Design and implementation of a symbolic computation framework for polynomials

Symbolic computation is used to find exact solution of a problem. Numerous applications have been developed that can quickly perform symbolic computations without errors. However, since these applications are designed to be used only with their own user interfaces, they can not be integrated into other computing environments or run as a component of those environments. In this study, the development stages of an application framework that can be used by users to support symbolic computation operations on polynomials are presented. Formal language definitions have been used to represent a polynomial problem. Firstly, grammar rules are defined for the forms of polynomial problems, and abstract syntax trees of related problems are generated by applying language parsing operations. These trees are converted to expressions in JSON (JavaScriptObjectNotation) data interchange format so that they can be used by all programming languages. Then simplification operations are applied to obtain object representations of these expressions. Finally, various numerical and symbolic computation operations are defined on these object representations to support the simplification of polynomial problems, the step by step solution of problems and the generation of similar problems.