Adding new Representations of Mathematical Objects to Aplusix

In the framework of the ReMath European project, we initiated two new representations for algebraic expressions in Aplusix: a Tree & Natural representation mixing tree representations and natural representations of algebraic expressions, and a graphical representations to show curves and sets of solutions. Our work has been driven by two approaches: (1) a traditional approach focusing on the definition of new objects with their functionalities, beginning with a specification phase and continuing with a development phase; (2) an experiment-driven approach taking into account future cross-experiments. Solutions arisen from the cross-fertilization of these two approaches are presented in the paper