# Ticket #3354(new defect)

Opened 5 years ago

## Bug in power series sqrt

Reported by: Owned by: robertwb somebody major sage-5.10 basic arithmetic

### 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).

## Change History

### comment:1 Changed 5 years ago by jason

Related:

```[00:12] <jason--> sage: t = QQ[['t']].0
[00:12] <jason--> sage: 1/(1-t)
[00:12] <jason--> 1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^18 + t^19 + O(t^20)
[00:12] <jason--> but log(1+t) doesn't work, for example
[00:12] <jason--> should it?
[00:12] <craigcitro> in principle, yes. :)
[00:13] <craigcitro> see if (1+t) has a log method ...
[00:13] <jason--> and sin(t), cos(t), etc.
[00:13] <jason--> so maybe a fallback method that calls for a taylor series?
```
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