Conversion to julia expressions

[BeastyBlacksmith]

Being able to convert WExprs to julia Expr, such that you can define julia functions, that you derived using Mathematica functions would be very nice to have.

[simonbyrne]

We need some sort of way to match up functions between Julia and Mathematica. This is obvious in some cases (e.g. sin => W"Sin"), but some functions differ in their usage or how certain arguments are handled (e.g. sum vs W"Sum").

[BeastyBlacksmith]

Is there a way we could query the signatures of the Mathematica functions, such that we could build a mapping via codegen? ( Check, if a method with a matching signature exists and if not, define a bridge )

[simonbyrne]

Not that I know of. MathLink only sees symbol names, it has no semantic knowledge.

This may be better handled in another package built on top of this.

[seadra]

Even a version which doesn't translate function calls would be immensely useful

[musoke]

https://github.com/AmplitudeGravity/usingMathLink/blob/master/useMathLink.ipynb uses https://github.com/chakravala/SyntaxTree.jl to do the very basics of this.

[Lightup1]

Is it possible to convert a pure complex number in type of WExpr to a julia ComplexF64? I recently used Meta.parse(W2Mstr(WExpr)) for real numbers and eval(Meta.parse(replace(W2Mstr(weval(WExpr)),"I"=>"im"))) for complex numbers. Function like pyconvert in PythonCall.jl is preferred.

[musoke]

I extracted part of @AmplitudeGravity's demo above and extended it in a package here: https://github.com/musoke/WolframExpr.jl. It converts Mathematica/Wolfram expressions to Julia expressions and functions. It only knows how to translate a handful of functions out of the box, but enough for complex rational functions. You can tell it how other functions are defined.

julia> using MathLink, WolframExpr

julia> s = "(1 + G[x])/(1 + x + I*x^2)";

julia> f = string_to_function(s, [:G, :x]);

julia> g(x) = im * x + x^2;

julia> f(g, 1)
1.0 + 0.0im

[fremling]

Hi, based on ticked (https://github.com/JuliaInterop/MathLink.jl/issues/72) I took the liberty to add the feature (`W2Julia ) in into the 0.5.3 release of today (https://github.com/JuliaInterop/MathLink.jl/releases/tag/v0.5.3). It aims to convert MathLink objects to Julia style objects.

For instance it can convert the "Assumptions" to a dictionary. Below are some examples:

@test W2Julia(W`{1,2,3}`) == [1,2,3]
@test W2Julia(W`{1,a,3}`) == [1,W"a",3]
@test W2Julia(W`{1,a,{1,2}}`) == [1,W"a",[1,2]]
@test W2Julia(W`Association["team" -> "HOU", "lastName" -> "Ching"]`) == Dict( "team" => "HOU" , "lastName" => "Ching")
@test W2Julia(W`Association["team" -> {1,2,3}, "lastName" -> "Ching"]`) == Dict( "team" => [1,2,3] , "lastName" => "Ching")
@test W2Julia(W`{1,Association["team" -> {1,2,3}, "lastName" -> "Ching"]}`) == [1,Dict( "team" => [1,2,3] , "lastName" => "Ching")]

As this is almost at the embryo stage, feel free to report strange (or lacking) behavior i other tickets.