[Rafael-SOWNet]

Part of #233.

Fourteen shapes of Rubi's family 1 and the Welz suite. The BREAKING-CHANGES entry lists each with its rule and an example. Among them:

• a half-odd power of x beside binomials in x^2;
• a rational function of a quadratic beside a half-odd power of it, under t = Q'/sqrt(Q);
• two equal half-odd powers of linears beside a power of a quadratic, as one power of their product;
• cube roots of two linears whose product is a quadratic;
• a power below −1 of a cube root of a binomial, divided out first.

Chain against master f7f2a7a, with the harness at its current revision on both arms:

• pocket of 988 rows: 923 → 954 solved, 0 wrong;
• samples: family 0 whole 1,805 → 1,807, family 1's sample 1,375 → 1,376, the rest unchanged;
• the 33 rows that moved, alone: 1 → 33 solved, each within 1.1 s. They span 1.3.2 (12 rows), 1.1.3.4 and 1.2.2.3 (4 each), 1.1.1.3 and 1.2.1.4 (3 each), Welz (2), and one each of 1.1.3.2, 1.1.3.3, 1.1.4.2, 1.2.1.6 and 1.2.2.2;
• no row's allocation grew past 1.3×.

The entry's "Now" lengths and its comparison with the unreleased master are re-measured on this build and on f7f2a7a. One answer is longer than master's: x^(7/2)/((a + b x^2)(c + d x^2)^2) is 1,246 characters here against 799 there. 56 tests pass locally across its test classes and the corpus gate.

Fixed after the first CI run, which failed two existing tests that this branch's local run had not included:

• A wrong answer. SolveByScalingTheVariableToNumbers multiplied two roots that scale to one polynomial into that polynomial. 1/(sqrt(-2 - b x) sqrt(2 + b x)) then came back with the opposite sign where 1 + b x/2 < 0, which is where PowersOfOneLinearAsOnePowerIntegralTest samples. The rule now declines that case, and master's answer stands.
• A longer answer. The rule under t = Q'/sqrt(Q) ran ahead of master's reduction over a power of the quadratic, and wrote 4,428 characters for 1/((d + b x + c x^2)^3 sqrt(a + b x + c x^2)) where the reduction writes 1,379. It now runs after the reduction, and answers the fifth power, which the reduction declines.

Re-chained against master f7f2a7a:

• The pocket went from 921 to 953 solved, with 0 wrong.
• Of the 34 rows that moved, run alone, master solved 1 and this branch solves all 34.
• 6,453 rows were compared for allocation, and none grew past 1.3x.

The full suite passes locally: 16321 passed, 0 failed. The branch is rebased onto 47ab958.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura