Classes for Computer Algebra

Abstract

In this chapter we introduce the basic building classes of our symbolic system. The chapter deals with many structures in mathematics as well as some common data structures in computer science. The description of the classes are arranged in such a way that primitive structures like very long integer, rational class are placed earlier in the chapter than the more sophisticated structures like vector, matrix class, etc. There are thirteen classes presented in this chapter:

• (1) Verylong provides the integer numbers abstract data type without upper and lower bound.

• (2) Rational provides the rational numbers abstract data type.

• (3) Complex provides the complex numbers abstract data type.

• (4) Quaternion provides the quaternion abstract data type.

• (5) Derive provides the exact differentiation class.

• (6) Vector provides the vector data structure.

• (7) Matrix provides the matrix data structure.

• (8) Array provides the array data structure.

• (9) String provides the string abstract data type.

• (10) BitVector provides the bit vector field abstract data type.

• (11) List provides the linked list abstract data type.

• (12) Polynomial provides the polynomial abstract data type.

• (13) Set provides the set abstract data type for finite sets.