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Split a symbolic power of a product beside a symbolic power of one of its factors - #1887
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Rafael-SOWNet merged 3 commits intoOct 14, 2026
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(P Q)^r is K P^r Q^r with K constant between the zeros of P and Q for any exponent free of x, not only a rational one: K is exp(2 pi i n r) for a whole n. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…-a-product-splits-beside-a-power-of-a-factor
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Part of #718
SolveBySplittingARootOfAProductBesideARootOfAFactor(#1876) wrote(P Q)^rasK P^r Q^ronly for a rationalr.K = (P Q)^r/(P^r Q^r)isexp(2 pi i n r)for a wholenthat is constant between the zeros ofPandQ, so the split holds for any exponent free of x. It now gathers symbolic exponents as well. In Rubi's 1.2.1.2:2389,(d + e x)^(-3 - 2p) (a d e + (c d^2 + a e^2) x + c d e x^2)^p, the radicand is(d + e x)(a e + c d x). Split, the powers ofd + e xgather into(d + e x)^(-3 - p) (a e + c d x)^p, which master already answers.Measured
intbench, this branch against master acd4702, 5 s budget. The pocket was 1.1.1.2–1.1.1.4, 1.2.1.2–1.2.1.4, 1.2.2.3 and 1.3.2 in full (10,159 rows), plus the usual family sample:
11 rows moved, all from unsolved to solved and all held when re-run alone; none went the other way:
(1 - x^4)^n/(1 + x + x^2 + x^3)^nEvery new answer was checked exactly with
exactcheck(exact pins, 50 and 2,000 digits, four points, three pin sets): 240 of 240 diff 0. The gate and the suite pass (15,385).The pins keep every exponent's denominator even. With
p = 3/10the check fails. The evaluator reads(-3.35)^(-18/5)as a real root but(-3.35)^(-3/10) (-3.35)^(-33/10)on the principal branch, so gathering powers of one base is not exact for it. Master's own normalisation does the same:(d + k x)^(-3 - 2p) (d + k x)^p (a k + c d x)^pfails there identically. I've added the measurement to #204.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura