World Scientific, Singapore, 2008.
SymbolicC++ 3Some of the improvements and features of the new SymbolicC++:
SymbolicC++ uses C++ and object-oriented programming to develop a computer algebra system. Object-oriented programming is an approach to software design that is based on classes rather than procedures. This approach maximizes modularity and information hiding. Object-oriented design provides many advantages. For example, it combines both the data and the functions that operate on that data into a single unit. Such a unit (abstract data type) is called a class.
We use C++ as our object-oriented programming language for the following reasons: C++ allows the introduction of abstract data types. Thus we can introduce the data types used in the computer algebra system as abstract data types. The language C++ supports the central concepts of object-oriented programming: encapsulation, inheritance, polymorphism (including dynamic binding) and operator overloading. It has good support for dynamic memory management and supports both, procedural and object-oriented programming. A less abstract form of polymorphism is provided via template support. We overload the operators
=, +, -, *, /
etc for our abstract data types, such as verylong integers, rational numbers, complex numbers or symbolic data types. The vector and matrix classes are implemented on a template basis so that they can be used with the other abstract data types.
Another advantage of this approach is that, since the system of symbolic
manipulations itself is written in C++, it is easy to enlarge it and to
fit it to the special problem at hand. The classes (abstract data types)
are included in a header file and can be provided in any C++ program by
giving the command
at the beginning of the program.
For the realization of this concept we apply the following features of C++:
The developed system SymbolicC++ includes the following abstract data types (classes):
Verylong: handles very long integers
Rational: template class that handles rational numbers
Quaternion: template class that handles quaternions
Derive: template class to handle exact differentiation
Vector: template class that handles vectors
Matrix: template class that handles matrices
Array: template class that handles multi-dimensional arrays
List: template class that handles linked lists
Set: template class that handles finite sets
Polynomial: template class that handles univariate polynomials
Multinomial: template class that handles multivariate polynomials
Symbolic: class that handles symbolic manipulations, such as rules, simplifications, differentiation, integration, commutativity and non-commutativity
Equation: class that represents symbolic equations
Type: handles the atom a LISP system
Pair: handles the dotted pair for a LISP system, all the standard LISP functions are included
Suitable type conversions between the abstract data types and between abstract data types and basic data types are also provided.
The advantages of SymbolicC++ are as follows: