#12179: Binomial of integer (mod n) returns integer
--------------------------------+-------------------------------------------
Reporter: scotts | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.8
Component: basic arithmetic | Keywords: binomial coefficiant, modulo
Work_issues: | Upstream: N/A
Reviewer: | Author: Sam Scott
Merged: | Dependencies:
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Changes (by johanbosman):
* status: positive_review => needs_work
Comment:
The line
{{{
Test of integers modulo n:
}}{
should end in two colons (for docbuilding). Furthermore,
{{{
return x.parent()(binomial(ZZ(x), m, **kwds))
}}}
is inefficient when computing modulo a small number n: the binomial
coefficient over ZZ may be huge, whereas its reduction modulo n will be
small. It is therefore better to to the entire calculation modulo n.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12179#comment:5>
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