`simplify`: Inconsistencies in common factor extraction between different number of terms

[JaydevSR]

While experimenting, I came across some inconsistencies when it comes to the extraction of common factors in simplify. Depending on the number of terms in the expressions, a sole common factor in all the terms is successfully determined in some case while not in the other case. I give an example below:

zarr = Symbolics.variables(:z, 1:N)
csum = [sum(zarr[1:i]) for i=1:N-1]
csum2_sum = expand.(sum(csum.^2))
quad_terms = filter(t -> Symbolics.degree(t) == 2, terms(csum2_sum))
cross_quad_terms = filter(qi -> length(Symbolics.get_variables(qi)) == 2, quad_terms)

cqt_decomposition = []
cqt_remaining = copy(cross_quad_terms)
for zi in reverse(zarr)
	push!(cqt_decomposition, filter(t -> Symbolics.coeff(t, zi) !== 0, cqt_remaining))
	filter!(t -> Symbolics.coeff(t, zi) === 0, cqt_remaining)
end
cqt_zi = sum.(cqt_decomposition)
cqt_zi_simplify = simplify.(cqt_zi)

cqt_zi_manual = []
for (cqt, zi) in zip(cqt_decomp_terms, reverse(zarr))
	push!(cqt_zi_manual,
		  simplify(Symbolics.coeff(cqt, zi)) * zi
	)
end

Output:

cqt_zi_simplify = Symbolics.Num[0, 2(z₁ + z₆)*z₉ + 2z₂*z₉ + 2(z₃ + z₅ + z₇ + z₈)*z₉ + 2z₄*z₉, 4(z₁ + z₆)*z₈ + 4z₂*z₈ + 4z₃*z₈ + 4z₄*z₈ + 4z₅*z₈ + 4z₇*z₈, 6(z₁ + z₂ + z₃ + z₄ + z₅ + z₆)*z₇, 8z₁*z₆ + 8z₂*z₆ + 8z₃*z₆ + 8z₄*z₆ + 8z₅*z₆, 10(z₁ + z₂ + z₃ + z₄)*z₅, 12z₁*z₄ + 12(z₂ + z₃)*z₄, 14z₁*z₃ + 14z₂*z₃, 16z₁*z₂, 0]

cqt_zi_manual = Any[0, (2//1)*(z₁ + z₂ + z₃ + z₄ + z₅ + z₆ + z₇ + z₈)*z₉, (4//1)*(z₁ + z₂ + z₃ + z₄ + z₅ + z₆ + z₇)*z₈, (6//1)*(z₁ + z₂ + z₃ + z₄ + z₅ + z₆)*z₇, (8//1)*(z₁ + z₂ + z₃ + z₄ + z₅)*z₆, (10//1)*(z₁ + z₂ + z₃ + z₄)*z₅, (12//1)*(z₁ + z₂ + z₃)*z₄, (14//1)*(z₁ + z₂)*z₃, (16//1)*z₁*z₂, 0]

In this example, what I expected to obtain was cqt_zi_manual whereas cqt_zi_simplify doesn't contain all the terms with the common factor resolved completely.

• Version info:

Julia Version 1.11.5
Commit 760b2e5b73 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 16 × AMD Ryzen 7 PRO 8840U w/ Radeon 780M Graphics  
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 8 default, 0 interactive, 4 GC (on 16 virtual cores)
Environment:
  JULIA_REVISE_WORKER_ONLY = 1

• Pkg.status():

Status `C:\Users\...`
⌅ [d1185830] SymbolicUtils v3.32.0
  [0c5d862f] Symbolics v6.57.0
  [44cfe95a] Pkg v1.11.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

This is a follow-up after the comments received on my discourse post here.

[ufechner7]

Could you share the examples in text form, enclosed in triple backticks, instead of pictures? They are then much easier to reproduce for others. And perhaps also share the output of pkg.status() and versioninfo() so that we know which version of the packages and of Julia you used?

[JaydevSR]

I have updated the issue body. It seem that the distribution rule over addition doesn't propagate from the leaves of the evaluation graph to the top completely which would explain something like this.

[ufechner7]

Thank you!