#13199: Use FLINT to compute the partition function
-------------------------------------+--------------------------------------
Reporter: fredrik.johansson | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.4
Component: combinatorics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: Andrew Mathas
Authors: Fredrik Johansson | Merged in:
Dependencies: #12173 | Stopgaps:
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Changes (by andrew.mathas):
* reviewer: => Andrew Mathas
Comment:
I am happy to review this, although it is not clear to me what the status
of #12173 is and until this patch is merged it seems rather cumbersome to
load the current patch on top of #12173 in order play around with this
patch and check to see that it actually works.
Assuming that it is OK, I would like to see some more explicit tests
inside the new number_of_partitions to show that it is working. I'd
suggest simply reusing the ones that are in
sage.combinat.partition.number_of_partitions. That is, adding the
following tests to the doc-string for your number_of_partitions:
{{{
sage: from sage.combinat.partitions import number_of_partitions
sage: number_of_partitions(3)
3
sage: number_of_partitions(10)
42
sage: number_of_partitions(40)
37338
sage: number_of_partitions(100)
190569292
sage: number_of_partitions(100000)
27493510569775696512677516320986352688173429315980054758203125984302147328114964173055050741660736621590157844774296248940493063070200461792764493033510116079342457190155718943509725312466108452006369558934464248716828789832182345009262853831404597021307130674510624419227311238999702284408609370935531629697851569569892196108480158600569421098519
TESTS::
sage: n = 500 + randint(0,500)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 1500 + randint(0,1500)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 1000000 + randint(0,1000000)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 1000000 + randint(0,1000000)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 1000000 + randint(0,1000000)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 1000000 + randint(0,1000000)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 1000000 + randint(0,1000000)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 1000000 + randint(0,1000000)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0
True
sage: n = 100000000 + randint(0,100000000)
sage: number_of_partitions( n - (n % 385) + 369) % 385 == 0 #
long time (4s on sage.math, 2011)
True
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13199#comment:2>
Sage <http://www.sagemath.org>
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