#10783: Implement dynamic posets
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Reporter: novoselt | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone:
Component: combinatorics | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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The idea is to allow creation of a poset without specifying all of its
elements but instead allow adding them later. Example: one creates a cone
and this cone becomes the top element of its face lattice, but the whole
lattice and its elements are not constructed until (and IF) it is
necessary.
Ticket #10777 is relevant.
I am personally interested only in such lattices and cone lattice of (not
necessarily complete) fans, in particular these posets are finite and they
are atomistic lattices. But for the implementation, perhaps, the only
convenient limitation is finiteness. Or maybe even this is not important:
if we don't construct all element, who cares how many are there?
The constructor probably has to have only one mandatory parameter: some
callable that can compare elements of this poset. Perhaps one can also
specify a callable for checking cover relations.
For elements it would be nice to compute their neighbours up/above/next
to, even if they are not constructed yet. If this it too difficult, there
may be a flag in the poset `has_all_elements` or something like this so
that functions that do require all elements can check if they are present
or not.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10783>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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