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Resolves #47565 and #36534. nthroot() for complex variables implemented. #47860

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Resolves #47565 and #36534. nthroot() for complex variables implemented. #47860

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c241993
Wrote nthroot function for complex variables. Tries to resolve #47565…
theWiseAman Dec 10, 2022
2792f1e
Resolves #47565 and #36534. nthroot function implemented for complex …
theWiseAman Dec 11, 2022
a04fb5c
Build issues fixed and properly throwing complex domain error
theWiseAman Dec 11, 2022
e70a61b
Implementation of RootsVector for nthroot in progress.
theWiseAman Dec 12, 2022
0f4dfbd
RootsVector size() fixed
theWiseAman Dec 12, 2022
c3ad117
RootsVector generalised for both z::Real and z::Complex
theWiseAman Dec 13, 2022
a5d1178
Merge branch 'master' into theWiseAman/nthroot
theWiseAman Dec 15, 2022
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14 changes: 13 additions & 1 deletion base/complex.jl
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Original file line number Diff line number Diff line change
@@ -1,5 +1,4 @@
# This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Complex{T<:Real} <: Number

Expand Down Expand Up @@ -561,6 +560,19 @@ end
# return Complex(abs(iz)/r/2, copysign(r,iz))
# end

struct RootsVector{T<:Union{Real,Complex}} <: AbstractVector{T}
z::T
n::Int
option::Char
end
RootsVector(z::Complex, n::Int) = RootsVector(z, n, 'm')
RootsVector(z::Real, n::Int) = RootsVector(z, n, 's')

Base.size(S::RootsVector) = (S.option == 's') ? (1,) : ((S.option == 'm') && ((S.z != zero(S.z)) ? (typeof(S.z)<:Complex) ? (S.n,) : ((iseven(S.n) && (S.z > zero(S.z)) ? (2,) : (1,))) : (1,)))
Base.IndexStyle(S::RootsVector) = IndexLinear()
Base.getindex(S::RootsVector, i::Int) = (typeof(S.z)<:Complex) ? abs(S.z)^(1/S.n)*cis((angle(S.z)+2*pi*(i-1))/S.n) : (isodd(S.n) ? copysign(abs(S.z)^(1/S.n), S.z) : ((S.z > zero(S.z)) ? copysign(abs(S.z)^(1/S.n), (-1)^(i-1)) : NaN))
# Base.getindex(S::RootsVector, i::Int) = (isa(typeof(S.z), Complex)) ? abs(S.z)^(1/S.n)*cis((angle(S.z)+2*pi*(i-1))/S.n) : (isodd(S.n) ? copysign(abs(S.z)^(1/S.n), S.z) : ((S.z > zero(S.z)) ? copysign(abs(S.z)^(1/S.n), (-1)^(i-1)) : throw(DomainError(S.z, LazyString(:RootsVector," will only return a complex result if called with a complex argument. Try ", :RootsVector,"(Complex(x), n).")))))

"""
cis(x)

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2 changes: 2 additions & 0 deletions base/exports.jl
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Expand Up @@ -74,6 +74,7 @@ export
Regex,
RegexMatch,
Returns,
RootsVector,
RoundFromZero,
RoundDown,
RoundingMode,
Expand Down Expand Up @@ -349,6 +350,7 @@ export
sinh,
sinpi,
sqrt,
nthroot,
tan,
tand,
tanh,
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