#14789: Implement hyperplane arrangements
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Reporter: kcrisman | Owner: sage-combinat
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-5.13
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:34 vbraun]:
> {{{
> sage: arrangement = (x + 2*y + 3*z - 4) and (y - 7) and (x + z)
> sage: arrangement == x + 2*y + 3*z - 4 and y - 7 and x + z #
brackets are optional
> True
> }}}
> If nobody objects then I'll work on that since I kind of need hyperplane
arrangements now...
Don't use "and". It explicitly has shortcutting behaviour specified on it:
{{{
sage: 1 and 2
2
sage: a = 1; b = 2
sage: b if a else a #it's specified to do this
2
}}}
so departing from this behaviour would be very surprising.
The operator possibly available would be the "bitwise" `&`, but I doubt
you want to repurpose it for union.? Being smart with overloading
operators often comes back to bite you (see `%` for string formatting in
python).
Also, since these are hyperplanes given by equations describing them,
`and` could easily be interpreted as ''intersection''. That's the most
direct interpretation coming from the boolean meaning of the operator in
sage.
Multiplication would come closer if you think about the arrangement as a
union of hyperplanes. Do you keep multiplicities?
If you think of the hyperplane arrangement as a collection of hyperplanes,
then they should probably be modelled as a set of hyperplanes, and python
does not overload any binary operation to take unions of sets.
--
Ticket URL: <http://trac.sagemath.org/ticket/14789#comment:37>
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