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Divide out a constant common to the denominator after the half-angle substitution - #1927
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Rafael-SOWNet merged 5 commits intoOct 17, 2026
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…substitution The rational function of t = tan(x/2) is written over the denominator's leading coefficient with each coefficient in lowest terms over the symbols. With k^2 left in the coefficients of 1/(k + k sin(x))^2 the rules below formed k^2/k^2, which the simplification does not cancel, so the quadratic's discriminant was not decidably zero, and x/(k + k sin(x))^2 was answered NaN through a branch of the piecewise that can never hold -- and so was Rubi's 5.1.4 (a + b asin(c x))/((d + c d x)^(5/2) sqrt(f - c f x)), which comes to it. 1/(d c + c d sin(x))^2 is 143 characters where it was 2166. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…nstant times numbers Written so for every integrand, fifteen Rubi 4.x problems the half-angle answered in a second timed out. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…alf-odd-power-pair-is-not-nan
…ING-CHANGES Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…alf-odd-power-pair-is-not-nan
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Part of #718.
After the half-angle substitution,
x/(k + k sin(x))^2has the denominatork^2 (t + 1)^4: a constant times a polynomial with number coefficients. The constant is now divided out before the partial fractions.WithTheLeadingCoefficientDividedOutdoes this only when every denominator coefficient, divided by the leading one (withInLowestTermsOverTheSymbols), is a number. A first version normalised every half-angle denominator, and a chain measured that it put 15 rows of family 4 into timeout or unsolved; the narrowing removes all 15.Master answers these wrongly, as
NaN. At 67d8e8d,x/(k + k sin(x))^2,x/(d c + c d sin(x))^2and Rubi's 5.1.4:650,(a + b asin(c x))/((d + c d x)^(5/2) sqrt(f - c f x)), come back asNaN(for 5.1.4:650 the harness marks it WRONG). 2.5.0 left all three asintegral(...). With this branch they are answered in 285, 329 and 927 characters.Rubi chain (master arm at adba48c, 5 s budget):
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura