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UltimaCalc ($30, 30-day feature-limited demo) falls into that category of "If you understand what it does, you probably want it." I was expecting something like the Windows calculator tool with a few dozen added buttons; what I got was a powerful mathematical tool with an extremely minimalist interface.
UltimaCalc very much assumes you know what you're doing, know what you want, and want a program which gets out of the way and gives you answers. The primary interface consists of two text boxes; one where you type equations, and one which shows you the result. You can type simple things like "2+2" and get "4", or you can type very long and complex formulae. The results can be logged to text files, which you can specify. There is no "history" function; each equation you type erases the one before, but, and this is important, any variables you define retain their value. So you can type "a=2", then type "b=4*a", and both "a" and "b" will be around for the remainder of the session for you to use in more formulae. This is very good for letting you plug values into equations.
In addition to the mathematics, UltimaCalc has a number of additional tools, such as one which will quickly solve trigonometry problems (wish I had that back in high school!), a program to find the roots of polynomials, solve linear and non-linear equations, and much more. This program seems ideal for people who need to do a lot of quick, but intricate, calculations as part of some other task, such as engineers or architects.
The interface is extremely Spartan, and it is often the case that one window must be closed before focus can be shifted to another, though this is not always obvious. Some things which should have default paths, such as the log file, must be set by the user before they can be used. Error messages are not always helpful, and the trial version, in addition to being time-limited, pops up "Buy now!" reminders with considerable frequency and is also limited in functionality, though not to the extent that evaluating the program is made more difficult. (For example, the trial allows only four equations for simultaneous linear equations, the full version up to ten.)
The $40 Professional version of UltimaCalc includes a symbolic algebra tool, which can simplify algebraic equations, so that y*(4*x)+y*(3*x) becomes 7 * x * y. It also includes a variety of other algebraic tools.
If you spend a lot of your day doing math that needs more than a calculator--but less than a high-powered tool such as Mathematica--UltimaCalc is worth evaluating. UltimaCalc is very lightweight in its system demands, making it preferable to firing up Excel for these sorts of things.
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