Axiom by Daly T.

By Daly T.

It is a instructional advent to the Axiom desktop Algebra method. It comprises examples that illustrate a number of the uncomplicated talents.

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Type: Stream Integer As a longer example a stream of Fibonacci numbers will be computed. The Fibonacci numbers start at 1 and each following number is the addition of the two numbers that precede it so the Fibonacci sequence is: 1, 1, 2, 3, 5, 8, . . 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.

At the top of this world is SetCategory, the class of algebraic sets. The notions of parents, ancestors, and descendants is clear. Thus ordered sets (domains of category OrderedSet) and rings are also algebraic sets. Likewise, fields and integral domains are rings and algebraic sets. However fields and integral domains are not ordered sets. SetCategory +---- Ring ---- IntegralDomain ---- Field | +---- Finite ---+ | \ +---- OrderedSet -----+ OrderedFinite Figure 1. A simplified category hierarchy.

0 can be converted to an integer type since it has no fractional part. Conversion from floating point values to integers is performed using the functions round and truncate. e. removes the fractional part). Both functions return the result as a floating point number. To extract the 20 CONTENTS fractional part of a floating point number use the function fractionPart but note that the sign of the result depends on the sign of the argument. 2. 3 21 Useful Functions To obtain the absolute value of a number the abs function can be used.

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