#16281: redesign projective plane
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: combinatorics | Resolution:
Keywords: design, | Merged in:
projective plane | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | 3e5628a2be9e09a15962dafba7a235d72b222888
u/vdelecroix/16281 | Stopgaps:
Dependencies: |
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Comment (by vdelecroix):
Three because of the definition I know... quotient out `K^3 \ {0}` by the
positive scalar acting by multiplication. Then, you can manage to
decompose into plane+line+point.
How about a HUGE comment as follows
{{{
# we decompose the points (x:y:z) of the projective space into an affine
# plane, an affine line and a point. At the same time, we relabel the
points
# with the integers from 0 to n^2 + n. It is done as follows:
# the affine plane is the set of points (x:y:1) and gets relabeled
# from 0 to n^2-1
affine_plane = lambda x,y: relabel[x] + n * relabel[y]
# the affine line is the set of points (x:1:0)
# and gets relabeld from n^2 to n^2 + n - 1
line_infinity = lambda x: n2 + relabel[x]
# the point is (1:0:0)
# and gets relabeld n^2 + n
point_infinity = n2 + n
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/16281#comment:21>
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