abs2 incorrectly defined for Taylor{Complex{T}} about taylorseries.jl HOT 4 CLOSED

Yes, I can prepare a PR in the coming days.

from taylorseries.jl.

I will check a few more complex related functions, e.g. angle seems also not defined.

from taylorseries.jl.

Thanks for reporting, and good catch! Yes, I think you are right and your proposed solution is correct.

Could you open a PR with your solution and perhaps some tests? I guess a good test could be (using your definition of t):

abs2(exp(im*t)) == 1.0

from taylorseries.jl.

Excelent! Thanks a lot!

I also noticed that there are more brittle peaces around... As an example,

julia> tim = im*Taylor1(16)
 ( 0.0 + 1.0im ) t + 𝒪(t¹⁷)

julia> isapprox( abs2(exp(tim)), 1.0)
ERROR: DomainError with  4.336808689942018e-19 t⁸ - 2.710505431213761e-20 t¹⁰ + 𝒪(t¹⁶):
The 0th order Taylor1 coefficient must be non-zero
(abs(x) is not differentiable at x=0).
Stacktrace:
 [1] abs
   @ ~/.julia/dev/TaylorSeries/src/other_functions.jl:86 [inlined]
 [2] isapprox(x::Taylor1{Float64}, y::Float64; atol::Int64, rtol::Float64, nans::Bool, norm::typeof(abs))
   @ Base ./floatfuncs.jl:281
 [3] isapprox(x::Taylor1{Float64}, y::Float64)
   @ Base ./floatfuncs.jl:281
 [4] top-level scope
   @ REPL[32]:1

It seems that norm, which is used in isapprox, defaults to abs, which is not defined for Taylor1{<:Complex}...

from taylorseries.jl.