A simple benchmark is the time it takes to factor a long integer. For comparison we did this benchmark in Maple and Mathematica. The Maple test was: >ifactor(5^100-1);

Another more realistic of many statistical computations involved computing the ideal bootstrap for the trimmed mean as suggested in Problem 6.10 of Hastie and Tibshirani (1993). The Maple code and which includes documentation is available, prob610.mpl.

Symbolic matrix inverse and eigenvector computations were also timed. The Maple code for these computations is very short and reproduced here:

>with(linalg); >time(inverse(toeplitz([a,b,c,d,e,f]))); >time(eigenvects(toeplitz([a,b,c,d])));

MACHINE | TEST | TIME IN SECONDS |

Thinkpad, pentium-120 | ifactor | 7684 |

Thinkpad, pentium-120 | prob610 | 117 |

Thinkpad, pentium-120 | symbolic inverse | 22 |

Thinkpad, pentium-120 | symbolic eigenvectors | 75 |

M40, Risc6000 (lexis) | ifactor | 10822 |

M40, Risc6000 (lexis) | prob610 | 67 |

M40, Risc6000 (lexis) | symbolic inverse | 44 |

M40, Risc6000 (lexis) | symbolic eigenvectors | 55 |