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Write an exponential of an arctangent algebraically at the question asked - #1917
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Rafael-SOWNet merged 7 commits intoOct 17, 2026
Merged
Rafael-SOWNet merged 7 commits into
Rafael-SOWNet merged 7 commits into
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…sked The rule that writes e^(n i arctan(L)) algebraically was reached only after the rules before it had spent the budget: Rubi's 5.3.6 e^(2 i atan(a + b x))/x^2 and e^(4 i atan(a x)) x^2/(c + a^2 c x^2)^9 ran out of time, where rewritten they are answered in half a second. It is now asked at the question asked as well, and beside a power of x and no quadratic it writes every n, not only +-1, as the two powers (1 + i L)^(n/2) (1 - i L)^(-n/2): as (1 + i L)^3 (1 + L^2)^(-3/2), e^(3 i atan(a + b x))/x was not answered. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…aN without Simplify The candidate search ran past a minute on the piecewise answer to e^(3 i atan(a + b x))/x^2, ready and checked at sampled points in a quarter of a second; InnerSimplified is what turns such an answer into NaN. Six more of Rubi's 5.3.6 are answered. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…y for an argument with a constant term For every n, the two powers ran out of time on `x^3 e^(-(3/2) i arctan(a x))` and `e^(3 i arctan(a x))/x`, which the root answers in under a second. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…n-inverse-is-written-algebraically-first # Conflicts: # Sources/AngouriMath/Functions/Continuous/Integration/Integration.Definition.cs
… rule leaves to the root Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
`x^2/e^((1/2) i arctan(a + b x))` was read as a pole and ran out of time as the two powers. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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.
e^(n i atan(a + b x))beside a power of x ran out of time in Rubi's 5.3.6. Three changes:(1 + i L)^(n/2) (1 - i L)^(-n/2), at the question asked, ahead of the rules that spent the budget. It is asked again in its usual place.withoutTheExponentialshas x in a denominator) and the argument has a constant term. Fora x, or for a polynomial beside the exponential, the root form stays: there the two powers ran out of time onx^3 e^(-(3/2) i atan(a x))ande^(3 i atan(a x))/x, which master answers in under a second.NaNwithInnerSimplifiedinstead ofSimplify. TheSimplifysearch ran past a minute on one of them.Rubi pocket (5.3.x and 5.4.x, 1774 rows, 5 s budget, fix arm run alone against the master run at bc175c2): master solves 1702, this branch 1719. Nothing is lost. Sixteen rows of 5.3.6 are gained (207, 216, 224–227, 253–256, 265, 270, 505, 506, 509, 510), plus 5.1.4:681, which master answers just past the budget. Families 0–8 sampled, the gate and the suite all passed on the chain for the branch's first commit. The later commits only narrow the rule back towards master on the rows it had lost.
All sixteen were
integral(...)on 2.5.0. Answer sizes now run from 175 to 35,041 characters. The largest ise^(3 i atan(a + b x))/x^4.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura