#3354: Bug in power series sqrt
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Reporter: robertwb | Owner: somebody
Type: defect | Status: needs_work
Priority: major | Milestone: sage-7.0
Component: commutative algebra | Resolution:
Keywords: power series | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by rws):
* status: needs_info => needs_work
* component: basic arithmetic => commutative algebra
Old description:
> {{{
> sage: t = QQ[['t']].0
> sage: sqrt(1+t)
> 1 + 1/2*t - 1/8*t^2 + 1/16*t^3 - 5/128*t^4 + 7/256*t^5 - 21/1024*t^6 +
> 33/2048*t^7 - 429/32768*t^8 + 715/65536*t^9 - 2431/262144*t^10 +
> 4199/524288*t^11 - 29393/4194304*t^12 + 52003/8388608*t^13 -
> 185725/33554432*t^14 + 334305/67108864*t^15 - 9694845/2147483648*t^16 +
> 17678835/4294967296*t^17 - 64822395/17179869184*t^18 +
> 119409675/34359738368*t^19 + O(t^20)
> sage: sqrt(2+t)
> ------------------------------------------------------------
> Traceback (most recent call last):
> File "<ipython console>", line 1, in <module>
> File "/Users/robert/sage/current/local/lib/python2.5/site-
> packages/sage/calculus/calculus.py", line 7664, in __call__
> return x.sqrt(*args, **kwds)
> File "power_series_ring_element.pyx", line 1120, in
> sage.rings.power_series_ring_element.PowerSeries.sqrt
> (sage/rings/power_series_ring_element.c:7887)
> <type 'exceptions.ValueError'>: power series does not have a square root
> since it has odd valuation.
> }}}
>
> Perhaps the error is just bad, but it should be able to compute this by
> extending to a field with sqrt(2).
New description:
{{{
sage: t = QQ[['t']].0
sage: sqrt(1+t)
1 + 1/2*t - 1/8*t^2 + 1/16*t^3 - 5/128*t^4 + 7/256*t^5 - 21/1024*t^6 +
33/2048*t^7 - 429/32768*t^8 + 715/65536*t^9 - 2431/262144*t^10 +
4199/524288*t^11 - 29393/4194304*t^12 + 52003/8388608*t^13 -
185725/33554432*t^14 + 334305/67108864*t^15 - 9694845/2147483648*t^16 +
17678835/4294967296*t^17 - 64822395/17179869184*t^18 +
119409675/34359738368*t^19 + O(t^20)
sage: sqrt(2+t)
------------------------------------------------------------
Traceback (most recent call last):
}}}
Now this error is expected because `sqrt()` has an `extend` keyword that
allows to extend the base ring, and to give the name of the generator of
the quadratic field, but this does not work:
{{{
sage: K.<t> = PowerSeriesRing(QQ, 5)
sage: (t+2).sqrt(extend=True, name='sqrt2')
sqrt2
}}}
The expected output would be `sqrt2 + sqrt2*x/4 + sqrt2*x^2/32 +...`
However, more convenient would be to make the default of `extend` to be
`True` and for square roots of integers `N` the name `sqrtN` provided.
Only raise an error for nonintegers if no name is given.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/3354#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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