[Rafael-SOWNet]

limitright(ln(x^x), x, -1) was ln(-1), which is i pi, where the limit is -i pi. As x comes down to -1, x^x comes to -1 from below the cut, and the principal logarithm is continuous on its cut from above only. Its value there is the limit along the real line and from above, and it was given as the limit from either side.

ArrivesOnTheCutOffTheRealLine asks whether a logarithm's argument, or the base of a power to an exponent that is not whole, tends to a negative real without being known to arrive there along the real line. A power's base and a logarithm's argument count as positive where their values at the destination are positive. This PR does not decide which side such an argument comes from, so a limit there is declined, wherever it was read: in substitution, the logarithm's and the power's descent, SolveAsLogarithm, the quotient of logarithms, and Gruntz, whose series took the principal logarithm of a negative coefficient.

Input	2.6.0 and master	Now
limitright(ln(x^x), x, -1)	ln(-1), which is i pi	unevaluated; the limit is -i pi
limit(ln(x^x), x, -1)	ln(-1)	unevaluated; there is no limit
limitleft(ln(-1 + i*x), x, 0)	ln(-1)	unevaluated; the limit is -i pi
limitright(sqrt(x^x), x, -1)	i	unevaluated; the limit is -i
limitleft(ln(x^x), x, -1)	ln(-1), which is right	unevaluated

Two costs:

• A limit from above is declined too, though its answer was right (the last row). Keeping those answers needs the side decided. For a logarithm, sampling the imaginary part could decide it. For (-1 + i x)^(1/3) it would not help, because this library's value of a cube root on the negative axis is the real root, not the principal one.
• A decline can be slow under Simplify. limitright(ln(x^x) / x, x, -1) takes 6.9 s, where master answered it wrongly in 44 ms. InnerSimplified declines in 0.4 s, and the rest is Simplify asking every candidate form again.

LimitOnABranchCutTest: 11 of its cases fail on master, and the 9 along the real line pass on both. The suite (18,366), the trio, F#, AOT and the eight harnesses pass locally on the rebased branch. Composed with #2268, #2275 and #2276, work/limitcheck no longer finds any of the 56 limits that master answered with a different value, out of 600 expressions.

#2278 removed the stack overflow this change first ran into.

Part of #2266.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 79.16667% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.70%. Comparing base (6cabd96) to head (74db309).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...ath/Functions/Continuous/Limits/Transformations.cs	75.86%	3 Missing and 4 partials ⚠️
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	75.00%	0 Missing and 3 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2294      +/-   ##
==========================================
- Coverage   86.71%   86.70%   -0.02%     
==========================================
  Files         310      310              
  Lines       67873    67918      +45     
  Branches    19703    19724      +21     
==========================================
+ Hits        58858    58889      +31     
- Misses       4891     4901      +10     
- Partials     4124     4128       +4     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.25% <79.16%> (-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
...iMath/Functions/Continuous/Limits/Gruntz/Gruntz.cs	77.57% <100.00%> (+0.27%)	⬆️
...nctions/Continuous/Limits/Solvers/Limit.Solvers.cs	85.71% <100.00%> (+0.50%)	⬆️
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	71.49% <75.00%> (+0.73%)	⬆️
...ath/Functions/Continuous/Limits/Transformations.cs	87.52% <75.86%> (-0.26%)	⬇️

... and 8 files with indirect coverage changes

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