Factor a sextic whose leading coefficient needs a monic scale past 2^512

[Rafael-SOWNet]

Part of #718.

To factor an integer polynomial with leading coefficient lc, the factorizer first makes it monic by rescaling the variable. That multiplies the coefficients by up to lc^(n-1), and past 2^512 it declined. Rubi's 1.3.1 rows 214–220 are x^k/((x^2 + 6)^3 + 324 x^3)^2. Hermite's reduction leaves a resultant to factor that is a sextic with a 107-bit leading coefficient, which needs 2^535. So the rows were declined, although the first power of the same denominator was answered.

The bound is now 2^1024 up to degree six and stays 2^512 past it. The first version raised it for every degree, and the chain caught 1/(1 + cosh(x)^5) going from 7 s to 72 s. That integral asks for 122 polynomials of degree eight and nine between 2^580 and 2^880, at about a second each, and uses none of them. With the bound tiered it is back to 7.4 s.

Measured

Pocket of 7,779 Rubi rows, 5 s per row, with both arms on master 34780ec:

	master	this branch
solved	7,699	7,706
wrong	0	0
timeout	15	15

All seven new answers (1.3.1:214–220) held when each row was rerun alone. They take 0.5–1.3 s at 372–394 characters, as sums over the roots of the sextic. 2.5.0 declined all seven. There are no losses in families 0–8 and no row is more than twice as slow. Rows both arms solve take 695 s against 696 s on master. The gate passes and the suite passes 15,393. Since then the branch has merged master cba4232; it builds for every target, and RothsteinTragerTest passes on the merge (17 tests).

BREAKING-CHANGES.md records the new answers.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura