By Daly T.

It is a instructional advent to the Axiom machine Algebra method. It contains examples that illustrate a number of the uncomplicated skills.

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By associating operations with categories, operation names can be reused whenever appropriate or convenient to do so. 1. INTRODUCTION TO AXIOM 15 denote lexicographic-comparison in an algorithm. However, it is wrong to use the same < with this definition of absolute-value: abs(x) == if x < 0 then − x else x Such a definition for abs in Axiom is protected by context: argument x is required to be a member of a domain of category OrderedSet. 17 Packages Are Clusters of Polymorphic Operations In Axiom, facilities for symbolic integration, solution of equations, and the like are placed in “packages”.

5 Control of Result Types In earlier sections the type of an expression was converted to another via the “::” operator. However, this is not the only method for converting between types and two other operators need to be introduced and explained. The first operator is “$” and is used to specify the package to be used to calculate the result. 6666666666 6666666667 Type: Float tells Axiom to use the “/” operator from the Float package to evaluate the expression 2/3. This doe not necessarily mean that the result will be of the same type as the domain from which the operator was taken.

Since the generation of any Fibonacci number only relies on knowing the previous two numbers we can look at the series through a window of two elements. To create the series the window is placed at the start over the values [1, 1] and their sum obtained. The window is now shifted to the right by one position and the sum placed into the empty slot of the window; the process is then repeated. To implement this we require a function that takes a list of two elements (the current view of the window), adds them, and outputs the new window.

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