The TagSetDelayed (shortcut notation /:) associates the rule with the symbol Unit. Here is a typical rule to teach it what happens when you get powers of units. We can proceed directly to teaching Mathematica what is special about the new type. Really, nothing! I can already enter and store data in that type and write functions that recognize that type because “type” is just an arbitrary symbol used as a wrapper for a collection of contents, and Mathematica eats symbolic data for breakfast! So having created this type in my mind, what do I need to do to make it available to Mathematica? Well, nothing. My new data type is going to look (internally) like this:Īnd I am going to represent composite units with composites of the name in the second argument. Just as in the existing version, the only function that needs to know about the ratio of Meter to, say, Inch, is Convert, though that might be invoked, in an abstracted way, by other commands. In order to do this in an extensible way, I don’t want to teach all these commands about Meter specifically, but I will create a new data type for units, so that I can teach the Mathematica commands about units abstractly.

So in this package I want as many of Mathematica‘s commands as possible to do sensible things automatically when they encounter unit-based quantities. All of the knowledge about units and Meter in particular is contained in the Convert command. The core reason is that it doesn’t teach the system, as a whole, anything about units, or even that the symbol “ Meter” is any different than the symbol “x”. But give it an input like…Īnd it does nothing with it until you specify that you want the result in a specific unit. It can convert between several hundred units and warn if a requested conversion is dimensionally inconsistent. Aside from being a really nice extension to Mathematica, it is also an interesting case study in adding a custom data “type” to Mathematica and extending the knowledge of the built-in functions to handle the new “type”.įirst I have to explain the point by answering the question, “What’s wrong with the built-in units package?” Well, there is nothing actually wrong with it, it just doesn’t apply Mathematica‘s automation principles. I just published a Mathematica package that provides an alternative, richer implementation of units and dimensional analysis than the built-in units package.

Wolfram mathematica documentation plot