substitute silently fails

[rrwormqueen]

Hi,

I've been experimenting with combining Symbolics.jl with other mathematical libraries. I've noticed that in some cases, the substitute can fail dramatically, without any error or indication of a missing method definition.

using CliffordNumbers, Symbolics
@variables X_sym[1:4]
# Extend a function from CliffordNumbers so the variable can be printed. (Unrelated to issue, but helps see the outputs.)
import CliffordNumbers.print_clifford_coefficient
print_clifford_coefficient(io::IO, c::Num, ffn::Bool) = print(io, " + "^ffn, '(', c, ')')
# Form a CliffordNumber whose coefficients are symbolic variables.
X = KVector{1, STA, Real}(X_sym...)

typeof(X) = 1-element KVector{0, LGAWest(3), Num} which is idiomatic and expected. Compare, for example, to c = X_sym[1] + X_sym[2] * im, for which typeof(c) = Complex{Num}.

There are several open issues at time of writing about the type Complex{Num}. A similar issue is likely happening here. The actual behavior seen is

Y = substitute(X, X_sym => [1,2,3,4])
# Produces (X_sym[1])γ₀ + (X_sym[2])γ₁ + (X_sym[3])γ₂ + (X_sym[4])γ₃ which is completely unchanged.
# To demonstrate:
Y == X # true

The behavior that should happen, as compared with the analogous Complex{Num} case:

substitute(c, X_sym => [1,2,3,4]) # 1 + 2im
substitute(X, X_sym => [1,2,3,4]) # 1γ₀ + 2γ₁ + 3γ₂ + 3γ₃, with type KVector{1, LGAWest(3), Real}

I'm really quite puzzled about what's going on here. The way substitute is behaving like an identity operator is really weird. As a final puzzle piece, I'll note differentiation also silently produces unexpected results. Differential(X_sym[1])(X) |> expand_derivatives should produce γ₀ (type KVector{1, LGAWest(3), Real}), but instead produces 0. Again, compare to Differential(X_sym[1])(c) |> expand_derivatives which correctly produces 1.

Thanks in advance!