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## 1.0 An Overview of Axiom

When we start cataloging the gains in tools sitting on a computer, the benefits of software are amazing. But, if the benefits of software are so great, why do we worry about making it easier -- don't the ends pay for the means? We worry becuase making such software is extraordinarily hard and almost no one can do it -- the detail is exhausting, the creativity required is extreme, the hours of failure upon failure requiring patience and persistence would tax anyone claiming to be sane. Yet we require people with such characteristics be found and employed and employed cheaply.

-- Christopher Alexander

(from Patterns of Software by Richard Gabriel)

Welcome to the Axiom environment for interactive computation and problem solving. Consider this chapter a brief, whirlwind tour of the Axiom world. We introduce you to Axiom's graphics and the Axiom language. Then we give a sampling of the large variety of facilities in the Axiom system, ranging from the various kinds of numbers, to data types (like lists, arrays, and sets) and mathematical objects (like matrices, integrals, and differential equations). We conclude with the discussion of system commands and an interactive ``undo.''

Before embarking on the tour, we need to brief those readers working interactively with Axiom on some details.

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