[Rafael-SOWNet]

Part of #233.

• A rational function over a binomial of degree three or four beside other factors, split over them. TrySplitOverWrittenFactors read linear and quadratic factors only, so two shapes were declined for want of a split:

  • the tangent's 1/((a + b u^3) (1 + u^2)), from Rubi's 4.3.7 1/(a + b tan(c + d x)^3);
  • the root of the sine's 2 u/((a + b u) (1 + u^4)), from 6.1.7's sech(c + d x)/(a + b sqrt(sinh(c + d x))).

  The system reads any degree, and the decomposition is checked at sampled points before it is returned. It now admits one binomial of degree three or four, written once, beside factors of degree one or two. The rules for a polynomial over a binomial answer the pieces.

• Not beside a power of the variable alone, nor beside a second such binomial. Its first chain found two shapes it must not take:

  • The cube root's substitution makes Rubi's 1.1.3.4 x^m (a + b x^3)^(1/3)/(c + d x^3) a rational function over u^3 (c + (a d - b c) u^3), or over (b u^3 - 1) (c + (a d - b c) u^3). Their numerators hold a^9 c^36 d^9 and a^17 b^16 c^43.
  • Split, nine of those came back two to nine times longer, and three were wrong in the corpus's judgement. (a + b x^3)^(1/3)/(x^5 (c + d x^3)) took 12,377 characters, where the rules for the cube root write 1,964.

  Fenced, all nine are master's answers to the character, and a test pins two of them by value and by size.

Chain against master 2a98be4, after the fence:

• The pocket of 3,508 rows went from 3,490 to 3,494 solved, with 0 wrong.
• Every family's sample is unchanged.
• The 4 rows that moved, run alone, went from 0 to 4 solved: 4.3.7:469/470 and 6.1.7:487/493.
• 9,027 rows were compared for allocation, and none grew past 1.3x and 300 MB.

The full unit suite passes locally: 16,555 passed, 0 failed. The BREAKING-CHANGES lengths were measured on the branch. Rebased onto 78cd31b.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura