#16671: implement harmonic number function H(n,m)
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Reporter: rws | Owner:
Type: | Status: needs_work
defect | Milestone: sage-6.4
Priority: major | Resolution:
Component: | Merged in:
symbolics | Reviewers:
Keywords: | Work issues:
special, log | Commit:
Authors: Ralf | fabf86397adf8c07ce9b63b64c64e5f724702d21
Stephan | Stopgaps:
Report Upstream: N/A |
Branch: |
u/rws/16671 |
Dependencies: |
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Comment (by rws):
Replying to [comment:47 jdemeyer]:
> Artificial example (this could be a doctest):
> {{{
> sage: harmonic_number._eval_(10, Qp(5)(1))
> 7381/2520
> }}}
> but the answer should be
> {{{
> sage: Qp(5)(harmonic_number(10))
> 4*5^-1 + 2 + 2*5 + 4*5^2 + 3*5^3 + 5^4 + 4*5^5 + 4*5^6 + 5^7 + 4*5^8 +
3*5^9 + 5^10 + 4*5^11 + 4*5^12 + 5^13 + 4*5^14 + 3*5^15 + 5^16 + 4*5^17 +
4*5^18 + O(5^19)
> }}}
I think this is the only example where `H(n,m)` would have a useful
meaning, and it can be computed, as you show, by staying in the rationals
and converting the result. Trying to support this case however will fail
in `BuiltinFunction.__call__`:
{{{
sage: harmonic_number(5,Qp(5)(8))
Traceback (most recent call last):
File "<ipython-input-9-03dbaa59749c>", line 1, in <module>
harmonic_number(Integer(5),Qp(Integer(5))(Integer(8)))
File "/home/ralf/sage/local/lib/python2.7/site-
packages/sage/functions/log.py", line 886, in __call__
return BuiltinFunction.__call__(self, z, m, **kwds)
File "sage/symbolic/function.pyx", line 993, in
sage.symbolic.function.BuiltinFunction.__call__
(build/cythonized/sage/symbolic/function.cpp:10572)
res = super(BuiltinFunction, self).__call__(
File "sage/symbolic/function.pyx", line 487, in
sage.symbolic.function.Function.__call__
(build/cythonized/sage/symbolic/function.cpp:6301)
raise TypeError, "cannot coerce arguments: %s"%(err)
TypeError: cannot coerce arguments: no canonical coercion from 5-adic
Field with capped relative precision 20 to Symbolic Ring
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16671#comment:54>
Sage <http://www.sagemath.org>
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