" button to show how the boundary is linked up.
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Find matrix: Click on a triangle to find out what the corresponding
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coset representative is, as a 2 by 2 matrix.
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Triangle Drawing mode:
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----------------------
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Here you can draw a triangle corresponding
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to transforming a standard domain by a given matrix.
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Currently only matrices of determinant 1 are allowed.
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You can enter the matrix, by typing in the appropriate spaces on the right
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of the screen, and then click on "draw"
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OR use the buttons TM, RM, etc to transform the matrix M.
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Matrices are T=[1,1;0,1], T'=[1,-1;0,1], S=[0,-1;1,0], R = [0,-1;1,1].
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move/copy: If move is selected, when the matrix is applied
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(eg, T, R, etc) the triangle is moved by this matrix.
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If copy is selected, a copy is made,
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which is a translate by the applied matrix.
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Move to: this moves the origin so that the triangle just drawn is
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in the middle of the screen
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Scale to: If you click on this, in addition to moving, it also scales,
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so the triangle just drawn is in the middle of the screen,
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AND at a reasonable size so you can see it.
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For more instructions for how to use the program see the web page at:
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http://hverrill.net/fundomain/index.html
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