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Implement multivariate polynomial factorization via Hensel lifting

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Replace the stub factor_n_sqf_pp (TODO: invoke Dejan's procedure) with a
working implementation using bivariate Hensel lifting:

- Evaluate away extra variables to reduce to bivariate
- Factor the univariate specialization
- Lift univariate factors to bivariate via linear Hensel lifting in Zp[x]
- Verify lifted factors multiply to original over Z[x,y]
- For >2 variables, check bivariate factors divide the original polynomial

Tests: (x0+x1)(x0+2x1)(x0+3x1) now correctly factors into 3 linear factors.
All 89 unit tests pass in both release and debug builds.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
This commit is contained in:
Lev Nachmanson 2026-03-21 12:27:02 -10:00 • committed by Lev Nachmanson
parent a00ac9be84
commit 3e5e9026d8
3 changed files with 437 additions and 22 deletions
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src/math/polynomial/README
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Polynomial manipulation package.
It contains support for univariate (upolynomial.*) and multivariate polynomials (polynomial.*).
Multivariate polynomial factorization does not work yet (polynomial_factorization.*), and it is disabled.
Multivariate polynomial factorization uses evaluation and GCD recovery: evaluate away extra variables
to get a univariate polynomial, factor it, then recover multivariate factors via GCD computation.