Opened 8 years ago

Last modified 3 years ago

## #17197 needs_work defect

# Bug creating Polyhedron from lines in number field — at Initial Version

Reported by: | Mark Bell | Owned by: | |
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Priority: | major | Milestone: | sage-7.4 |

Component: | number theory | Keywords: | Polyhedron, Number field |

Cc: | Frédéric Chapoton, Jean-Philippe Labbé, Jakob Kroeker | Merged in: | |

Authors: | Reviewers: | ||

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

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

I reported this to the google group (https://groups.google.com/forum/#!topic/sage-support/ew0bnGzjm98) but was told to repeat it here.

To create polyhedra quickly, the final suggestion in the Polyhedron documentation (http://www.sagemath.org/doc/reference/geometry/sage/geometry/polyhedron/constructor.html#base-rings) is to work in a set number field. Although this appears to work for setting vertices, it does not appear to work for lines (or rays).

For example:

sage: var('x') x sage: K.<sqrt3> = NumberField(x^2-3, embedding=1.732) sage: P = Polyhedron(lines=[(1,sqrt3)]) sage: P A 1-dimensional polyhedron in (Number Field in sqrt3 with defining polynomial x^10 + x^2 - 3)^2 defined as the convex hull of 1 vertex and 2 rays sage: P.rays() (A ray in the direction (0, -sqrt3), A ray in the direction (1, sqrt3))

This should be compared with:

sage: P = Polyhedron(lines=[(1, sqrt(3))]) sage: P A 1-dimensional polyhedron in (Symbolic Ring)^2 defined as the convex hull of 1 vertex and 1 line

and

sage: P = Polyhedron(lines=[(1, sqrt(3))], base_ring=AA) sage: P A 1-dimensional polyhedron in AA^2 defined as the convex hull of 1 vertex and 1 line

Additionally, how can a "1-dimensional polyhedron" be "defined as the convex hull of 1 vertex and 2 rays"?

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