undocumented exported functions `solve_single_eq` and `solve_system_eq`

[nsajko]

I notice that Symbolics defines and exports two functions, solve_single_eq and solve_system_eq. Even though they are exported, they are not documented. That said, the function signatures are somewhat self-explanatory.

Are they supposed to be exposed to external users? Otherwise they probably shouldn't be exported?

Furthermore, I wonder what is the relation of these two functions with Symbolics.solve_for supposed to be, because they seem to provide roughly similar functionality? The latter function is documented, but not exported.

[nsajko]

FTR, solve_single_eq is useful:

julia> solve_single_eq((x^3) ~ false, x)
x ~ 0^(1//3)

julia> simplify(ans)
x ~ 0.0

However, it's not foolproof:

julia> solve_single_eq((x^2) ~ false, x)
ERROR: MethodError: no method matching occursin(::Num, ::Int64)

Closest candidates are:
  occursin(::SymbolicUtils.Symbolic, ::Any)
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/Oyu8Z/src/substitute.jl:52
  occursin(::Any, ::SymbolicUtils.Symbolic)
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/Oyu8Z/src/substitute.jl:51
  occursin(::Any)
   @ Base strings/search.jl:724

Stacktrace:
 [1] _occursin(needle::Num, haystack::SymbolicUtils.BasicSymbolic{Rational{Int64}})
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/Oyu8Z/src/substitute.jl:59
 [2] move_to_other_side(eq::Equation, var::Num)
   @ Symbolics ~/.julia/packages/Symbolics/BQlmn/src/solver.jl:379
 [3] solve_single_eq_unchecked(eq::Equation, var::Num, single_solution::Bool)
   @ Symbolics ~/.julia/packages/Symbolics/BQlmn/src/solver.jl:287
 [4] solve_single_eq(eq::Equation, var::Num, single_solution::Bool, verify::Bool)
   @ Symbolics ~/.julia/packages/Symbolics/BQlmn/src/solver.jl:17
 [5] reverse_powers(eq::Equation, var::Num, single_solution::Bool)
   @ Symbolics ~/.julia/packages/Symbolics/BQlmn/src/solver.jl:629
 [6] solve_single_eq_unchecked(eq::Equation, var::Num, single_solution::Bool)
   @ Symbolics ~/.julia/packages/Symbolics/BQlmn/src/solver.jl:301
 [7] solve_single_eq(eq::Equation, var::Num, single_solution::Bool, verify::Bool)
   @ Symbolics ~/.julia/packages/Symbolics/BQlmn/src/solver.jl:17
 [8] top-level scope

[nsajko]

solve_system_eq doesn't have the same bug as solve_single_eq:

julia> solve_system_eq([(x^2) ~ false], [x])
Dict{Any, Any} with 1 entry:
  x => 0.0

It, however, doesn't find all possible solutions:

julia> solve_system_eq([(x^2) ~ true], [x])
Dict{Any, Any} with 1 entry:
  x => 1

[shashi]

@YingboMa we should not export this.