`inv` of symbolic matrix failing

[michakraus]

In the process of updating EulerLagrange.jl to Symbolics v7.0, I encountered an issue with the inversion of a symbolic matrix, which worked up to the latest pre-7 version of Symbolics. The stracktrace reads:

  Got exception outside of a @test
  LoadError: TypeError: non-boolean (SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}) used in boolean context
  Stacktrace:
    [1] _isbanded_impl(A::Matrix{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}}, kl::Int64, ku::Int64)
      @ LinearAlgebra /Applications/Julia-1.12.app/Contents/Resources/julia/share/julia/stdlib/v1.12/LinearAlgebra/src/generic.jl:1543
    [2] _isbanded
      @ /Applications/Julia-1.12.app/Contents/Resources/julia/share/julia/stdlib/v1.12/LinearAlgebra/src/generic.jl:1489 [inlined]
    [3] isbanded
      @ /Applications/Julia-1.12.app/Contents/Resources/julia/share/julia/stdlib/v1.12/LinearAlgebra/src/generic.jl:1483 [inlined]
    [4] isdiag
      @ /Applications/Julia-1.12.app/Contents/Resources/julia/share/julia/stdlib/v1.12/LinearAlgebra/src/generic.jl:1606 [inlined]
    [5] inv(A::Matrix{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}})
      @ LinearAlgebra /Applications/Julia-1.12.app/Contents/Resources/julia/share/julia/stdlib/v1.12/LinearAlgebra/src/dense.jl:1080
    [...]

The matrix is typically 2x2 or 4x4. The code around its generation is a bit involved, but I can try to cook up a MWE if the error message itself is not sufficiently indicative of the issue.

This is with Julia v1.12.1, SymbolicUtils v4.4.0 and Symbolics v7.0.1.

[michakraus]

It seems, the corresponding matrix was

Matrix{Symbolics.Num}

and now it is a

Matrix{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}}

I am not sure if this is due to changes I did in the process of updating or due to changes in Symbolics.

[michakraus]

I think I can pinpoint the origin to a call to scalarize. I am not sure why I needed this in the past, but at some point this was necessary.

The issue can be seen in following code

using LinearAlgebra
using Symbolics

@variables t
@variables x(t)[1:2]
@variables v(t)[1:2]

p(t, x, v) = [log(x[2]) / x[1] / 2, -log(x[1]) / x[2] / 2]
l = p(t, x, v) ⋅ v

typeof(l)

ls = Symbolics.scalarize(l)

typeof(ls)

which produces

julia> using LinearAlgebra

julia> using Symbolics

julia> @variables t
1-element Vector{Num}:
 t

julia> @variables x(t)[1:2]
1-element Vector{Symbolics.Arr{Num, 1}}:
 (x(t))[1:2]

julia> @variables v(t)[1:2]
1-element Vector{Symbolics.Arr{Num, 1}}:
 (v(t))[1:2]

julia> p(t, x, v) = [log(x[2]) / x[1] / 2, -log(x[1]) / x[2] / 2]
p (generic function with 1 method)

julia> l = p(t, x, v) ⋅ v
(-(v(t))[2]*log((x(t))[1])) / (2(x(t))[2]) + ((v(t))[1]*log((x(t))[2])) / (2(x(t))[1])

julia> typeof(l)
Num

julia> ls = Symbolics.scalarize(l)
(-(v(t))[2]*log((x(t))[1])) / (2(x(t))[2]) + ((v(t))[1]*log((x(t))[2])) / (2(x(t))[1])

julia> typeof(ls)
SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}

So scalarize changes the type of the expression from Num to SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}, which causes the issues with inv.

In my tests, the call to scalarize does not seem to be required, however, I am pretty sure that I have some real-world examples that required scalarization.

Is there a canonical way to scalarize but retain the Num type of the expression?