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Take a constant with a minus written in it out of a fractional power for either sign - #1986
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Rafael-SOWNet merged 1 commit intoOct 21, 2026
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…for either sign DistributeAFractionalPower writes (c g)^b as c^b g^b provided c > 0. For c = -k that arm is k < 0, so (a + b tan(x))/sqrt(-k tan(x)) was answered for k < 0 only, though the integrand is real for k > 0 wherever tan(x) < 0. Where exactly one symbolic constant comes out and a negative number is written in it, the rule also takes it out as (-c)^b (-g)^b with -c > 0, which holds on the principal branch for any g, and the answer is the piecewise of the two arms. A constant written without a minus, as in sqrt(b sec(x)) or sqrt(a - a sin(x)), keeps its one arm. Rubi's 4.3.2.1:670 is answered for both signs of k, checked by quadrature on an interval where -k tan(x) > 0 for each. 300 solved neighbours with a symbolic constant under a fractional power answer as before, character for character. 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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October 29, 2026 00:44
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DistributeAFractionalPowerwrites(c g)^basc^b g^b provided c > 0. Forc = -kthat arm isk < 0, so(a + b tan(x))/sqrt(-k tan(x))was answered fork < 0only. The integrand is real fork > 0too, wherevertan(x) < 0, and there the answer had no value.Where exactly one symbolic constant comes out and a negative number is written in it, the rule now also takes it out as
(-c)^b (-g)^bwith-c > 0, which holds on the principal branch for anyg. The answer is the piecewise of the two arms. A constant written without a minus, as insqrt(b sec(x))orsqrt(a - a sin(x)), keeps its one arm, which leaves solved rows as they are. Widening this to every symbolic constant would add a second arm to every existingprovided c > 0answer, and is not done here.Measured on
8270086f, branch against master:Re-run alone, 4.3.2.1:670 goes from an answer for one sign to a verified answer, in 186 ms. The other two moves, 4.3.1.2:109 and 7.4.1:369, come out the same on both builds.
sqrt(-k tan(x)),1/sqrt(-k tan(c+dx)),(-k cot(x))^(3/2)and their kin are answered at both signs; master answers each only fork < 0. Quadrature agrees on intervals where-k tan(x) > 0: fork = 0.9on [1.4, 2.5], and fork = -0.9on [0.1, 1.1].Of 300 solved neighbours with a symbolic constant under a fractional power, every one answers as before, character for character. None of the problems answered on both builds allocates more on the branch. No run had a wrong answer.
ANegatedConstantTakenOutOfAFractionalPowerIntegralTestdifferentiates the answers back at both signs ofk.BREAKING-CHANGES.mdhas the entry, with the 2.5.0 column measured on v2.5.0.Part of #233.
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