Variant Handling, Inheritance and Composition in the ObjectMath Computer Algebra Environment

ObjectMath is a high-level programming environment and modeling language for scientific computing which supports variants and graphical browsing in the environment and integrates object-oriented constructs such as classes and single and multiple inheritance within a computer algebra language. In addition, composition of objects using the part-of relation and support for solution of systems of equations is provided. This environment is currently being used for industrial applications in scientific computing. The ObjectMath environment is designed to handle realistic problems. This is achieved by allowing the user to specify transformations and simplifications of formulae in the model, in order to arrive at a representation which is efficiently solvable. When necessary, equations can be transformed to C++ code for efficient numerical solution. The re-use of equations through inheritance in general reduces models by a factor of two to three, compared to a direct representation in the Mathematica computer algebra language. Also, we found that multiple inheritance from orthogonal classes facilitates re-use and maintenance of application models.