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Merge pull request #60 from fremling/master
Included the W2Mstr function
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‎README.md

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@@ -132,6 +132,43 @@ julia> P12 * [W"a" W"b" ; W`a+b` 2] == [ W"b" 2-W"b" ; W"a" W"b"]
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true
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```
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## W2Mstr - Mathematica conversion
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Sometimes one wants to be able to read the Julia MathLink expressions back into Mathematica. For that purpose, `W2Mstr` is also supplied. This implementation is currently quite defensive with parentheses, which gives a more verbose output than necessary. Here are a few examples
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```julia
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julia> W2Mstr(W`x`)
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"x"
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julia> W2Mstr(W"Sin"(W"x"))
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"Sin[x]"
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julia> W2Mstr(weval(W`a + c + v`))
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"(a + c + v)"
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julia> W2Mstr(weval(W`a^(b+c)`))
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"(a^(b + c))"
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julia> W2Mstr(weval(W`e+a^(b+c)`))
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"((a^(b + c)) + e)"
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julia> W2Mstr(W"a"+W"c"+W"v"+W"Sin"(2 +W"x" + W"Cos"(W"q")))
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"(a + c + v + Sin[(2 + x + Cos[q])])"
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julia> W2Mstr(im*2)
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"(2*I)"
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julia> W2Mstr(weval(W"Complex"(W"c",W"b")))
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"(c+b*I)"
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julia> W2Mstr(W"c"+im*W"b")
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"(((1*I)*b) + c)"
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julia> W2Mstr(W`b/(c^(a+c))`)
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"(b*((c^(a + c))^-1))"
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```
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## LateX printing in JuPyter Notebooks
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Printing in Juypter notebooks is by defaults done in latex.
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This can be turned off with the command `MathLink.set_texOutput(false)`

‎src/display.jl

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@@ -93,4 +93,116 @@ function Base.show(io,::MIME"text/latex",x::MathLink.WExpr)
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end
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export Wprint
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####..............
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function Wprint(WExpr)
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weval(W"Print"(WExpr))
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return
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end
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export W2Mstr
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###function that prints the W-form back to Mathematica Input-language
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W2Mstr(x::Number) = "$x"
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W2Mstr(z::Complex) = W2Mstr(WComplex(z))
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W2Mstr(x::Rational) = "($(x.num)/$(x.den))"
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function W2Mstr(x::Array)
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Dim = length(size(x))
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Str="{"
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for j in 1:size(x)[1]
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if j>1
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Str*=","
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end
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if Dim == 1
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Str*=W2Mstr(x[j])
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elseif Dim == 2
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Str*=W2Mstr(x[j,:])
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else
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###Arrays with larger dimension: $Dim != 1,2 not implemented yet
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end
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end
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Str*="}"
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return Str
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end
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W2Mstr(x::MathLink.WSymbol) = x.name
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function W2Mstr(x::MathLink.WExpr)
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#println("W2Mstr::",x.head.name)
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if x.head.name == "Plus"
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Str = W2Mstr_PLUS(x.args)
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elseif x.head.name == "Times"
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Str = W2Mstr_TIMES(x.args)
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elseif x.head.name == "Power"
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Str = W2Mstr_POWER(x.args)
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elseif x.head.name == "Complex"
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Str = W2Mstr_COMPLEX(x.args)
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else
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Str=x.head.name*"["
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for j in 1:length(x.args)
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if j>1
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Str*=","
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end
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Str*=W2Mstr(x.args[j])
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end
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Str*="]"
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end
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return Str
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end
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function W2Mstr_PLUS(x::Union{Array,Tuple})
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#println("W2Mstr_PLUS:",x)
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Str="("
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for j in 1:length(x)
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if j>1
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Str*=" + "
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end
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Str*=W2Mstr(x[j])
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end
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Str*=")"
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end
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function W2Mstr_TIMES(x::Union{Array,Tuple})
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#println("W2Mstr_TIMES:",x)
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Str="("
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for j in 1:length(x)
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if j>1
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Str*="*"
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end
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Str*=W2Mstr(x[j])
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end
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Str*=")"
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end
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function W2Mstr_POWER(x::Union{Array,Tuple})
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#println("W2Mstr_POWER:",x)
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if length(x) != 2
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error("Power takes two arguments")
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end
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Str="("*W2Mstr(x[1])*"^"*W2Mstr(x[2])*")"
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end
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function W2Mstr_COMPLEX(x::Union{Tuple,Array})
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#println("W2Mstr_COMPLEX:",x)
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if length(x) != 2
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error("Complex takes two arguments")
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end
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if x[1] == 0
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###Imaginary
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Str="("*W2Mstr(x[2])*"*I)"
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elseif x[2] == 0
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### Real
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###Complex
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Str=W2Mstr(x[1])
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else
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###Complex
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Str="("*W2Mstr(x[1])*"+"*W2Mstr(x[2])*"*I)"
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end
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end
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‎test/runtests.jl

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@@ -5,6 +5,71 @@ import MathLink: WExpr, WSymbol
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@testset "W2Mstr" begin
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###Test of a naive MathLink to Mathematica converter function (to resuts can be copied into mathematica directly"
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@testset "Basic Algebra" begin
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@test W2Mstr(W"a") == "a"
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@test W2Mstr(W"x") == "x"
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@test W2Mstr(W"x"+W"y") == "(x + y)"
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@test W2Mstr(W`Sqrt[a + b]`) == "Sqrt[(a + b)]"
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@test W2Mstr(W`Pow[x,2]`) == "Pow[x,2]"
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@test W2Mstr(W`x^2`) == "(x^2)"
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@test W2Mstr(W`a+b`) == "(a + b)"
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@test W2Mstr(weval(W`a + c + v`)) == "(a + c + v)"
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@test W2Mstr(2) == "2"
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@test W2Mstr(W`x`) == "x"
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@test W2Mstr(W"Sin"(W"x")) == "Sin[x]"
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@test W2Mstr(W`Sin[x]`) == "Sin[x]"
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end
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@testset "Nested functions" begin
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@test W2Mstr(weval(W`a + c*b + v`)) == "(a + (b*c) + v)"
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@test W2Mstr(weval(W`(a + c)*(b + v)`)) == "((a + c)*(b + v))"
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@test W2Mstr(weval(W`a^(b+c)`)) == "(a^(b + c))"
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@test W2Mstr(weval(W`a^2`)) == "(a^2)"
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@test W2Mstr(weval(W`e+a^(b+c)`)) == "((a^(b + c)) + e)"
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@test W2Mstr(weval(W`a + c + v + Sin[2 + x + Cos[q]]`)) == "(a + c + v + Sin[(2 + x + Cos[q])])"
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set_GreedyEval(true)
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@test W2Mstr(W"a"+W"c"+W"v"+W"Sin"(2 +W"x" + W"Cos"(W"q"))) == "(a + c + v + Sin[(2 + x + Cos[q])])"
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set_GreedyEval(false)
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@test W2Mstr(W"a"+W"c"+W"v"+W"Sin"(2 +W"x" + W"Cos"(W"q"))) == "(((a + c) + v) + Sin[((2 + x) + Cos[q])])"
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@test W2Mstr(W`Sqrt[x+Sin[y]+z^(3/2)]`) == "Sqrt[(x + Sin[y] + (z^(3*(2^-1))))]"
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end
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@testset "Complex values" begin
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@test W2Mstr(weval(W`2*I`)) == "(2*I)"
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@test W2Mstr(weval(W`2/I`)) == "(-2*I)"
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@test W2Mstr(W`2 + 0*I`) == "(2 + (0*I))"
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@test W2Mstr(W"Complex"(W"c",0)) == "c"
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@test W2Mstr(weval(W"Complex"(W"c",0))) == "c"
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@test W2Mstr(weval(W"Complex"(W"c",W"b"))) == "(c+b*I)"
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@test W2Mstr(im) == "(1*I)"
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@test W2Mstr(2*im) == "(2*I)"
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end
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@testset "Factions" begin
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@test W2Mstr(W`3/4`) == "(3*(4^-1))"
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@test W2Mstr(3//4) == "(3/4)"
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@test W2Mstr(W`b/c`) == "(b*(c^-1))"
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@test W2Mstr(W`b/(c^(a+c))`) == "(b*((c^(a + c))^-1))"
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@test W2Mstr(W`(b^2)/(c^3)`) == "((b^2)*((c^3)^-1))"
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@test W2Mstr(weval(W`(b^2)/(c^3)`)) == "((b^2)*(c^-3))"
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end
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@testset "Lists & Arrays" begin
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@test W2Mstr([W`x`,W`a`]) == "{x,a}"
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@test W2Mstr([W`x`]) == "{x}"
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@test W2Mstr([W`x` W`y`; W`z` W`x`]) == "{{x,y},{z,x}}"
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end
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end
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@testset "integers" begin
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w = W"Factorial"(30)
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@test_throws MathLink.MathLinkError weval(Int, w)

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