Add a "Rosetta Stone" to the README

[sebasguts]

It would be nice to have a small list of comparisons between polymake and Polymake.jl code in the README, i.e., lines like

$x->VERTICES => x.VERTICES

[kalmarek]

First draft:

Rosetta stone:

Variables

Polymake	Julia
$p (reference to 'scalar' variable)	p (reference to any variable)
print $p;	print(p) or println(p) or @show p, or just p in REPL
$i=5; $j=6;	i,j = 5,6 or i=5; j=6 (; is needed for separation, can be used to suppress return value in REPL)
$s = $i + $j; print $s;	s = i + j

Arrays

Polymake	Julia
Linear containers with random access	Linear containers with random access + all the algebra attached
@A = ("a", "b", "c");	A = ["a", "b", "c"]
$first = $A[0]; (first is equal to a)	first = A[1] (note the 1-based indexing!)
@A2 = (3,1,4,2);	A2 = [3,1,4,2]
print sort(@A2); (a copy of A2 is sorted)	println(sort(A2)) (to sort in place use sort!(A2))
$arr = new Array<Int>([3,2,5]); (a C++ object)	arr = Int[3,2,5] (although the type would have been inferred)
$arr->[0] = 100; (assignment)	arr[1] = 100 (assignment; returns 100)

Dictionaries/Hash Tables

Polymake	Julia
%h = ();	h = Dict() it is MUCH better to provide types, e.g. h = Dict{String, Int}()
$h{"zero"}=0; $h{"four"}=4;	h["zero"] = 0; h["four"] = 4 (call returns the value)
print keys %h;	@show keys(h) (order is not specified)
print join(", ",keys %hash);	join(keys(h), ", ") (returns String)
%hash=("one",1,"two",2);	Dict([("one",1), ("two",2)]) (will infer types)
%hash=("one"=>1,"two"=>2);	Dict("one"=>1,"two"=>2) (will infer types)

Sets

Polymake	Julia
Balanced binary search trees	Hash table with no content
$set=new Set<Int>(3,2,5,3);	set = Set{Int}([3,2,5,3])
print $set->size;	length(set)
@array_from_set=@$set	collect(set) (creates a Vector , order is not specified)

Matrices

Polymake	Julia
Containers with algebraic operations	Matrix{T} = Array{T, 2} – (linear) container of elements of type T with available indexing by 2-ples; all algebra attached
$mat=new Matrix<Rational>([[2,1,4,0,0],[3,1,5,2,1],[1,0,4,0,6]]);	mat = Rational{Int}[2 1 4 0 0; 3 1 5 2 1; 1 0 4 0 6]
$row1=new Vector<Rational>([2,1,4,0,0]); $row2=new Vector<Rational>([3,1,5,2,1]); $row3=new Vector<Rational>([1,0,4,0,6]); @matrix_rows=($row1,$row2,$row3); (Perl object) $matrix_from_array=new Matrix<Rational>(\@matrix_rows);(C++ object)	row1 = Rational{Int}[2, 1, 4, 0, 0]; row2 = Rational{Int}[3, 1, 5, 2, 1]; row3 = Rational{Int}[1, 0, 4, 0, 6]; matrix_rows = hcat(row1', row2', row3') (Julia stores matrices in column major format, so ' i.e. transposition is needed)
$mat->row(1)->[1]=7; $mat->elem(1,2)=8;	mat[2,2] = 7; mat[2,3] = 8
$unit_mat=4*unit_matrix<Rational>(3);	unit_mat = Diagonal([4//1 for i in 1:3]) or UniformScalin(4//1), depending on application (both require using LinearAlgebra)
$dense=new Matrix<Rational>($unit_mat);	Array(unit_mat)
$m_rat=new Matrix<Rational>(3/5*unit_matrix<Rational>(5)); $m2=$mat/$m_rat;	m_rat = Diagonal([3//5 for i in 1:5]) m2 = mat/m_rat
$m_int=new Matrix<Int>(unit_matrix<Rational>(5)); $m3=$m_rat/$m_int; (results in an error due to incompatible types)	m_int = Diagonal([1 for i in 1:5]) m_rat/m_int (succeeds due to promote happening in /)
convert_to<Rational>($m_int)	convert(Diagonal{Rational{Int}}, m_int)
$z_vec=zero_vector<Int>($m_int->rows) $extended_matrix=($z_vec|$m_int); (adds z_vec as the first column, result is dense)	z_vec = zeros(Int, size(m_int, 1)) extended_matrix = hcat(z_vec, m_int) (result is sparse)
$set=new Set<Int>(3,2,5); $template_Ex=new Array<Set<Int>>((new Set<Int>(5,2,6)),$set)	set = Set([3,2,5]); template_Ex = [Set([5,2,6]), set]
$p=new Polytope<Rational>(POINTS=>cube(4)->VERTICES); $lp=new LinearProgram<Rational>(LINEAR_OBJECTIVE=>[0,1,1,1,1]); $p->LP=$lp; p->LP->MAXIMAL_VALUE;	p = p = perlobj("Polytope", :POINTS=>Polymake.polytope.cube(4).VERTICES) lp = perlobj("LinearProgram", :LINEAR_OBJECTIVE=>[0,1,1,1,1]) p.LP = lp p.LP.MAXIMAL_VALUE
$i = ($p->N_FACETS * $p->N_FACETS) * 15;	i = (p.N_FACETS * p.N_FACETS) * 15

[kalmarek]

It'd be preferable to call p = Polytope(:POINTS=>[1 0 1; 1 0 -1; 1 1 0; 1 -1 0]) etc. instead of perlobj("Polytope", ...), which requires resolution to the BigObjects-sometimes-need-template-parameter problem

[saschatimme]

Maybe we could also just make a macro?

E.g.

p = @pm Polytope(:POINTS=>[1 0 1; 1 0 -1; 1 1 0; 1 -1 0])

[sebasguts]

That way we could do Polytope<Rational>, right?

[sebasguts]

I like that solution pretty much :). May I implement it? I have not yet worked with the Julia macros, and would like to learn it a bit more :)

[kalmarek]

@pm Polytopes.Polytope{Rational}(...)

[saschatimme]

Macros still need to be valid Julia syntax. So Polytope{Rational} you probably need to have.

[kalmarek]

what redundancy checks:-)

[sebasguts]

@saschatimme The () seem fine to me, too. We do not need to jackhammer all polymake syntax into Julia.

On the other hand, Cxx.jl does some pretty fancy and shady stuff with macros. Are you completely sure you really need to have valid Julia syntax?

[sebasguts]

But while this is discussion got out of scope pretty fast
@kalmarek I like this draft already. Do you like to make a PR to the readme? We can always adjust it to the syntax changes we make.

[saschatimme]

I think the PR is great now, and if we add such a macro we just update this.