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.
Keywords:
Mathematica, analytic, numerical, computations, simplification, expressions, FortranDownloads
References
S. Wolfram, The Mathematica book, 3rd Edition, Cambridge University Press, Cambridge, UK, 1996
M. Wester, “A critique of the mathematical abilities of CA systems” In: Computer Algebra Systems: A Practical Guide, John Wiley & Sons, Chichester, United Kingdom, pp. 25–60, 1999
S. P. Kiselev, E. V. Vorozhtsov, V. M. Fomin, Foundations of fluid mechanics with applications: Problem solving using Mathematica. Birkhäuser, Boston, 1999
V. G. Ganzha, E. V. Vorozhtsov, “Implementation of aerodynamic computations with Mathematica”, 2nd Workshop on Computer Algebra in Scientific Computing, pp. 101–114, Munich, 1999 DOI: https://doi.org/10.1007/978-3-642-60218-4_8
S. R. Chakravarthy, S. Osher, “A new class of high accuracy TVD schemes for hyperbolic conservation laws”, AIAA Paper, No. 85-0363, 1985 DOI: https://doi.org/10.2514/6.1985-363
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