polynomial

case class DiscreteRoots(roots: List[Double]) extends RootSet with Product with Serializable
sealed trait RootSet extends AnyRef

This trait represents sets of real solutions of equations of type p(x) = 0 where p is a polynomial with real coefficients

object RealLine extends RootSet
def cubicMinimum(a: Double, b: Double, c: Double, d: Double): Option[Double]

Finds a minimum of a polynomial of third degree, if possible.
Finds a minimum of a polynomial of third degree, if possible. There is at most one, so we use an Option as return type.
The coefficients are specified as follows: p(x) = ax3 + bx2 + cx + d
See second red numerics notebook p. 48 for all the funny signum-manipulations.
def quadraticMinimum(a: Double, b: Double, c: Double): Option[Double]

Attempts to find local minimum of a quadratic polynomial p(x) = ax2 + bx + c
def quadraticRoots(a: Double, b: Double, c: Double): RootSet

Solves ax2 + bx + c = 0