TOPCAT allows you to enter algebraic expressions in a number of contexts:
What you write are actually expressions in the Java language, which are compiled into Java bytecode before evaluation. However, this does not mean that you need to be a Java programmer to write them. The syntax is pretty similar to C, but even if you've never programmed in C most simple things, and some complicated ones, are quite intuitive.
The following explanation gives some guidance and examples for writing these expressions. Unfortunately a complete tutorial on writing Java is beyond the scope of this document, but it should provide enough information for even a novice to write useful expressions.
The expressions that you can write are basically any function of all the column values and subset inclusion flags which apply to a given row; the function result can then define the per-row value of a new column, or the inclusion flag for a new subset, or the action to be performed when a row is activated by clicking on it. If the built-in operators and functions are not sufficient, or it's unwieldy to express your function in one line of code, you can add new functions by writing your own classes - see Section 7.9.
Note: if Java is running in an environment with certain security restrictions (a security manager which does not permit creation of custom class loaders) then algebraic expressions won't work at all, and the buttons which allow you to enter them will be disabled.