A piecewise is defined where the case it takes is

[Rafael-SOWNet]

Fixes #1817. Part of #718.

A piecewise is defined where the case it takes is, but its DomainCondition was the disjunction of the predicates and the domain condition of every child, and c < 0 is defined only where c is real:

	2.5.0	master c21de3ef	this
piecewise(1 provided not i in RR, 2 provided i < 0)	false	false	true
piecewise(2 * x provided not x = 0, 3 * x ^ 2 provided i - 1 < 0)	false	false	not x = 0

Piecewise.InnerSimplify already passes over a predicate that evaluates to NaN; the domain condition did not. It reached integration through substitutions that carry the domain condition of the answer they found back with them: 1/(sqrt(a + i a x) (c + d x)^(3/2) (a - i a x)) is answered on master with an arm for each sign of a discriminant and one for its not being real, under provided ... and 8 a^3 c - 8 i a^3 d in RR -- an answer with no value at any real point. It is answered here, 3,267 characters, and differentiates back.

What changes. DomainCondition of a Piecewise is now the disjunction over its cases of: the case's predicate, its expression's domain condition, and for every earlier case, that its predicate does not hold or has no value. A case whose predicate evaluates to NaN or false is never taken and is left out. The earlier cases are kept in each term so that a case taken where its expression is undefined leaves the piecewise undefined there: piecewise(1/x provided x > -1, 0 provided true) is undefined at 0, not defined because the second case would hold.

Tests: UndefinedPiecewiseConditionTest gains the domain of four piecewises, one with an arm for a quantity off the real line at two points, and the first-case-decides case above at three.

Measured on every corpus problem with i in its integrand, 2,253 of them, and on the Rubi corpus, against master c21de3ef at the corpus's 5-second budget: no verdict changes anywhere -- 2,002 solved on both in the pocket, 1782, 1341 and 2328 in families 0, 1 and 2 to 8 sampled -- and the time on the problems both answer is the same, 2,099 seconds and 2,097.
The suite passes on 2d3bf4e9, this change on c21de3ef: 15,146 passed, 13 skipped, none failed. Rebased onto 77899a6f without a conflict, the domain and piecewise tests pass again. The allocation gate passes: every gated benchmark allocates what the baseline says. The library builds for every target.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura