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ByMonicisation​(AngouriMath.​Functions.​MultivariatePolynomial,​System.​Int32,​System.​Int32,​System.​Int32)

 Method (no overloads)

Summary

The factorisation of a polynomial whose leading coefficient in
main is not a constant, by making it one.

Remarks

This is Wang's leading-coefficient problem, and the answer here is not Wang's.
His is to factor the leading coefficient and distribute its factors among the lifted
ones, which needs a way to tell which goes where. The older answer needs none:
g(z, y) = L^(n-1) · f(z/L, y) = Σ a_i L^(n-1-i) z^i is a polynomial, because
n - 1 - i is never negative below the leading term, and it is monic in
z, because the leading term contributes L · L^(-1). A monic polynomial
has a constant leading coefficient, which is the case the lift already handles.
 A factor h(z, y) of the monic form comes back as h(L·x, y) with its
content in y divided out — the substitution multiplies the coefficient of
z^j by L^j, and the content is what that puts in and the original never
had.
 The cost is that deg_y g grows by up to (n-1)·deg_y L, so the lift is
deeper and the polynomial larger. Nothing is asserted about staying inside
MultivariatePolynomial's bounds: the construction returns
null when it leaves them, which is a refusal.

























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