Overview of Data Structures and Operators

APU implements two primary levels of data structures :

Polynomials

These represent the high level data structure which the user will typically use. A polynomial is represented in (sparse) recursive form, i.e. as a polynomial in one variable whose coefficients are either polynomials in another variable or field elements. Polynomials come with the standard arithmetic operators as well as other functions like Sylvester resultants, Sturm sequences etc.

Field elements

These represent the lower level structures which can used by themselves for arithmetic or, usually, as structures over which polynomials are defined. A variety of different types are defined including integers modulo a prime, ``big'' integers, and straight-line programs. In addition to the standard operators provided within a sub-class, (binary) operators are also provided for certain pairs of classes (e.g. arithmetic operators are provided for two objects of types ``small'' integer and big integer).

In addition to the above two primary classes, APU provides subsidiary functions, operators and utilities such as reading and writing polynomials, interacting with polynomials in Maple format etc.