For completeness, here is the definition I ended up using (probably using map
is bad performance wise but I don’t actually use that yet):
sqrtx2(z::Complex)=sqrt(z-1).*sqrt(z+1)
sqrtx2(x::Real)=sign(x)*sqrt(x^2-1)
sqrtx2(x::Vector)=map(sqrtx2,x)
function sqrtx2(f::Fun)
B=Evaluation(first(domain(f)))
A=Derivative()-f*differentiate(f)/(f^2-1)
linsolve([B,A],sqrtx2(first(f));tolerance=length(f)*10E-15)
end
> On 13 Feb 2015, at 3:11 pm, Sheehan Olver <[email protected]> wrote:
>
> thanks! Will take a look.
>
> For my own case I realized I could avoid the issue by solving the ODE
> it satisfies using ApproxFun:
>
> u’ - u*z/(z^2-1)
>
> with a boundary condition using the pointwise definition.
>
>
>
>
>
>> On 13 Feb 2015, at 2:52 pm, Jiahao Chen <[email protected]
>> <mailto:[email protected]>> wrote:
>>
>> I haven't looked at this issue, but perhaps the algorithm of Dingle and
>> Fateman ("Branch Cuts in Computer Algebra") may be helpful for detecting
>> removable branch cuts.
>>
>> Thanks,
>>
>> Jiahao Chen
>> Staff Research Scientist
>> MIT Computer Science and Artificial Intelligence Laboratory
>>
>> On Thu, Feb 12, 2015 at 10:05 PM, Sheehan Olver <[email protected]
>> <mailto:[email protected]>> wrote:
>>
>> For z < -1 the branch cuts cancel and the function should be equivalent to
>> -sqrt(z^2-1) (the only non-removeable branch cut is along [-1,1]), but in
>> Julia it is not defined. I'm wondering if there is a special function in
>> Julia that can take care of this, or is the only solution to write my own
>> (with special handlers for Arrays, etc.)?
>>
>>
>>
>>
>
