NormalizePolynomialDim0(f, rc, R)

We consider two bivariate polynomials and want to compute their common solutions

We first compute their subresultant chain using FFT techniques

We deduce their resultants

We observe below that no root of r2 cancels the leading coefficients of f1 or f2. Hence, any roots of r2 can be extended into a solution of the system by a GCD computation.

We define the regular chain consisting of r2

We compute the GCD of f1 and f2 modulo r2

We normalize this GCD w.r.t. r2 which leads to a simpler expression with one as leading coefficient  

NormalForm, NormalFormDim0, NormalizeRegularChainDim0, ReduceCoefficientsDim0, RegularChains