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Ask a hyperbolic quotient over a quadratic in its sine or cosine as the sine's, before the tangent - #2042
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Rafael-SOWNet merged 1 commit intoOct 22, 2026
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…he sine's, before the tangent Rubi's 6.7.1 sinh(x)^2/(a + b sinh(x) + c sinh(x)^2) ran past the budget in SolveARationalFunctionOfTheHyperbolicTangent: under the tangent of the half argument it is a quartic with symbols in it, and the partial fractions over it did not return. Under Osborn's rule it is a rational function of a sine over a symbolic quadratic in it, which SolveARationalFunctionOfASineOverASymbolicQuadratic answers at once; the Osborn rule asked it only after the exponential substitution had declined, and the tangent is before both. A mode of the Osborn rule now asks that one rule directly, cheap to decline, ahead of the tangent. 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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…, before the tangent (#2053) Rubi's 6.2.5 sech(x)^3/(a + b cosh(x)) and 6.5.3 sech(x)^4/(a + b sech(x)) ran past the corpus's budget. SolveARationalFunctionOfTheHyperbolicTangent answered each under the tangent of the half argument, a cube of 1 + t^2 beside a symbolic quadratic, in about 118,000 characters. By Osborn's rule each is a rational function of a cosine alone over a sum linear in it, which partial fractions in the cosine answer: 1/(cos(s)^3 (a + b cos(s))) is 2,121 characters. A third mode of SolveAHyperbolicIntegrandAsATrigonometricOne asks that question beside #2042's, ahead of the tangent, only where s stands in cos(s) alone and the sums below the bar are linear in it, to the first power: over the square of one, written out, 6.7.1's (a + b cosh(x))/(b + a cosh(x))^2 took four times the memory in s. The answer in s goes back as the rule writes every one, and is checked by its derivative. Part of #233. Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura Co-authored-by: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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Part of #233.
sinh(x)^2/(a + b sinh(x) + c sinh(x)^2)ran past the budget inSolveARationalFunctionOfTheHyperbolicTangent. Under the tangent of the half argument it is a quartic with symbols in it, and the partial fractions over it did not return.SolveARationalFunctionOfASineOverASymbolicQuadraticanswers at once. But the Osborn rule asked it only after the exponential substitution had declined, and the tangent comes before both.i/slopestays out of the question, which the sine's rule reads without it.sinh(x)^2/(a + b sinh(x) + c sinh(x)^2)sinh(x)^3/(a + b sinh(x) + c sinh(x)^2)cosh(x)^2/(a + b cosh(x) + c cosh(x)^2)Chain against master 78cd31b:
The full unit suite passes locally: 16,552 passed, 0 failed. The BREAKING-CHANGES lengths were measured on the branch. Rebased onto 86fb398.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura