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Answer a difference of two cubes where the sampled check cannot tell - #1907
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Rafael-SOWNet merged 3 commits intoOct 16, 2026
Merged
Rafael-SOWNet merged 3 commits into
Rafael-SOWNet merged 3 commits into
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With a negative second cube the real cube root makes all three quadratics complex at the pinned values, the intervals settle too few points, and 8 x^2/(8 a x^3 - b (x^2 + 1)^3) -- which 1/(a - b cosh(x)^3) is under u = e^x -- was refused where its + b twin was answered. The answer is now refused only where it differs. Rubi's 6.2.7 1/(a - b cosh(x)^3) was declined. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…-cubes-is-split-over-the-cube-roots-of-unity
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.
1/(a - b cosh(x)^3)is8 u^2/(8 a u^3 - b (u^2 + 1)^3)underu = e^x, a difference of two cubes.SolveAPowerOfXOverASumOfTwoCubes(#1895) splits it over the cube roots of unity correctly, for either sign of the second cube, and then refused its own answer. With the second cube negative, the real cube root makes all three quadratics' coefficients complex at the valuesDerivativeHoldsAtSampledPointspins. The intervals then settle too few points, so it reported neither agreement nor difference (holds = false,differs = false), and the rule declined. Its+ btwin was answered.The rule now refuses an answer only where it differs, through
DerivativeDiffersWhereReal. #1905 does the same for the same reason. This is the case #1905 left aside when it narrowed its own split ton >= 5: the rules before it write1/(a + b cosh(x)^3)in 655 characters, and this is their- bspelling.Checks
ASumOfTwoCubesIntegralTest: 3 more cases, the differences.Corpus, measured against master 55a8044 (this branch then merged 90c9d3e):
Three other rows disagreed in the chain (1.3.1:568, 4.1.7:286, 4.1.7:326). Each fails on both arms re-run alone. No losses. Gate passed; suite 15,416 passed, 0 failed.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura