sqrt at zero about taylorseries.jl HOT 2 CLOSED

Thanks for reaching out and for your question! I'm not sure the following answers the question, so I'll try to guide you through the code, and indicate where you can modify something.

sqrt(::Taylor1) executes this line. The first code block checks where the first non-zero coefficient of the Taylor1 polynomial is located; that is actually where the error is thrown, since for t=Taylor1(5) the first non-zero coefficient in this case is odd. The reason to distinguish odd and even first non-zero coefficients is, essentially, to be able to factor an expression of the form $\sqrt{t^{2n}* p(t)} = t^n*\sqrt{p(t)}$, with $p(t)$ a polynomial with non-zero 0-th order coefficient.

The next code block computes order by order the Taylor expansion. It uses sqrt! to update (modify in place) the Taylor coefficient of order k of c, which is the returned result. sqrt! is coded here, and you can check the docstrings here or in the REPL (? TaylorSeries.sqrt!). The function essentially implements the relevant formula (which does not appear properly displayed as it should in the documentation).

Let me point out that sqrt! throws no error, that sqrt(::Taylor1) computes the 0-th order coefficient separatelly, and that the rest of the coefficients are computed using sqrt!. So, if you want to code your own mysqrt, you should perhaps compute the Taylor expansion using sqrt! directly, including the first non-zero coefficient. Be aware that Infs and NaNs may propagate in the series, because the computation is recursive. This means that mysqrt(t) may return something like Inf t - Inf t² + Inf t³ - Inf t⁴ + Inf t⁵ + 𝒪(t⁶).

I hope this is useful for your application.

from taylorseries.jl.

Closing. Feel free to reopen this issue if you want further explanations..

from taylorseries.jl.