UACalc, A Universal Algebra Calculator


Ralph Freese

New installation directions

  1. Make sure java is installed on your computer.
  2. Download 3 jar files:
  3. To run it do (from the command line of a terminal window)
    java -jar uacalc.jar

Macs with M1 or M2 chip

Java has not been ported to those chips but Apple has a workaround: just start UACalc from the command line as above. If a window pops up and asks you if you want to install Rosetta, click the install button. It should run fine and won't ask again about installing Rosetta. (And it may not ask you in the first place.)

Getting the newest version

The above instructions retrieve version 1.17 from 2017. To get the latest, currently version 1.19 (Jun 10, 2022), is tricky but the following seems to work:
  1. Do 1. to 3. above and make sure 3. works.
  2. Optionally move the uacalc.jar file aside.
  3. Download the (newest) jar file: This may be tricky since this jar is unsigned. Your OS will probably tell you it won't allow this but if you are persistent, you can override this.
  4. Put this newest uacalc.jar in the same directory (folder) as the LatDraw.jar and miglayout-3.7-swing.jar, and do 3.
Another alternative is to download the source from our github repository and compile it yourself.

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 (revised Sept 8, 2015)

  • Get the latest Java. (Java 8 update 60 is the latest as of Sept 2015.)
    • 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 third 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.)

  • If it doesn't bring up a menu and you are on a Mac:
    • Go to System Preferences → Security & Privacy → [Unlock the lock] → Allow apps downloaded from: (Select Anywhere) and try the link below again. After successfully getting the program you can turn the Allow apps downloaded from: back to one of the safer options.

  • If you're still having trouble try Use the Firefox browser, especially from macs.

  • 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: