Ket (
http://sourceforge.net/projects/ket/)
For most trivial algebra, it's quicker to use paper and pencil than a full algebra system. Ket is a faster alternative with the benefit of clipboards, save/load and export to LaTeX and HTML.
Most algebra consists of recombining existing expressions. These can be added in plain text and substituted into one another by clicking and dragging one equation into another. You can then reorganize the resulting equation using click-and-drag algebra by dragging terms to different parts of the equation, e.g.
y=mx+c
y-c=mx
(y-c)/m=x
x=(y-c)/m.
Most real-world algebra problems require translation from real-world information into a coherent mathematical framework. For simple cases, the standard approach is the back-of-the-envelope calculation. This shows only enough working to keep the idea organized in your mind as you solve it. This part of a maths problem is more akin to writing the first draft of an essay. That is, you list relevant known equations and solution fragments which you organize into a coherent narrative.
For this you need an algebra-centred text editor. Most of the time spend doing algebra on computers or on paper is writing and rewriting respectively. To avoid this, Ket is a modal editor (built around Vim-like commands) in which keyboard letters correspond to simple editing commands. That is, the editor focuses on transforming existing expressions and only incidentally on adding new ones. In addition to redrafting working, with each command, the user performs an algebraic step.
A text editor represents a line of text as a list of characters. Ket represents an equation as a tree of functions, constants and variables. And instead of a cursor editing around a particular character, editing takes place around a tree branch. So editing commands edit a function, variable or value at a time in plain text while keeping the larger whole in conventional mathematical notation. And because each command is a single key press, each editing step is as quick as touch typing. Furthermore, while some commands perform algebraic transformations, others simply edit the data structure. This is analogous to algebra on paper where symbols are cancelled by scoring them out.
A text editor represents an essay as a list of lines of characters. Ket represents a document as a list of equations where each is represented as a tree of functions, constants and variables. Instead of a cursor editing around a particular character, editing takes place around a tree branch. So editing commands edit a function, variable or value at a time in plain text while keeping the larger whole in conventional mathematical notation. And because each command is a single key press, each editing step is as quick as touch typing. Furthermore, while some commands perform algebraic transformations, others simply edit the data structure.