Question

Examples for axiom 6 plzzzz

Answer 1

far, Axiom does most of the calculation we would expect of any computer algebra system. But now we look at an aspect of Axiom which sets it apart from other systems: its use of types. In Axiom, “type” is another word for “domain”, or “domain of computation”, which is a method of organizing all objects. Objects include standard mathematical constructs such as matrices, functions, integers, abelian groups; data structures such as lists and arrays; as well as constructs built up from other constructs. Thus in Axiom we can create and use the type: “List of square matrices of polynomials over integer fractions”. The type of the operand indicates the type of the operation: a simple multiplication * will have a different interpretation depending on whether the operands are integers, real numbers (floats), matrices, elements of a finite field, or many other types.

There are three special symbols which are used when dealing with types:

::
This is used for converting from one type to another. In the form object::type it takes the object object and converts it to type type.
</tt></dt> <dd>This means to take the operation as defined for objects of the given type. It is used in the form <tt>(operand1 operation operand2)type.
@
This means to choose the operation (and possibly convert the types of the objects, if needed) so that the result is of the given type.
As examples of the use and misuse of these symbols, let’s investigate the calculation

3^{10^9}pmod{2^{20}}=3^{1000000000}pmod{1048576}

The type we will use is IntegerMod, which can be abbreviated ZMOD:

Types in Axiom - ZMOD