Bug in power series sqrt

[robertwb]

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.

Component: commutative algebra

Keywords: power series

Issue created by migration from https://trac.sagemath.org/ticket/3354

[jasongrout]

comment:1

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?

[fchapoton]

Changed keywords from none to power series

[mezzarobba]

comment:7

Message fixed in #6998.