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Write each linear once under a symbolic power - #1974
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Rafael-SOWNet merged 1 commit intoOct 20, 2026
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A product of powers of quotients of linears whose exponents carry a symbol, e^atanh(a x) x^m sqrt(c - a^2 c x^2) or e^(2 p atanh(a x)) (c - a^2 c x^2)^p, was declined or ran out of time: the rule that writes each linear once reads rational exponents only. Each linear's exponent is now the symbolic sum of those it has in the bases, and K, the integrand over that product, has a logarithmic derivative of zero on every branch, so it stands in front. Only where the product is one power that is not whole beside whole ones; the answer is checked at sampled points. Rubi pocket (1,818 rows of 7.3.x and 7.4.x): 1726 -> 1748 solved, none lost; the moves re-run alone gain 22 rows of 7.3.6 and 7.4.2. Samples of every family unchanged. Part of #233. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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A product of powers of quotients of linears whose exponents carry a symbol, such as
e^atanh(a x) x^m sqrt(c - a^2 c x^2)(which issqrt((1 + a x)/(1 - a x)) x^m sqrt(c - a^2 c x^2)) ore^(2 p atanh(a x)) (c - a^2 c x^2)^p, was declined or ran out of time. The rule that writes each linear once reads rational exponents only.Each linear's exponent is now the sum, symbols and all, of the exponents it has in the bases.
K, the integrand over that product, has a logarithmic derivative of zero on every branch, so it stands in front of the answer. The rule applies only where the product comes to one power that is not whole, beside whole powers of the other linears above the bar. On every interval between the roots the antiderivative is then a sum of powers of it, and it is checked at sampled points. Two powers that are not whole are left to the rules that answer them as a power of the quotient.Measured on
8a1ef454, branch against master:The 22 pocket gains go from unevaluated or timed out to answered in 8–137 ms when re-run alone on both builds: 7.3.6:856, 882, 1173–1175, 1179–1181, 1448 and 1680–1683, and 7.4.2:228, 422, 423, 841, 842, 876, 877, 1011 and 1037. None goes the other way.
The five sampled problems that master answered and the branch did not (3.2.1:152 and 292, 6.6.1:25, 7.3.5:50 and 7.4.1:369) are the ones master answers in 17–25 s, against a 5 s budget. Re-run alone, master times out on four of them, and the branch answers three of those and 7.4.1:369. No run had a wrong answer.
EachLinearWrittenOnceUnderASymbolicPowerIntegralTestdifferentiates the answers back, with ten points on both sides of every root.BREAKING-CHANGES.mdhas the entry, with the 2.5.0 column measured on v2.5.0.Part of #233.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura