#15463: Implement crystal morphisms, subcrystals, and virtual crystals
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: combinatorics | Resolution:
Keywords: crystals, | Merged in:
morphisms, subcrystals | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 5ee50cd5c9b2d8f6aa2d0fbced80c154f1884f25
public/combinat/crystals/crystal_morphisms| Stopgaps:
Dependencies: #15462 |
-------------------------------------+-------------------------------------
Comment (by tscrim):
Okay, so I've changed KR crystals to return honest crystal morphisms and
made `DirectSumOfCrystals` into a proper facade parent (when requested).
I've also changed `morphism()` to `crystal_morphism()` and moved the old
function to `kirillov_reshetikhin.py` in case we want to revive it. I also
added references to `virtual_crystal.py` and had `Subcrystal` redirect to
`VirtualCrystal` depending on parameters so we could have in the future a
more uniform interface with the `subcrystal()` method.
Here's some timing tests for KR crystals.
The test I ran:
{{{#!python
def test_KR(ct, r, s):
print "construction:"
%time B = KirillovReshetikhinCrystal(ct, r, s)
print "TestSuite:"
%time TestSuite(B).run()
print "Digraph:"
%time G = B.digraph()
}}}
With the branch:
{{{
sage: test_KR(['A',4,1], 3, 2)
construction:
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.04 s
TestSuite:
CPU times: user 2.61 s, sys: 0.09 s, total: 2.70 s
Wall time: 3.21 s
Digraph:
CPU times: user 0.23 s, sys: 0.01 s, total: 0.24 s
Wall time: 0.26 s
sage: test_KR(['D',4,1], 2, 1)
construction:
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
TestSuite:
CPU times: user 2.07 s, sys: 0.00 s, total: 2.08 s
Wall time: 2.33 s
Digraph:
CPU times: user 0.23 s, sys: 0.01 s, total: 0.24 s
Wall time: 0.27 s
sage: test_KR(['E',6,1], 1, 1)
construction:
CPU times: user 0.19 s, sys: 0.00 s, total: 0.19 s
Wall time: 0.31 s
TestSuite:
CPU times: user 0.57 s, sys: 0.00 s, total: 0.57 s
Wall time: 0.70 s
Digraph:
CPU times: user 0.12 s, sys: 0.02 s, total: 0.14 s
Wall time: 0.16 s
sage: test_KR(['A',6,2], 2, 1)
construction:
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.02 s
TestSuite:
CPU times: user 2.23 s, sys: 0.01 s, total: 2.24 s
Wall time: 2.71 s
Digraph:
CPU times: user 0.24 s, sys: 0.00 s, total: 0.24 s
Wall time: 0.27 s
sage: test_KR(['D',4,2], 2, 1)
construction:
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
TestSuite:
CPU times: user 2.91 s, sys: 0.02 s, total: 2.92 s
Wall time: 3.36 s
Digraph:
CPU times: user 0.27 s, sys: 0.01 s, total: 0.28 s
Wall time: 0.38 s
sage: K = KirillovReshetikhinCrystal(['D',4,1], 2,2)
sage: %time TestSuite(K).run()
CPU times: user 58.50 s, sys: 0.10 s, total: 58.60 s
Wall time: 70.46 s
}}}
Develop:
{{{
sage: test_KR(['A',4,1], 3, 2)
construction:
CPU times: user 0.04 s, sys: 0.00 s, total: 0.04 s
Wall time: 0.18 s
TestSuite:
CPU times: user 2.59 s, sys: 0.06 s, total: 2.65 s
Wall time: 3.97 s
Digraph:
CPU times: user 0.23 s, sys: 0.01 s, total: 0.24 s
Wall time: 0.33 s
sage: test_KR(['D',4,1], 2, 1)
construction:
CPU times: user 0.01 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.07 s
TestSuite:
CPU times: user 0.52 s, sys: 0.02 s, total: 0.54 s
Wall time: 0.75 s
Digraph:
CPU times: user 0.10 s, sys: 0.00 s, total: 0.10 s
Wall time: 0.12 s
sage: test_KR(['E',6,1], 1, 1)
construction:
CPU times: user 0.01 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.07 s
TestSuite:
CPU times: user 0.45 s, sys: 0.00 s, total: 0.45 s
Wall time: 0.58 s
Digraph:
CPU times: user 0.10 s, sys: 0.01 s, total: 0.11 s
Wall time: 0.12 s
sage: test_KR(['A',6,2], 2, 1)
construction:
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.09 s
TestSuite:
CPU times: user 0.64 s, sys: 0.02 s, total: 0.65 s
Wall time: 0.86 s
Digraph:
CPU times: user 0.21 s, sys: 0.00 s, total: 0.21 s
Wall time: 0.28 s
sage: test_KR(['D',4,2], 2, 1)
construction:
CPU times: user 0.00 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
TestSuite:
CPU times: user 0.38 s, sys: 0.01 s, total: 0.39 s
Wall time: 0.50 s
Digraph:
CPU times: user 0.12 s, sys: 0.01 s, total: 0.13 s
Wall time: 0.28 s
sage: K = KirillovReshetikhinCrystal(['D',4,1], 2,2)
sage: %time TestSuite(K).run()
CPU times: user 5.30 s, sys: 0.02 s, total: 5.32 s
Wall time: 6.30 s
}}}
So there's a major speed penality with using promotion as a crystal
morphism directly. My guess is caused from the fact we are no longer
caching things. On develop we have:
{{{
sage: K = KirillovReshetikhinCrystal(['D',4,1], 2,2)
sage: K.promotion()
Cached version of <function morphism at 0xc77133c>
}}}
So I have a the following questions:
1 - The code and the documentation for the old `crystal_morphism()` did
not match as the default was to not cache (i.e. `cache = False` but the
code did return a cached function when the `cache` argument was `False`.
Do we want to cache the output of the promotion (or something else that's
related)?
2 - Do we want to use honest crystal morphisms or use the old function
returned from the old `crystal_morphism()`?
3 - Do we want to have an option to cache the output of a crystal
morphism, or morphisms in general?
--
Ticket URL: <http://trac.sagemath.org/ticket/15463#comment:10>
Sage <http://www.sagemath.org>
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