/// <summary>
/// Assumes that this current basis is already minimal and converts it to reduced (from Definition 5 of section 2.7, CLO).
/// CAUTION - if basis is not already minimal, a non- descriptive exception will be thrown from somewhere in the monomial code.
/// Based on algorithm 2 from - https://www.kent.ac.uk/smsas/personal/gdb/MA574/week6.pdf
/// </summary>
public void MakeReduced()
{
var tempPolynomials = this.polynomialData.ToList();
Polynomial hi = polynomialData.ElementAt(0);
Polynomial gi;
tempPolynomials.RemoveAt(0);
for (int i = 0; i < tempPolynomials.Count; i++)
{
gi = hi.GetRemainder(tempPolynomials);
hi = tempPolynomials[i];
tempPolynomials[i] = gi;
}
gi = hi.GetRemainder(tempPolynomials);
tempPolynomials.Add(gi);
this.polynomialData = new HashSet <Polynomial>(tempPolynomials);
}
