#19279: IncidenceStructure.is_generalized_quadrangle
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/19279 | c26038e543830f388cdceafb139d33e5f28359cd
Dependencies: #19277 | Stopgaps:
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Comment (by dimpase):
you might want to check out the definition (7.4.1 p.323) of polar space
here:
https://drive.google.com/file/d/0B92yb82dH00zM1lNc1Y1eGVHZDQ/view?usp=sharing
that I keep in mind, instead of the wikipedia one:
A line space (P,L) is a polar space if, for each point p ∈ P and
each line l ∈ L, the set of points of l which are collinear with p, is
either a singleton
or l.
They keep on mentioning GQs immediately after this definition, in Example
7.4.2:
Each projective space is a polar space in which, for each point p
and each line l, the set of points of l collinear with p, coincides with
l. At the other
extreme, a generalized quadrangle is a polar space in which, for each
point p and
each line l not on p, the set of points of l collinear with p, is a
singleton.
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Ticket URL: <http://trac.sagemath.org/ticket/19279#comment:15>
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