UACalc, A Universal Algebra Calculator


Ralph Freese

This page has the new version of the Universal Algebra Calculator. It is based on the Matt Valeriote's original version and the revised version by Emil Kiss and myself. Mike Behrisch and William DeMeo have also made important contributions.

Getting and Launching UACalc

  • Use the Firefox browser, especially from macs.

  • Get the latest Java from (Java 7 update 51 is the latest as of Jan 2014.)
    • If you want to do any programming/development work, you need the jdk. To find and download it, try Java SDK or google jdk.

  • Click one of the links below. (I suggest the second one.)

  • This should bring up a menu with choices for opening. Choose Java Web Start if that is a choice. On unix systems it will be javaws. (If Java Web Start is not a choice, see below.)

  • The program should start. An icon that is an 8-element BA should be on your desktop. In the future you can start the program with that.

  • Click on one of these:

Java Web Start Not a Choice (Macs)

  • If you click one of the above and the menu does not include Java Web Start, then choose to save the file.

  • Use Finder to find this file. Highlight (but don't open) it.

  • From the Finder menu choose Get Info.

  • This will have a drop down list of choices to open it with. Java Web Start will be on the list. Choose it.

  • Also click the button that says open all files with this extension (which is jnlp) with Java Web Start.

A Sample of What You Might Try:

  1. choose File -> Built in Algs -> lyndon.
  2. choose Tasks -> Free Algebra; set the number of generators to 2. you'll be switched automatically to the Computations tab and you'll see its 5 terms and it will be added to the list of algebras at the bottom.
  3. make this free algebra the current algebra by highlighting it (at the bottom)
  4. choose Drawing -> Con; try the buttons to do things like rotate the diagram (you can see there are two congruences with 4 blocks; neither mi)
  5. highlight lyndon at the bottom and draw its con. Note you can switch from one diagram to the other by changing the algebra at the bottom.
  6. choose Tasks -> B in V(A). Choose A to be F(2) (listed as A1) and B to be lyndon. It gives the failing equation (zx)y = (zy)x. Also try this with n5 and m3, both directions.
  7. choose File -> Built In Algs -> m3, and find F(4) over it. after a bit you will see information on how long it will take (20 to 30 minutes, you may need to scroll right). You can press the cancel and it will stop or you can do other stuff. If you let it run you can verify J. Berman and B. Wolk's result that it has 19,982 elements. In the tasks table in the middle, you can highlight a different task and see its result and log info.
  8. Make lyndon the current algebra by highlighting it at the bottom and switch to the Con tab. There are three atoms; two of them are meet irreducible. Click on one of them and the right-click (to get a popup menu) and choose Make quotient algebra (the only choice). Now use Tasks -> B in V(A) to verify that this 6 element quotient algebra generates the same variety (and so could have been used by Lyndon). This fact was discovered by Edmond Lee.

TCT type colors in the diagram:

  1. red
  2. yellow
  3. cyan
  4. blue
  5. black


New Command Line Version: