[tombouctou]

Fixes most of #2071. The canonical order (Sort, Order, Orderless heads) now follows WMA 15 in three more ways.

1. Sums. A sum whose largest term is a monomial sorts with the monomials of its largest variable, after all of them. Its key is that variable to an infinite power (Expression._sum_element_order). Two such sums are compared term by term from the largest term down, and if one runs out first, it comes first.

Sort[{a, a + b, b, c, x}]                        {a, b, a + b, c, x}
Sort[{x, 1 + x, y, x^2, 1 + x^2, x y}]           {x, x^2, 1 + x, 1 + x^2, y, x y}
Sort[{f[x], 1 + x, g[x], a + b + c, h[a, b, c]}] {a + b + c, 1 + x, f[x], g[x], h[a, b, c]}
Collect[a x + b y + c x + d y, y]                a x + c x + (b + d) y

Monomial now handles two equal infinite exponents; before, inf - inf gave nan.

2. Symbols from other contexts. Symbols are ordered by their names without the context, and the full name only breaks ties (wma_symbol_sort_key). Before, Globalxcame beforeSystemPi:

x + Pi                   Pi + x        (was x + Pi)
Sort[{x, Pi, E, a, z}]   {a, E, Pi, x, z}

3. Coefficients. Monomials that differ only in a numeric coefficient are ordered by it: Sort[{x, -x, 2 x}] is {-x, x, 2 x}.

How much closer to WMA

I took 78 expressions (numbers, strings, symbols including Pi and E, monomials with coefficients, sums, products with general factors, general expressions) and computed Order for all 3003 pairs in WMA 15 and in Mathics3:

	pairs that differ from WMA
master	1152
this PR	425

767 pairs are fixed. 40 get worse, all of one kind: products with a factor that is not a symbol, such as Pi g[x] or Sqrt[Pi] Erf[1/x]. element_order skips such factors in a product. Before this PR, the context in SystemPihappened to hide that. WMA treatsf[x], Erf[1/x]andE^xas variables of the monomial. That is the next step, in a separate PR. Because of it,Integrate[Exp[-1/x^2], x]intest_calculus.pyis markedxfail, and one Hypergeometric1F1` doctest now shows the other order of its two terms.

Still left as before (listed in #2071):

• a sum whose largest term has a negative coefficient, such as 1 - x, or a sum with a negative constant: WMA puts these before their largest variable;
• powers and sums of general expressions, such as f[x]^2 and 1 + f[x].

Tests

• New test_canonical_order in test/builtin/test_testing_expressions.py: 16 cases with WMA 15 values; 13 of them fail on master.
• Doctests and tests whose expected output was the old order are updated (15 doctests, 8 test cases). I checked each new output against WMA 15. Where WMA simplifies differently (e.g. Sqrt[2/Pi] in BesselJ[1/2, x]), the order of the factors still matches WMA.
• Full run on kimmy: doctests 4622 passed, 0 failed. pytest with -n 4 --dist loadfile: 15 failed. They are in test_tensor.py, test_eol.py, test_latex.py and test_diffeqns.py, and those files pass on their own (test_diffeqns.py fails on master in the same run too). These are the order-dependent failures that master has as well.

The developer's guide page on the canonical order (Mathics3/Mathics3-development-guide#51) lists the place of sums as a difference from WMA; I'll update it there once this lands.

🤖 Generated with Claude Code

[tombouctou]

The 40 regressions listed above are fixed in #2074, stacked on this branch: factors such as f[x], Erf[1/x] and E^x become variables of the monomial, as in WMA. With both, Order differs from WMA 15 on 20 of the 3003 pairs (1152 on master), and the xfail added here is gone.

[rocky]

Yay! The whole str/symbol thing was a mistake (and it is also buried deep inside definitions) that I'd love to see corrected. This is a small step, but one in the right direction.

[rocky]

LGTM