Opened 19 months ago

Last modified 3 months ago

## #31744 new enhancement

# ManifoldSubset: Propagate emptiness/nonemptiness using LP

Reported by: | Matthias Köppe | Owned by: | |
---|---|---|---|

Priority: | major | Milestone: | sage-9.8 |

Component: | manifolds | Keywords: | |

Cc: | Eric Gourgoulhon, Michael Jung, Travis Scrimshaw, Yuan Zhou | Merged in: | |

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

Introduce a binary variable z_S for each subset S, z_S = 1 if nonempty, z_S = 0 if empty. Fix a variable z_S to this value if emptiness/nonemptiness of the set S is known.

If A is a subset of B, write a constraint z_A <= z_B.

If [A, B] is an open cover of C, write a constraint z_C <= z_A + z_B or z_C <= z_A + z_B - z_A_inter_B.

Then solving a linear or integer linear optimization problem maximizing/minimizing variables z_S can prove that S has to be empty or nonempty.

### Change History (4)

### comment:1 Changed 17 months ago by

Milestone: | sage-9.4 → sage-9.5 |
---|

### comment:2 Changed 12 months ago by

Milestone: | sage-9.5 → sage-9.6 |
---|

### comment:3 Changed 9 months ago by

Milestone: | sage-9.6 → sage-9.7 |
---|

### comment:4 Changed 3 months ago by

Milestone: | sage-9.7 → sage-9.8 |
---|

**Note:**See TracTickets for help on using tickets.