Split a root of a product beside a root of one of its factors

[Rafael-SOWNet]

(P Q)^r is K P^r Q^r, where K = (P Q)^r/(P^r Q^r). It is the same constant-K argument as #1875: K is constant wherever it is defined. The rule applies when P^s is another factor of the integrand, so the powers of P gather. For example, (a + b x^2)^(5/2)/sqrt(a^2 - b^2 x^4) is K (a + b x^2)^2/sqrt(a - b x^2), which the chain already answers. Q comes from the existing exact multivariate division, and the rule reads only factors of the integrand, only at the question asked.

Corpus, measured against the #1875 commit (the same code as master 7df6694):

Set	before	this
pocket (1.3.2, 4.1.12, 1.2.2.3, 4.1.0, 4.1.7, 4.1.1.2)	2,060 / 2,160	2,072 / 2,160
families 0–8, sampled	—	equal, except family 1 +2

• 12 moves, all Unsolved → Solved: 1.2.2.3:282–293.
• 0 wrong, and no move the other way. The gate and suite pass.
• The answers are 0.6–6.5K chars, the same size as master's answers to the split integrands, which are piecewise in the signs of a and b.
• Exact checks: 12 rows, pins (a, b) = (2, 3), (2, −3) and (−2, 3), 5 points on both sides of each factor's zeros. The residual is 0 at 50 and 2,000 digits.

Part of #718

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura