[Rafael-SOWNet]

Part of #2134: its second row. The first row, a condition left out, is the question #1648 decides.

The defect: PolynomialLongDivision divides by the divisor's leading coefficient. Its first attempt, on the pair as written, declines a symbolic one for the simplifier, since a quotient that loses a value of a parameter is not an equivalence. The second attempt, with the variables replaced by temporaries, has no such guard. It predates the guard, and #1269 left it as it was.

(t x + y)/(1 - y x) divided there in y gives -1/x + (t x + 1/x)/(1 - x y). That is undefined at x = 0, where the divisor is 1, and Simplify passed the condition on:

Simplify	2.6.0	this PR
-(t*x + y)/(1 - y*x) + (t*x + y)/(1 - y*x)	0 provided not 1 - x * y = 0 and not x = 0	0 provided not 1 - x * y = 0

At x = 0 the input is -y + y, so the old answer was undefined at a point where the input is defined.

The change: the replaced attempt now also declines a symbolic leading coefficient, where the divisor has more than one term in the variable.

A divisor of one term, a x^k, is still divided. It is zero wherever its coefficient is, so dividing by that coefficient loses nothing the input had. That case is load-bearing: the limit of (tan(a x) - sin(b x))/(a x) at 0 reaches (a - b)/a through it. Without it the limit comes out 1 - b/a, because Simplify does not put 1 - b/a over one denominator (#2137).

Checked:

• SimplifiedConditionNotStricterTest evaluates the answer at x = 0, y = 2, t = 3 and expects 0. The old answer gives NaN there.
• Unit suite: 17,130 passed, 0 failed.
• SimpSweep: 10,463/10,463 agree.
• CanonCheck: matches its baseline.
• BoundCheck: 0 disagreements.
• CasBench: 120/121, unchanged.
• BREAKING-CHANGES entry added, measured on the 2.6.0 package.
• codecov/project is red at −0.02% (5 hits fewer). The new guard returns before lines that tests used to reach, so that is expected. The status fails on any decrease at all, which is a configuration problem rather than a finding, and is taken up separately.

🤖 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 86.41%. Comparing base (689fd01) to head (d91296a).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2171      +/-   ##
==========================================
- Coverage   86.42%   86.41%   -0.02%     
==========================================
  Files         295      295              
  Lines       64806    64808       +2     
  Branches    19059    19060       +1     
==========================================
- Hits        56009    56004       -5     
- Misses       4768     4774       +6     
- Partials     4029     4030       +1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	86.98% <100.00%> (-0.02%)	⬇️
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
...AngouriMath/Functions/TreeAnalyzer/LongDivision.cs	90.21% <100.00%> (+0.21%)	⬆️

... and 7 files with indirect coverage changes

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