### On Some Unsolved Problems of Mathematica

#### 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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PDF#### References

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