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LiftPair​(AngouriMath.​Functions.​RationalPolynomial[],​AngouriMath.​Functions.​RationalPolynomial,​AngouriMath.​Functions.​RationalPolynomial,​System.​Int32)

 Method (no overloads)

Summary

g = A·B modulo y^depth, from
g(x, 0) = u·v.

Remarks

Writing the next pair as A + α y^k and B + β y^k and asking that the
product agree one power further leaves α·v + β·u = e, where e is the
coefficient of y^k in the error so far. The Bezout pair s·u + t·v = 1 answers it at once — α = e·t, β = e·s — and reducing α below the
degree of u, pushing the quotient into β, is what keeps each side at
the degree it started at. It is the same step as the p-adic lift in
PolynomialFactorization, over (y) rather than over a prime.
 The Bezout pair is computed once: neither side changes modulo y as it is
lifted, which is the whole reason the same pair keeps answering.

























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