[Rafael-SOWNet]

#1956 asks a function of the hyperbolic tangent in u = tanh(L). The rules in u answer on the real domain of the question in u, and tanh(L) takes only the values in (-1, 1). sqrt(1 - coth(x)^2), which is i |csch(x)|, is real in u only for |u| > 1. Its answer came back as two arms, for u <= -1 and u >= 1, and neither holds anywhere on the real line, so the answer had no value at any real x.

Written back in x, an answer that has no value at any sampled point where the integrand has one is now declined, and the rules in x answer as they did before #1956. The check is PartialFractions.SaysNothingWhereTheIntegrandIsDefined. It uses HoldsAtSampledPoints's pins and points, takes a value it cannot tell as a value, and stops at the first point where the answer has one. It evaluates under the settings the answer is returned in, because with the downcasting off a shared subtree kept a 1/1 that the answer then printed.

Measured on 8270086f, branch against master:

Run	Problems	Master	Branch
Pocket: all of Rubi's family 6	3,690	3,633 solved	3,635 solved
Family 1, 40 a file	1,381	1,368	1,368
Family 0, whole	1,814	1,789	1,789
Families 2 to 8, sampled	2,410	2,380	2,383

Re-run alone, Rubi's 6.4.7:31, 33 and 37 (sqrt(1-coth(x)^2), (1-coth(x)^2)^(3/2) and 1/sqrt(1-coth(x)^2)) go from an answer with no value to verified answers, in 0.5 s. Those answers are identical, character for character, to the ones before #1956. The other three moves, 3.2.1:292, 6.6.1:25 and 7.4.1:369, are answered on both builds in 16–24 s, against a 5 s budget.

Of 253 rows of 6.3.x and 6.4.x with roots or fractional powers of tanh or coth, only these three move, and #1956's 36 gained rows answer as on master. v2.5.0 declined all three, so BREAKING-CHANGES.md has no entry. No run had a wrong answer except 6.1.5:94 on both builds, the evaluator artefact of #1944.

This touches the same rule as #1982; whichever merges second takes one rebase. AFunctionOfTheHyperbolicTangentIntegralTest answers the three and differentiates them back at six points, negative x included, comparing complex values.

Part of #233.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura