# computing the square root of a polynomial with variable coefficients [closed]

I am new to sage and programming in general. I want to compute the power series representation of the square root of a polynomial with variable coefficients. Here is my attempt:

i,z=var('i,z') c=function('c') p=sum(c(i)*z^i,i,0,6) sqrt(p)

This returns

sqrt(z^6c(6) + z^5c(5) + z^4c(4) + z^3c(3) + z^2c(2) + zc(1) + c(0)).

How can I get sage to return a power series expression?

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### Closed for the following reason duplicate question by vdelecroix close date 2017-12-08 15:10:56.707473

is really hard to describe in sage terminology.
I supposed the other question wants some / any symbolic expression, and these one only a power series result. I would start to give an answer only in case there is also a precise question specifying the point to develop around, that it is the variable z to be used, the ring to work in, etc. (My answer to the other question was trying to make a bridge between the worlds, it was immediately explicitly rejected, so i will also wait for precision in such cases.)