#17197: document Polyhedron defined over number field
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Reporter: mbell | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-7.3
Component: number theory | Resolution:
Keywords: Polyhedron, Number field | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by vdelecroix:
Old 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"?
>
> --------------------------------------------
>
> 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
> }}}
New description:
As reported in this google group (https://groups.google.com/forum/#!topic
/sage-support/ew0bnGzjm98), it was not possible to create Polyhedron
defined over number fields. Now that #17830 is merged it does work and it
should be documented and even advertised in the documentation!
---------
from the previous report:
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
}}}
--
--
Ticket URL: <https://trac.sagemath.org/ticket/17197#comment:10>
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