The expanded terms of a sum are gathered again over a shared radical, and each group is asked as one term - #1310
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The expanded terms of a sum are gathered again over a shared radical, and each group is asked as one term#1310Rafael-SOWNet wants to merge 1 commit into
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… and each group is asked as one term
Hearn's `(-2 sqrt(1 + x^3) + 5x^4 sqrt(1 + x^3) - 3x^2 sqrt(1 - 2x + x^5))/(2 sqrt(1 + x^3) sqrt(1 - 2x + x^5))`
had no antiderivative. Expanded, it is `-1/sqrt(P)`, `5x^4/(2 sqrt(P))` and
`-3x^2/(2 sqrt(1 + x^3))`, and the first two are not elementary apart -- each is
an elliptic integral -- while together they are `P'/(2 sqrt(P))`, the derivative
of the root. When the expanded terms fail one by one, they are gathered again
by what is not polynomial in them and each group is asked as one term, its
polynomial parts added. At the top only, since each group is a search of its
own and one level down the sums are what by parts and the substitutions hand
on, where the groups cost sixteen seconds of the corpus for nothing; and only
where the gathering both joins and separates something, since every term in a
group of its own is the split that has just failed, and every term in one group
is the integrand that has just been asked.
## Measured
Every answer differentiated back.
Rubi corpus, 463-problem sample, on the same afternoon:
master at #1306 394/463, 0 wrong, 0 timeouts, 95 s
with this 395/463, 0 wrong, 0 timeouts, 95 s
One more, nothing lost: Hearn 232. The first draft was measured at 111 s, the
groups being asked one level down as well; the second at 106, one group being
the integrand asked again. Both bounds are what those measurements asked for.
The five test suites are green.
Part of #718.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Hearn's
(-2 sqrt(1 + x^3) + 5x^4 sqrt(1 + x^3) - 3x^2 sqrt(1 - 2x + x^5))/(2 sqrt(1 + x^3) sqrt(1 - 2x + x^5))had no antiderivative. Expanded, it is
-1/sqrt(P),5x^4/(2 sqrt(P))and-3x^2/(2 sqrt(1 + x^3)), and the first two are not elementary apart -- each isan elliptic integral -- while together they are
P'/(2 sqrt(P)), the derivativeof the root. When the expanded terms fail one by one, they are gathered again
by what is not polynomial in them and each group is asked as one term, its
polynomial parts added. At the top only, since each group is a search of its
own and one level down the sums are what by parts and the substitutions hand
on, where the groups cost sixteen seconds of the corpus for nothing; and only
where the gathering both joins and separates something, since every term in a
group of its own is the split that has just failed, and every term in one group
is the integrand that has just been asked.
Measured
Every answer differentiated back.
Rubi corpus, 463-problem sample, on the same afternoon:
One more, nothing lost: Hearn 232. The first draft was measured at 111 s, the
groups being asked one level down as well; the second at 106, one group being
the integrand asked again. Both bounds are what those measurements asked for.
The five test suites are green.
Part of #718.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura