The (n+1)-dimensional harmonic oscillator equation is of the form:

Before generating the system, we transform
*t* *it*, so the
equation has no complex coefficients, and can be more easily dealt with.

The determining systems for this PDE are slightly more complex than the
systems for the Laplace equation, as the independent variables occur
explicitly in the determining systems, and there is an unknown constant
*a*.

The determining systems consists of equations the dependent variables
, *T* and
*X*01, *X*02,..., *Xn* which depend on the independent variables
, *t* and
*x*01, *x*02,..., *xn*. There is also the constant *a*.

The systems for *n* = 3..16 can be downloaded
here
(the files in the archive are named harosc_n).

For the benchmark, the additional assumption was made that
*a* 0,
which is present in the *N* list for the systems.

Input | PureElim | |||

Dimension | Equations | Length | Time (sec) | Mem (MB) |

3 | 47 | 5200 | 0.01 | 0.72 |

4 | 75 | 8819 | 0.04 | 0.73 |

5 | 109 | 13620 | 0.06 | 0.76 |

6 | 149 | 19747 | 0.10 | 0.80 |

7 | 195 | 27344 | 0.17 | 0.90 |

8 | 247 | 36555 | 0.32 | 0.98 |

9 | 305 | 47524 | 0.48 | 1.03 |

10 | 369 | 60395 | 0.71 | 1.11 |

11 | 439 | 75312 | 1.01 | 1.22 |

12 | 515 | 92419 | 1.77 | 1.82 |

13 | 597 | 111860 | 2.53 | 2.06 |

14 | 685 | 133779 | 3.89 | 2.16 |

15 | 779 | 158320 | 6.63 | 2.56 |

16 | 879 | 185627 | 10.45 | 2.63 |

Allan Wittkopf 2000-06-15