On 21/12/2017 17:07, Nils Bruin wrote:
On Thursday, December 21, 2017 at 3:19:57 AM UTC-8, vdelecroix wrote:
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])
As long as this only affects the behaviour when "extend=True" is specified
I don't mind. I am very attached to
R.<x> = QQ[[]]
f = 1+x
parent(f.sqrt()) == parent(f)
so I wouldn't want that to break, or at least have an alternative for it.
This will definitely not change. The behavior will change for series
whose term of lower degree has no square root in the base ring such as
2+x or x+x^2 or 2x+x^2. And the intended behavior are respectively
sage: f = 2 + x
sage: f.sqrt()
ERROR
With the same for the other examples. For them, the alternative would be
something like
sage: (2 + x).sqrt(extend=True)
power series in x with coeffs in QQ[sqrt(2)]
sage: (x + x^2).sqrt(extend=True)
Puiseux series in x^(1/2) and coeffs in QQ
sage: (2x + x^2).sqrt(extend=True)
Puiseux series in (2x)^(1/2) and coeffs in QQ
Vincent
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