function_string of Symmetric matrix includes the entire matrix

[LebedevRI]

using JuMP
import LinearAlgebra
import MathOptInterface as MOI

function main()
    model = Model() 

    @variable(model, v[1:3,1:3], Symmetric)

    @constraint(model, c0, LinearAlgebra.Symmetric(v.-1)  == LinearAlgebra.Symmetric(fill(41, 3,3))) # Yay!
    @show(c0) # Uhh, why is it not symmetric?
    print(c0) # Uhh, why is it not symmetric?
    display(c0) # Oh, but it is symmetric here.
    print(model) # And it is symmetric here too.
end

main()

c0 = c0 : [v[1,1] - 42  v[1,2] - 42  v[1,3] - 42;
 v[1,2] - 42  v[2,2] - 42  v[2,3] - 42; ∈ Zeros()
 v[1,3] - 42  v[2,3] - 42  v[3,3] - 42]

This is even worse for text-only output, looks like only pretty-printing does it right.

[odow]

text/latex has a special check for Symmetric. We don't have the check in text/plain. But that's also because we defer the printing to Base.show, so I'm not sure this is easy to fix.

JuMP.jl/src/print.jl

Lines 884 to 919 in 56b186f

	function function_string(
	::MIME"text/plain",
	A::AbstractMatrix{<:AbstractJuMPScalar},
	)
	str = sprint() do io
	return show(IOContext(io, :limit => true), MIME("text/plain"), A)
	end
	lines = split(str, '\n')
	# We drop the first line with the signature "m×n Array{...}:"
	popfirst!(lines)
	# We replace the first space by an opening `[`
	lines[1] = '[' * lines[1][2:end]
	return join(lines, "\n") * "]"
	end
	function function_string(
	mode::MIME"text/latex",
	A::AbstractMatrix{<:AbstractJuMPScalar},
	)
	str = "\\begin{bmatrix}\n"
	for i in axes(A, 1)
	line = ""
	for j in axes(A, 2)
	if j != 1
	line *= " & "
	end
	if A isa LinearAlgebra.Symmetric && i > j
	line *= "\\cdot"
	else
	line *= function_string(mode, A[i, j])
	end
	end
	str *= line * "\\\\\n"
	end
	return str * "\\end{bmatrix}"
	end

In the REPL, Julia prints the full symmetric matrix:

julia> using LinearAlgebra

julia> Symmetric([1 2; 2 3])
2×2 Symmetric{Int64, Matrix{Int64}}:
 1  2
 2  3

[LebedevRI]

In the REPL, Julia prints the full symmetric matrix:

Right, i just saw that too. I thought it didn't, but apparently it does.

[odow]

Arguably someone might interpret out current text/latex printing as the upper triangular, with zeros in the lower.

Here's what UpperTriangular prints.

julia> UpperTriangular([1 2; 2 3])
2×2 UpperTriangular{Int64, Matrix{Int64}}:
 1  2
 ⋅  3

I don't even know if the current text/latex approach is a good idea.

[LebedevRI]

IMHO, the text/latex approach is generally the right way to do it. Perhaps a different symbol should be used?

[odow]

Thoughts @blegat? I would err on the side of sticking to Base.

[odow]

See #3768

[LebedevRI]

@odow thank you!