/// <summary>
/// Gets the amount of polynom sequence's sign variations either
/// at positive or negative infinity using polynom's degree and the sign of its higher coefficient.
///
/// Works fast.
/// </summary>
/// <typeparam name="T">The type of polynom coefficients.</typeparam>
/// <typeparam name="C">The calculator for the coefficients' type.</typeparam>
/// <param name="list">The sequence of polynoms to be evaluated for sign variations.</param>
/// <param name="negativeInfinity">If this flag is set to FALSE, the evalution is at positive infinity. Otherwise, at negative infinity.</param>
/// <returns>The number of polynom's sign variations.</returns>
public static int InfinitySignVariations <T, C>(this IList <Polynom <T, C> > list, bool negativeInfinity) where C : ICalc <T>, new()
{
int signPrev = 0;
int signNew = 0;
int k = 0;
for (int i = 0; i < list.Count; i++)
{
if (list[i].Degree == 0)
{
signNew = WhiteMath <T, C> .Sign(list[i][0]);
}
else
{
signNew = WhiteMath <T, C> .Sign(list[i][list[i].Degree]) *
(negativeInfinity ? ((list[i].Degree % 2 == 0 ? 1 : -1)) : 1);
}
if (signNew == 0)
{
continue;
}
else if (signNew != signPrev && signPrev != 0)
{
k++;
}
signPrev = signNew;
}
return(k);
}
// --------------------------------------------
// --------- ЗНАК ФУНКЦИИ ---------------------
// --------------------------------------------
/// <summary>
/// Returns the number of sign variations in the function list for some certain
/// point.
/// </summary>
/// <typeparam name="T">The type of polynom coefficients.</typeparam>
/// <typeparam name="C">The type of polynom coefficients' calculator.</typeparam>
/// <param name="list">The list of the polynoms to be analyzed.</param>
/// <returns>The number of sign variations within the list. Zero values do not count.</returns>
public static int SignVariations <T, C>(this IList <IFunction <T, T> > list, Numeric <T, C> point) where C : ICalc <T>, new()
{
int signPrev = 0;
int signNew = 0;
int k = 0;
for (int i = 0; i < list.Count; i++)
{
signNew = WhiteMath <T, C> .Sign(list[i].Value(point));
if (signPrev == 0)
{
if (signNew != 0)
{
k++;
}
else
{
continue;
}
}
else if (signPrev < 0 || signPrev > 0)
{
if (signNew != 0)
{
k++;
}
else
{
continue;
}
}
signPrev = signNew;
}
return(k);
}