What a reduction leaves over its block is integrated in named coefficients

[Rafael-SOWNet]

Part of #718.

Two reductions integrate what they leave over a block using coefficients they computed, such as (a^2 g - 3 a b d + 6 b^2 c)/a^2:

• the split at a power of x beside a block;
• the one that takes a polynomial over a power of a trinomial in x^n down to its first power.

The substitution search spent up to a minute simplifying quotients in those coefficients before another rule answered. Now each compound coefficient is a fresh symbol while the rest is integrated, and the original is put back into the answer.

The x-route's rest still tries #1843's split at another linear first. The merge with master keeps both: the split at another linear runs first, then the integration in named coefficients.

Corpus, against master 2be3573 (a Rubi pocket of 14,158 problems, families 0–8 sampled):

	solved	wrong	timeout
master	13,996	0	55
this branch	14,009	0	41

Fourteen problems moved, all timeouts on master; this branch solves 13 of them:

• 1.1.3.8: 393, 394, 408 and 410
• 1.1.3.4: 141
• 1.2.2.5: 52, 66–70 and 83
• 4.1.7: 298

The fourteenth, 4.5.7:537, is answered by #1843 and still is after the merge. Every family file agrees between the two arms. The allocation gate and the suite (15,206 passed) are green.

Sizes. The 1.1.3.8 answers are 547 to 1,859 characters, where master's slower ones were 832 to 2,117. The answers over a power of the trinomial are 22,000 to 98,000 characters, against master's 45,000 to 152,000 where it answered at all.

One answer grew. 1/(x^7 (a + b x^3)(c + d x^3)) took master 52 s and came to 14,565 characters; now it takes 6 s and comes to 265,499. csc(c + d x)^2/(a - b sin(c + d x)^4)^3 is 157,787 characters, where master gave nothing within two minutes. Both are verified numerically by the corpus harness. They are listed in the BREAKING-CHANGES entry with their sizes.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura