`<ₑ` not fully reliable

[bowenszhu]

<ₑ is normally used for sorting arguments.

sort!(v; lt=isless, ...) requires that only one of lt(x,y) and lt(y,x) can return true.

Here is an example where both return true.

using SymbolicUtils
using SymbolicUtils: <ₑ
@syms x
a = 28(x^14)
b = 44(x^7)
a <ₑ b # true
b <ₑ a # true

We got strange results sometimes.

using SymbolicUtils
using SymbolicUtils: <ₑ, unsorted_arguments
@syms x
n = 4
expr = sum((n + 1 - i) * x^i for i in 1:n)
args = unsorted_arguments(expr)

julia> sort(args, lt = <ₑ)
4-element Vector{Any}:
 x^4
 2(x^3)
 4x
 3(x^2)

julia> sort(reverse(args), lt = <ₑ)
4-element Vector{Any}:
 x^4
 3(x^2)
 4x
 2(x^3)

Note that the two above are different.

[bowenszhu]

• inconsistent order of terms causes incorrect derivative calculation Symbolics.jl#791

describes a bug caused by this issue.

And it is also important to take

• Ordering polynomials with respect to each terms' degree Symbolics.jl#390

into account. Sometimes symbolic software are used in math classes for educational purpose. Printing results in an appropriate order is important to avoid making bad first impression.

[bowenszhu]

• please sort polynomials  Symbolics.jl#796

[bowenszhu]

Maple's sort:
https://www.maplesoft.com/support/help/maple/view.aspx?path=sort

[karlwessel]

Note that the example in the first comment got fixed at some point, at least for me with SymbolicsUtils 3.6.0 it gives:

julia> using SymbolicUtils
julia> using SymbolicUtils: <ₑ
julia> @syms x
(x,)
julia> a = 28(x^14)
28(x^14)
julia> b = 44(x^7)
44(x^7)
julia> a <ₑ b # true
false
julia> b <ₑ a # true
true

[bowenszhu]

OK. Thank you! @karlwessel