Add tests for arithmetic on arrays

[ojwoodford]

Basic arithmetic involving arrays and scalars is broken (see #691). The goal of this PR is to fix it.

I'm new to Julia, and unfortunately understanding the internals of Symbolics.jl is beyond me. I've added some tests that catch the error. I'd love to collaborate with someone on fixes.

[ChrisRackauckas]

Is this supposed to be listed as WIP, or just add to the tests?

[ojwoodford]

Is this supposed to be listed as WIP, or just add to the tests?

WIP

[shashi]

Thanks these should act as test for #696

[shashi]

I think the left hand side of isequal needs Symbolics.scalarize calls.

julia> y[1] / y[2]
(broadcast(*, x, Ref(s)))[1] / (broadcast(*, x, Ref(s)))[2]

julia> Symbolics.scalarize(y[1] / y[2])
x[1] / x[2]

[ojwoodford]

@shashi Done. Are you able to approve the workflows?

[codecov-commenter]

Codecov Report

Merging #692 (c16881a) into master (0d7db80) will decrease coverage by 67.59%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master    #692       +/-   ##
==========================================
- Coverage   76.49%   8.90%   -67.60%     
==========================================
  Files          23      23               
  Lines        2719    2651       -68     
==========================================
- Hits         2080     236     -1844     
- Misses        639    2415     +1776     

Impacted Files	Coverage Δ
src/groebner_basis.jl	0.00% <0.00%> (-100.00%)	⬇️
src/semipoly.jl	0.00% <0.00%> (-91.00%)	⬇️
src/linear_algebra.jl	0.00% <0.00%> (-89.48%)	⬇️
src/array-lib.jl	0.00% <0.00%> (-80.34%)	⬇️
src/diff.jl	0.37% <0.00%> (-80.00%)	⬇️
src/complex.jl	0.00% <0.00%> (-75.00%)	⬇️
src/build_function.jl	0.00% <0.00%> (-74.70%)	⬇️
src/difference.jl	0.00% <0.00%> (-70.00%)	⬇️
src/utils.jl	7.31% <0.00%> (-68.47%)	⬇️
src/arrays.jl	11.13% <0.00%> (-68.34%)	⬇️
... and 11 more

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[ojwoodford]

Shouldn't isequal on symbolic expressions resolve this kind of kind of problem?: isequal(s - x[2] + x[1] - s, x[1] - x[2]) returns false
In fact, if I write the expression above, it does return true. It's only when I write:

@variables x[1:2] s
y = x .+ s
@test isequal(scalarize(y[1] - y[2]), x[1] - x[2])

that the test throws an error. This is not the expected behaviour.

[ojwoodford]

The problem has been suggested in #704