In this section we briefly describe an internal process by which resolve Axiom determines a type to which two objects of possibly different types can be converted. We do this to give you further insight into how Axiom takes your input, analyzes it, and produces a result.
What happens when you enter to Axiom? Let's look at what you get from the two terms of this expression.
This is a symbolic object whose type indicates the name.
This is a positive integer.
There are no operations in PositiveInteger that add positive integers to objects of type Variable(x) nor are there any in Variable(x). Before it can add the two parts, Axiom must come up with a common type to which both and can be converted. We say that Axiom must resolve the two types into a common type. In this example, the common type is Polynomial(Integer).
Once this is determined, both parts are converted into polynomials, and the addition operation from Polynomial(Integer) is used to get the answer.
Axiom can always resolve two types: if nothing resembling the original types can be found, then Any is be used. Any This is fine and useful in some cases.
In other cases objects of type Any can't be used by the operations you specified.
Although this example was contrived, your expressions may need to be qualified slightly to help Axiom resolve the types involved. You may need to declare a few variables, do some package calling, provide some target type information or do some explicit conversions.
We suggest that you just enter the expression you want evaluated and see what Axiom does. We think you will be impressed with its ability to ``do what I mean.'' If Axiom is still being obtuse, give it some hints. As you work with Axiom, you will learn where it needs a little help to analyze quickly and perform your computations.