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On Some Unsolved Problems of Mathematica

Keywords: Mathematica , analytic , numerical , computations , simplification , expressions , Fortran

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Abstract:

In this paper, some unsolved problems of the Mathematica software package are documented. At first, it is shown, using a number of examples, that the processing (simplification) of rational-fractional expressions involving powers in the general form, has been implemented in Maple more carefully than in Mathematica. Then, an error in Mathematica is demonstrated, leading to incorrect results at a change of a function’s body. For each example of symbolic or symbolic-numeric computations, alternate routes for solving the emerged problem are proposed (where possible). An added problem, related to Mathematica’s computing speed is documented, employing examples related to two-dimensional gas dynamics problems. It is shown that Mathematica computes rather slowly (about one thousand times slower) compared to a Fortran code.

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