Error with iszero for symbolic matrix elements

[Suavesito-Olimpiada]

I got to this when working with symbolic matrices. This is the MWE

using Symbolics

@variables a[1, 1]

iszero(a[1, 1]) # throw really long error

The stack-trace is the folowing

Stack Trace

julia> iszero(α[1,1])
ERROR: MethodError: no method matching ^(::SymbolicUtils.Sym{Matrix{Real}, Base.ImmutableDict{DataType, Any}}, ::Int64)
Closest candidates are:
  ^(::Union{AbstractChar, AbstractString}, ::Integer) at strings/basic.jl:718
  ^(::SymbolicUtils.Mul, ::Number) at /home/jose/.julia/packages/SymbolicUtils/L2Usn/src/types.jl:966
  ^(::LinearAlgebra.UniformScaling, ::Number) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/uniformscaling.jl:298
  ...
Stacktrace:
  [1] unstable_pow(a::SymbolicUtils.Sym{Matrix{Real}, Base.ImmutableDict{DataType, Any}}, b::Int64)
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/L2Usn/src/types.jl:742
  [2] (::SymbolicUtils.var"#111#119"{SymbolicUtils.var"#resolve#116"{PolyForm{Matrix{Real}, Base.ImmutableDict{DataType, Any}}, SymbolicUtils.var"#get_var#115", SymbolicUtils.var"#is_var#114"}})(::Tuple{DynamicPolynomials.PolyVar{true}, Int64})
    @ SymbolicUtils ./none:0
  [3] iterate
    @ ./generator.jl:47 [inlined]
  [4] grow_to!(dest::Vector{Any}, itr::Base.Generator{Base.Iterators.Filter{SymbolicUtils.var"#112#120", Base.Iterators.Zip{Tuple{Vector{DynamicPolynomials.PolyVar{true}}, Vector{Int64}}}}, SymbolicUtils.var"#111#119"{SymbolicUtils.var"#resolve#116"{PolyForm{Matrix{Real}, Base.ImmutableDict{DataType, Any}}, SymbolicUtils.var"#get_var#115", SymbolicUtils.var"#is_var#114"}}})
    @ Base ./array.jl:739
  [5] collect(itr::Base.Generator{Base.Iterators.Filter{SymbolicUtils.var"#112#120", Base.Iterators.Zip{Tuple{Vector{DynamicPolynomials.PolyVar{true}}, Vector{Int64}}}}, SymbolicUtils.var"#111#119"{SymbolicUtils.var"#resolve#116"{PolyForm{Matrix{Real}, Base.ImmutableDict{DataType, Any}}, SymbolicUtils.var"#get_var#115", SymbolicUtils.var"#is_var#114"}}})
    @ Base ./array.jl:676
  [6] arguments(x::PolyForm{Matrix{Real}, Base.ImmutableDict{DataType, Any}})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/L2Usn/src/polyform.jl:202
  [7] unsorted_arguments
    @ ~/.julia/packages/SymbolicUtils/L2Usn/src/types.jl:300 [inlined]
  [8] (::SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false})(x::PolyForm{Matrix{Real}, Base.ImmutableDict{DataType, Any}})
    @ SymbolicUtils.Rewriters ~/.julia/packages/SymbolicUtils/L2Usn/src/rewriters.jl:162
  [9] (::SymbolicUtils.Rewriters.PassThrough{SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false}})(x::PolyForm{Matrix{Real}, Base.ImmutableDict{DataType, Any}})
    @ SymbolicUtils.Rewriters ~/.julia/packages/SymbolicUtils/L2Usn/src/rewriters.jl:152
 [10] iterate
    @ ./generator.jl:47 [inlined]
 [11] _collect(c::Vector{Any}, itr::Base.Generator{Vector{Any}, SymbolicUtils.Rewriters.PassThrough{SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false}}}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{1})
    @ Base ./array.jl:691
 [12] collect_similar
    @ ./array.jl:606 [inlined]
 [13] map(f::SymbolicUtils.Rewriters.PassThrough{SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false}}, A::Vector{Any})
    @ Base ./abstractarray.jl:2294
 [14] (::SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false})(x::SymbolicUtils.Term{Real, Nothing})
    @ SymbolicUtils.Rewriters ~/.julia/packages/SymbolicUtils/L2Usn/src/rewriters.jl:162
 [15] PassThrough
    @ ~/.julia/packages/SymbolicUtils/L2Usn/src/rewriters.jl:152 [inlined]
 [16] iterate
    @ ./generator.jl:47 [inlined]
 [17] _collect(c::Vector{SymbolicUtils.Term{Real, Nothing}}, itr::Base.Generator{Vector{SymbolicUtils.Term{Real, Nothing}}, SymbolicUtils.Rewriters.PassThrough{SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false}}}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{1})
    @ Base ./array.jl:691
 [18] collect_similar
    @ ./array.jl:606 [inlined]
 [19] map(f::SymbolicUtils.Rewriters.PassThrough{SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false}}, A::Vector{SymbolicUtils.Term{Real, Nothing}})
    @ Base ./abstractarray.jl:2294
 [20] (::SymbolicUtils.Rewriters.Walk{:post, typeof(identity), typeof(similarterm), false})(x::PolyForm{Real, Nothing})
    @ SymbolicUtils.Rewriters ~/.julia/packages/SymbolicUtils/L2Usn/src/rewriters.jl:162
 [21] expand(expr::SymbolicUtils.Term{Real, Nothing})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/L2Usn/src/polyform.jl:228
 [22] (::ComposedFunction{typeof(SymbolicUtils._iszero), typeof(expand)})(x::SymbolicUtils.Term{Real, Nothing})
    @ Base ./operators.jl:938
 [23] _any(f::ComposedFunction{typeof(SymbolicUtils._iszero), typeof(expand)}, itr::Vector{SymbolicUtils.Term{Real, Nothing}}, #unused#::Colon)
    @ Base ./reduce.jl:876
 [24] any(f::Function, a::Vector{SymbolicUtils.Term{Real, Nothing}}; dims::Function)
    @ Base ./reducedim.jl:883
 [25] any(f::Function, a::Vector{SymbolicUtils.Term{Real, Nothing}})
    @ Base ./reducedim.jl:883
 [26] fraction_iszero(x::SymbolicUtils.Term{Real, Nothing})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/L2Usn/src/polyform.jl:310
 [27] iszero(x::Num)
    @ Symbolics ~/.julia/packages/Symbolics/GAvUr/src/num.jl:91
 [28] top-level scope
    @ REPL[3]:1

This happens both in Julia-1.7rc4 and Julia-1.6.2, I'm working with Symbolics v3.3.0.

[moble]

This isn't just matrices; it's also true of just plain vectors. And it's still a problem on v3.3.1.

using Symbolics
@variables a[1:2] b
iszero(b) # Works just fine; returns `false`
iszero(a[1])  # Raises the error Suavesito noted

I suspect this has to do with the fact that a[1] and b actually have different types deep down. Their actual types are Num in both cases, but Num is just a wrapper containing a val field, and those fields have different types for the two variables:

julia> typeof(a[1].val)
SymbolicUtils.Term{Real, Nothing}

julia> typeof(b.val)
SymbolicUtils.Sym{Real, Base.ImmutableDict{DataType, Any}}

Note that a[1] is really a Term, and b is really a Sym.

[moble]

@Suavesito-Olimpiada A workaround would be to define

a = [Symbolics.variable(:a, i, j) for i in 1:N, j in 1:M]

for any NxM matrix. I don't think this should be necessary, though; see #379.

[YingboMa]

This is fixed.