Opened 8 years ago

Last modified 3 years ago

#17197 needs_work defect

Bug creating Polyhedron from lines in number field — at Version 6

Reported by: Mark Bell Owned by:
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:

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Description (last modified by Mark Bell)

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"?


As pointed out below this is an issue with Polyhedron using a number fields < comparison

sage: K.<x> = NumberField(x^3 - 1001, embedding=10)
sage: x > x + 1
True

Change History (6)

comment:1 Changed 8 years ago by Volker Braun

With 6.4.beta6 I get

sage: Polyhedron(lines=[(1,sqrt3)])
A 1-dimensional polyhedron in (Number Field in sqrt3 with defining polynomial x^2 - 3)^2 defined as the convex hull of 1 vertex and 1 line

comment:2 Changed 8 years ago by Volker Braun

Though the original example fails:

sage: K.<L> = NumberField(x^3 + 3*x^2 - 83*x - 1022, embedding=11.6515)
sage: Polyhedron(eqns=[[0, -L - 2, -8, 2], [0, -2, -L + 6, 9], [0, -9, 5, -L - 7]])
A 3-dimensional polyhedron in (Number Field in L with defining polynomial x^3 + 3*x^2 - 83*x - 1022)^3 defined as the convex hull of 1 vertex, 2 rays, 1 line

Slightly simpler failure:

sage: Polyhedron(eqns=[[0, -L - 2, -8], [0, -2, -L + 6], [0, -9, 5]])
A 2-dimensional polyhedron in (Number Field in L with defining polynomial x^3 + 3*x^2 - 83*x - 1022)^2 defined as the convex hull of 1 vertex and 2 rays
Last edited 8 years ago by Volker Braun (previous) (diff)

comment:3 Changed 8 years ago by Volker Braun

This originates at the following comparison:

sage: v = -1/392*L^2 - 45/392*L - 239/392
sage: v > 0
True
sage: v.n()
-2.29356924372991

comment:4 in reply to:  3 Changed 8 years ago by Mark Bell

Thanks for tracking this down. Should I file a separate ticket for this under the number theory?

comment:5 Changed 8 years ago by Volker Braun

You can just change the description and use this ticket. I think we agree that this is not a bug in polyhedra. See also the discussion on sage-devel.

comment:6 Changed 8 years ago by Mark Bell

Component: geometrynumber theory
Description: modified (diff)
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