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Ask the radicand rule's rewriting without the condition its inner simplification writes - #2045

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ask-the-radicands-rewriting-without-its-condition
Oct 22, 2026
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Part of #233.

  • A pair of linear roots written over the radicand of an inverse hyperbolic cosine, asked without the condition it gained. Rubi's 7.2.5 x/(acosh(x) sqrt(x - 1) sqrt(x + 1)) ran past the budget. SolveByWritingAConstantMultipleOfARadicandOverIt writes the pair as the root of x^2 - 1 that acosh(x) holds, times a factor K that is constant where it is defined.
  • Why it stalled. The rewritten question was inner-simplified, which wrote provided not x - 1 = 0 over the whole of it. The integrator declines f provided C, and nothing below read the condition. The point it excludes is outside the integrand's domain anyway.
  • The change. The rewriting is handed on bare (PartialFractions.Bare), as SimplifiedWithoutTheImaginaryUnit already does elsewhere. A derivative check was tried as well. It cost three 5.1.4 rows their budget and was dropped.
Rubi row master ef4150e this branch
7.2.5:408 x/(acosh(x) sqrt(x - 1) sqrt(x + 1)) declined, 2.0 s and 0.57 GB 93 characters, K Chi(acosh(x)), 0.7 s and 0.04 GB

Chain against master 78cd31b:

  • The pocket of 4,289 rows went from 4,286 to 4,287 solved.
  • Every family's sample is unchanged.
  • The one row that moved is 7.2.5:408, run alone: declined on master, solved here.
  • The allocation check flagged 7.1.4:670 at 3.9x (0.14 to 0.55 GB). Run alone twice on each build, it is 0.56 GB on both. The chain's 0.14 was a warm cache.

The suite is left to CI. The BREAKING-CHANGES length was measured on the branch. Rebased onto ef4150e.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

…plification writes

Rubi's 7.2.5 x/(acosh(x) sqrt(x - 1) sqrt(x + 1)) ran past the budget.
SolveByWritingAConstantMultipleOfARadicandOverIt writes the pair of roots as
the root of x^2 - 1 that acosh(x) holds, with the constant factor K, and the
inner simplification of the rewriting put provided not x - 1 = 0 over the
whole of it: the inverse hyperbolic substitution did not read the condition,
and the search split the sum and went by parts. The point it excludes is
outside the integrand's domain, and the question is now asked bare. (A
derivative check on the rule's answer was tried and dropped: it took three
of Rubi's 5.1.4 arcsine rows, answered in 0.2 to 1.4 s, past the budget.)

Part of #233.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
@Rafael-SOWNet Rafael-SOWNet added this to the 2.6.0 milestone Oct 22, 2026
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Rafael-SOWNet merged commit e006a79 into master Oct 22, 2026
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@github-project-automation github-project-automation Bot moved this from Todo to Done in AngouriMath Oct 22, 2026
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Rafael-SOWNet deleted the ask-the-radicands-rewriting-without-its-condition branch October 29, 2026 00:43
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