Dear all,
I might introduce a non backward incompatible change for square root
(and more generally n-th roots) of power series.
While working on [1] I stumbled on a weird implementation of square root
for power series [2]. Namely, when extend=True it might just return a
formal element p so that p^2 is the initial series (example at [3])
sage: K.<t> = PowerSeriesRing(QQ, 5)
sage: f = 2*t + t^3 + O(t^4)
sage: s = f.sqrt(extend=True, name='sqrtf'); s
sqrtf
sage: s^2
2*t + t^3 + O(t^4)
A much more meaningful answer is to return a Puiseux series in t^(1/2)
which is the natural algebraic closure of power series (at least in
characteristic zero). Of course, I am aware that Puiseux series are not
yet there... and this is one of our oldest open ticket [4].
Anybody disagree?
[1] https://trac.sagemath.org/ticket/10720
[2]
https://github.com/sagemath/sagetrac-mirror/blob/master/src/sage/rings/power_series_ring_element.pyx#L1186
[3]
https://github.com/sagemath/sagetrac-mirror/blob/master/src/sage/rings/power_series_ring_element.pyx#L1253
[4] https://trac.sagemath.org/ticket/4618
Vincent
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