Multivariate Taylor expansion with HypergeometricFunctions

[Li-shiyue]

using TaylorSeries
using HypergeometricFunctions
function bbb(params)
x,y = params
return _₁F₁(2,3,x+0.5*y-1)
end
x, y = set_variables("x y", order=8)
bbb([x,y])
ERROR: MethodError: no method matching AbstractFloat(::TaylorN{Float64})

Closest candidates are:
(::Type{T})(::T) where T<:Number
@ Core boot.jl:792
(::Type{T})(::AbstractChar) where T<:Union{AbstractChar, Number}
@ Base char.jl:50
(::Type{T})(::Base.TwicePrecision) where T<:Number
@ Base twiceprecision.jl:266
...

Can anybody tell me how to solve it?

[lbenet]

This one is more complicated. So I'll explain you where I am.

julia> using TaylorSeries, HypergeometricFunctions

julia> x, y = set_variables("x y", order=8);

julia> Base.float(t::HomogeneousPolynomial) = HomogeneousPolynomial(float.(t.coeffs))

julia> Base.float(t::TaylorN) = TaylorN(float.(t.coeffs), t.order)

julia> TaylorSeries.TaylorN{T}(a::S) where {T,S} = (R=promote_type(T,S); TaylorN(R(a), get_order()))

julia> Base.eps(::Type{TaylorN{T}}) where {T} = eps(one(T))

julia> Base.eps(a::TaylorN) = eps(constant_term(a))

julia> _₁F₁(2,3,x+0.5*y-1)
 0.5284822353142297 + 0.32120558828564066 x + 0.16060279414282033 y + 0.11392894125311108 x² + 0.11392894125613448 x y + 0.02848223531327777 y² + 0.029278774897663628 x³ + 0.0439181620949485 x² y + 0.02195908104747425 x y² + 0.0036598468622079535 y³ + 0.005941825591207862 x⁴ + 0.01188368338042503 x³ y + 0.008912756962586393 x² y² + 0.0029709208451062577 x y³ + 0.00037136409945049136 y⁴ + 0.0010004169168939174 x⁵ + 0.002497931469181667 x⁴ y + 0.0024982484957348523 x³ y² + 0.0012491242478674261 x² y³ + 0.00031226124780728244 x y⁴ + 3.126302865293492e-5 y⁵ + 6.657557616881685e-5 x⁶ + 0.0003943810321619436 x⁵ y + 0.0005199235472231411 x⁴ y² + 0.0003170265531848421 x³ y³ + 0.00012617656816756717 x² y⁴ + 2.3222195020789684e-5 x y⁵ + 1.0402433776377632e-6 y⁶ + 0.00295215126325725 x⁷ + 0.0015420171546910721 x⁶ y - 0.0016231759523063917 x⁵ y² + 0.0007304291785378762 x⁴ y³ + 0.0006695600803263865 x³ y⁴ + 5.072424850957474e-5 x² y⁵ + 9.891228459367074e-5 x y⁶ + 2.3063681744197264e-5 y⁷ - 0.08602832547223875 x⁸ - 0.0389562228553534 x⁷ y + 0.17790008437278051 x⁶ y² + 0.11816720932790531 x⁵ y³ + 0.01753030028490903 x⁴ y⁴ + 0.00941442052337707 x³ y⁵ + 0.002597081523690227 x² y⁶ - 0.0018159280966427757 x y⁷ - 0.0003360481463759326 y⁸ + 𝒪(‖x‖⁹)

Please check if this should be the expected output.

[Li-shiyue]

It doesn't work
function tele_gf111(params,t,z)
a,b = params
pfq1 = HypergeometricFunctions.pFq((1+a,), (b,),t*(z-1))
pfq2 = HypergeometricFunctions.pFq((a+b,), (b,), t*(z-1))
return pfq1+pfq2
end
x, y = set_variables("x y",order=8)
Base.float(t::HomogeneousPolynomial) = HomogeneousPolynomial(float.(t.coeffs))
Base.float(t::TaylorN) = TaylorN(float.(t.coeffs), t.order)
TaylorSeries.TaylorN{T}(a::S) where {T,S} = (R=promote_type(T,S); TaylorN(R(a), get_order()))
Base.eps(::Type{TaylorN{T}}) where {T} = eps(one(T))
Base.eps(a::TaylorN) = eps(constant_term(a))
@time taylor_cof = tele_gf111([2,2],x,y)
ERROR: MethodError: no method matching iterate(::Type{HypergeometricFunctions.ℕ})

Closest candidates are:
iterate(::Union{LinRange, StepRangeLen})
@ Base range.jl:880
iterate(::Union{LinRange, StepRangeLen}, ::Integer)
@ Base range.jl:880
iterate(::T) where T<:Union{Base.KeySet{<:Any, <:Dict}, Base.ValueIterator{<:Dict}}
@ Base dict.jl:698
...

[lbenet]

One single hint: copy-pasting my code above, and including the following, shows the problem:

julia> a = 2
2

julia> b = 2
2

julia> pfq1 = HypergeometricFunctions.pFq((1+a,), (b,),x*(y-1))
ERROR: AssertionError: !(iszero(constant_term(b)))
Stacktrace:
  [1] /(a::TaylorN{Float64}, b::TaylorN{Float64})
    @ TaylorSeries ~/.julia/dev/TaylorSeries/src/arithmetic.jl:662

You cannot divide two TaylorN objects, when the denominator contains a zero constant term.

[Li-shiyue]

function tele_gf111(params,t,z)
a,b = params
pfq1 = HypergeometricFunctions.pFq((1+a,), (a,),t+b*(z-1))
pfq2 = HypergeometricFunctions.pFq((a+b,), (a,), t+b*(z-1))
return pfq1+pfq2
end
x, y = set_variables("x y",order=8)
Base.float(t::HomogeneousPolynomial) = HomogeneousPolynomial(float.(t.coeffs))
Base.float(t::TaylorN) = TaylorN(float.(t.coeffs), t.order)
TaylorSeries.TaylorN{T}(a::S) where {T,S} = (R=promote_type(T,S); TaylorN(R(a), get_order()))
Base.eps(::Type{TaylorN{T}}) where {T} = eps(one(T))
Base.eps(a::TaylorN) = eps(constant_term(a))
@time taylor_cof = tele_gf111([21,4],x,y)

This works fine for me,!!!!!

However,here is a little change,When I seperate TaylorN,so I define:
function tele_gf111(params,t,z)
a,b = params
pfq1 = HypergeometricFunctions.pFq((1+a,), (a,),t+b*(z-1))
pfq2 = HypergeometricFunctions.pFq((a+t,), (a,), t+b*(z-1))
return pfq1+pfq2
end
or
function tele_gf111(params,t,z)
a,b = params
pfq1 = HypergeometricFunctions.pFq((1+a,), (a,),t+b*(z-1))
pfq2 = HypergeometricFunctions.pFq((t+z-1,), (a,), t+b*(z-1))
return pfq1+pfq2
end
Then I get error:
ERROR: MethodError: no method matching iterate(::Type{HypergeometricFunctions.ℕ₀})

Closest candidates are:
iterate(!Matched::Union{LinRange, StepRangeLen})
@ Base range.jl:880
iterate(!Matched::Union{LinRange, StepRangeLen}, !Matched::Integer)
@ Base range.jl:880
iterate(!Matched::T) where T<:Union{Base.KeySet{<:Any, <:Dict}, Base.ValueIterator{<:Dict}}
@ Base dict.jl:698
...
I am interesting about get the Series when TaylorN is seperated

[Li-shiyue]

I divide two TaylorN while the denominator doesn't contain a zero constant term.but get the error,I don't know how to solve it
x, y = set_variables("x y", order=8)
Base.float(t::HomogeneousPolynomial) = HomogeneousPolynomial(float.(t.coeffs))
Base.float(t::TaylorN) = TaylorN(float.(t.coeffs), t.order)
TaylorSeries.TaylorN{T}(a::S) where {T,S} = (R=promote_type(T,S); TaylorN(R(a), get_order()))
Base.eps(::Type{TaylorN{T}}) where {T} = eps(one(T))
Base.eps(a::TaylorN) = eps(constant_term(a))
HypergeometricFunctions.pFq((x,),(2,),x+y)pFq((2,),(4,),x+0.5y)
ERROR: MethodError: no method matching iterate(::Type{HypergeometricFunctions.ℕ₀})

Closest candidates are:
iterate(!Matched::Union{LinRange, StepRangeLen})
@ Base range.jl:880
iterate(!Matched::Union{LinRange, StepRangeLen}, !Matched::Integer)
@ Base range.jl:880
iterate(!Matched::T) where T<:Union{Base.KeySet{<:Any, <:Dict}, Base.ValueIterator{<:Dict}}
@ Base dict.jl:698
...

[Li-shiyue]

Is there anyone to help? Thanks.