[Rafael-SOWNet]

Part of #2133: the part where the result depends on how a sum is written.

The defect: the gathered Pythagorean rule matches sin(x)^2 and cos(x)^2 wherever they sit in a sum, but only with a coefficient of 1. With a coefficient, the pair was left to SharedFactor, which sees two siblings only, so the order the sum was sorted into decided:

• y + (-2) cos(x)^2 + (-2) sin(x)^2 came out y - 2;
• 2 + (-2) cos(x)^2 + (-2) sin(x)^2, where the constant sorts between the two, stayed as written.

#2133's 2 + (-2) cos(2x) + (-4) sin(x)^2 opens to that second form and stopped there, while 2 - 2 cos(2x) - 4 sin(x)^2 reached 0.

The change: a second rule in the set, squared-sine-and-cosine-with-one-coefficient-sum-to-it. It gathers k sin(x)^2 and k cos(x)^2 with the same argument and the same coefficient, and writes k.

• It is Sound for every complex k and x, has a pattern on both sides, and its growth is Collects.
• It has no backwards reading, since it forgets the angle, as the first rule does.
• Unequal coefficients and different arguments are left alone: 2 sin(x)^2 + 3 cos(x)^2, and k sin(x)^2 + k cos(y)^2.

The census moves by one in WritingARule.md, in the remark in Saturation.cs, and in the tests that pin them. ReversibleRuleTest now checks every rule of the set, where it used Single().

Simplify	2.6.0	this PR
2 + (-2)*cos(x)^2 + (-2)*sin(x)^2	unchanged	0
2 + (-2) * cos(2 * x) + (-4) * sin(x) ^ 2	unchanged	0

Not in this PR: (cos(2x) - 1)^2 + sin(2x)^2 - 4 sin(x)^2 still stops at 2 + (-2) cos(2x) + (-4) sin(x)^2, which one more Simplify now takes to 0. That is #2133's main point, Simplify not simplifying its own answer. Making it iterate would cost every call whose answer differs from its input, so it needs its own measurement.

Checked:

• PythagoreanPairWithACoefficientTest: 8 rows. It includes Simplify can stop before its own answer is simplified #2133's two rational rows, which A sum of fractions that is a constant over one denominator simplifies to it #2174 answered.
• The intbench chain against master 966f26a9f: identical verdicts in all nine families, 0 moves.
• Performance gate: passed on all 19 gated benchmarks.
• Unit suite: 17,159 passed, 0 failed.
• RuleCheck passes; Confluence and CanonCheck match their baselines; SimpSweep 10,463/10,463.
• BREAKING-CHANGES entry added, measured on the 2.6.0 package.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.45%. Comparing base (966f26a) to head (20743ad).

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2175   +/-   ##
=======================================
  Coverage   86.44%   86.45%           
=======================================
  Files         295      295           
  Lines       64905    64930   +25     
  Branches    19092    19092           
=======================================
+ Hits        56108    56132   +24     
+ Misses       4770     4769    -1     
- Partials     4027     4029    +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.02% <100.00%> (+<0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...Math/Core/Transformations/Matching/MatchedRules.cs	99.57% <100.00%> (+<0.01%)	⬆️
...ces/AngouriMath/Core/Transformations/Saturation.cs	93.33% <ø> (ø)

... and 8 files with indirect coverage changes

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