Universal Algebra Calculator
Quickly see it in action!!

  1. First download a small algebra file: z3_2.alg (you might want to do a "save link as" to get this). z3 is multiplicative part of the integers mod 3 and z3_2 is its square. Its congruence lattice has 34 elements; it type set is {2, 5}.

  2. Start the calculator.

  3. From the Compute menu choose Congruence Lattice. When it asks for a file, give z2_3.alg.

  4. A new window will pop up. From that choose Compute and Label from the Lattice menu. The window will get bigger and have information about the congruence lattice.

  5. Choose Draw Lattice from the Graphics menu and click the improve button. The type 2 coverings are yellow and the type 5 are black. The two windows are tied together: clicking on an element or cover in the draw window changes the info window and vice versa.

Go to UA Calculator home for instructions on getting the program and using it.