Benchmarks

- Example 6.4 of [VW1988]: Inputs & Logs
- Example 7 of [CM2014]: Inputs & Logs
- Example 8 of [CM2014]: Inputs & Logs
- Example 9 of [CM2014]: Inputs & Logs
- Example 5 of [FIS2015]: Inputs & Logs
- Example 6 of [FIS2015]: Inputs & Logs
- Example 7 of [FIS2015]: Inputs & Logs
- Example 8 of [FIS2015]: Inputs & Logs
- Example 9 of [FIS2015]: Inputs & Logs
- Example 10 of [FIS2015]: Inputs & Logs
- Example 1 of [FIS2016]: Inputs & Logs
- Example 2 of [FIS2016]: Inputs & Logs
- Example 3 of [FIS2016]: Inputs & Logs
- Example 4 of [FIS2016]: Inputs & Logs
- Example 5 of [FIS2016]: Inputs & Logs

- CGSQE-20160509@Maple2015 is denoted by "cgs".
- SyNRAC@Maple2015 is denoted by "syn".
- RegularChains-20151027@Maple2015 is denoted by "rc".
- Resolve@Mathematica10.4.0 is denoted by "res".
- Reduce@Mathematica10.4.0 is denoted by "red".
- rlhqe@RedLog@Reduce(Free CSL version),04-Aug-11 is denoted by "rlh".
- rlqe@RedLog@Reduce(Free CSL version),04-Aug-11 is denoted by "rl".
- QEPCAD Version B 1.69, 16 Mar 2012 is denoted by "qep".

- All the computations are done by the same computer environment with CPU Intel CORE i7 with 64GB memory OS Ubuntu 14.04.
- Computing time is written in second.
- "N" means that the computation does not terminate within 1 hour.
- "E" means the computation is crashed with some error.

cgs | syn | rc | res | red | rlh | rl | qep | |
---|---|---|---|---|---|---|---|---|

01 | 0.287 | 0.167 | 120.741 | 0.054373 | 0.432344 | N | 0.03 | 6.374 |

02 | 1.153 | N | 2.145 | 0.098667 | 0.464517 | N | N | E |

03 | 0.987 | 0.537 | 29.931 | 0.262904 | N | 0.07 | N | N |

04 | 105.810 | 111.379 | 2.020 | 0.055026 | 0.123643 | 59.82 | N | E |

05 | 29.187 | N | N | 31.054 | N | N | N | N |

06 | 5.325 | N | N | N | N | N | E | E |

07 | 1.480 | N | N | 274.349 | 274.894 | 247.68 | N | N |

08 | 0.311 | N | N | N | 0.588577 | N | N | N |

09 | 564.126 | 17.481 | N | N | N | N | N | E |

10 | 20.277 | E | E | N | N | N | N | N |

11 | 0.393 | N | 2.970 | N | N | 1.479 | N | E |

12 | 0.288 | N | N | N | N | 1.529 | N | E |

13 | 0.761 | N | N | N | N | E | N | N |

14 | 1.305 | 54.373 | 7.424 | 0.273433 | 1143.79 | E | 0.09 | 523.29 |

15 | 0.859 | E | N | N | N | N | N | N |

[CM2014] Chen, C. and Maza, M, M.:

Quantifier Elimination by Cylindrical Algebraic Decomposition Based on Regular Chains.

Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 91-98, ACM, 2014.

[FIS2015] Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato.:

Real Quantifier Elimination by Computation of Comprehensive Gröbner Systems.

Proceedings of the International Symposium on Symbolic and Algebraic Computation, pp. 173-180, ACM, 2015.

[FIS2016] Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato.:

On the Implementation of CGS Real QE.

To appear in Proceedings of the International Congress on Mathematical Software, LNCS, Springer, 2016.

[VW1998] Weispfenning, V.:

A New Approach to Quantifier Elimination for Real Algebra.

Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 376-392, Springer, 1998.