An odd half power of a quadratic with i in it is reduced as one without

[Rafael-SOWNet]

Part of #718.

sqrt(3 i x + 4 x^2) was answered and (3 i x + 4 x^2)^(5/2) declined, with the rest of the odd half powers of a quadratic with i among its coefficients:

integrand	master 15aae3d3	this
(3 i x + 4 x^2)^(5/2)	declined	203 characters
1/(3 i x + 4 x^2)^(7/2)	declined	149 characters
(1 + i x + x^2)^(3/2)	declined	148 characters
x (1 + i x + x^2)^(3/2)	declined	176 characters

What changes. SolveAPolynomialTimesAnOddHalfPowerOfAQuadratic reduces P Q^(m/2) to R Q^(k + 1/2) + K/sqrt(Q) by one linear solve, and declined any coefficient off the real line. The solve is exact whatever the coefficients are, the table answers K/sqrt(Q) off the real line as on it -- as a logarithm -- and the answer is differentiated back at sampled points before it is returned, so the guard declined nothing it had to. It is gone.

Tests: HalfOddPowerOfAQuadraticOffTheRealLineIntegralTest, five rows, differentiated back at real points and compared as complex numbers.

Measured on the 1,017 corpus problems with i and a root in the integrand, at the corpus's 5-second budget, against master 221d3c5f:

	master	this
solved	797	803
unevaluated	71	66
wrong	1	1
unverifiable on the reals	29	29
past the budget	119	118

One answer is counted wrong on each build.

The 7 problems the two builds disagreed on, run again one build at a time: master answers none of them, declines 6 and runs past the budget on 1; this answers 6 and runs past the budget on 1.

The suite on the commit measured, d75d5841, passes, 15,048 tests, and so does the allocation gate: every gated benchmark allocates what the baseline says. The head here, fb50974c, merges master 15aae3d3; the calculus and corpus tests pass on it, 4,363 tests, and the library builds for netstandard2.0.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura