Axiom by Daly T.

By Daly T.

It is a educational advent to the Axiom computing device Algebra process. It comprises examples that illustrate a number of the easy skills.

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Example text

For example, the following conversion appears to be without error but others might not: %::Fraction Integer 23 5 Type: Fraction Integer where “%” represents the previous result (not the calculation). Although Axiom has the ability to work with floating-point numbers to a very high precision it must be remembered that calculations with these numbers are not exact. Since Axiom is a computer algebra package and not a numerical solutions package this should not create too many problems. The idea is that the user should use Axiom to do all the necessary symbolic manipulation and only at the end should actual numerical results be extracted.

For efficiency reasons the most common domains are preloaded but most (there are more than 1100 domains, categories, and packages) are not. Once these domains are loaded they are immediately available to the interpreter. Once a domain tower is built, it contains all the operations specific to the type. Computation proceeds by calling operations that exist in the tower. For example, suppose that the user asks to square the above matrix. To do this, the function “*” from Matrix is passed the matrix M to compute M ∗ M .

The result of the last expression is displayed. remember also that the percent symbol “%” is used to represent the result of a previous calculation. To display rational numbers in a base other than 10 the function radix is used. The first argument of this function is the expression to be displayed and the second is the base to be used. 032412 Type: RadixExpansion 5 Rational numbers can be represented as a repeated decimal expansion using the decimal function or as a continued fraction using continuedFraction.

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