/// <summary>
 /// Check that the endpoints specify an interval and the function takes
 /// opposite signs at the endpoints.
 /// </summary>
 /// <param name="lower">Lower endpoint.</param>
 /// <param name="upper">Upper endpoint.</param>
 /// <exception cref="NullArgumentException"> if the function has not been set.</exception>
 /// <exception cref="NoBracketingException"> if the function has the same sign at
 /// the endpoints.</exception>
 protected void verifyBracketing(double lower, double upper)
 {
     UnivariateSolverUtils.verifyBracketing(function, lower, upper);
 }
 /// <summary>
 /// Check that <c>lower < initial < upper</c>.
 /// </summary>
 /// <param name="lower">Lower endpoint.</param>
 /// <param name="initial">Initial value.</param>
 /// <param name="upper">Upper endpoint.</param>
 /// <exception cref="NumberIsTooLargeException"> if <c>lower >= initial</c> or
 /// <c>initial >= upper</c>.</exception>
 protected void verifySequence(double lower, double initial, double upper)
 {
     UnivariateSolverUtils.verifySequence(lower, initial, upper);
 }
 /// <summary>
 /// Check whether the arguments form a (strictly) increasing sequence.
 /// </summary>
 /// <param name="start">First number.</param>
 /// <param name="mid">Second number.</param>
 /// <param name="end">Third number.</param>
 /// <returns><c>true</c> if the arguments form an increasing sequence.</returns>
 protected Boolean isSequence(double start, double mid, double end)
 {
     return(UnivariateSolverUtils.isSequence(start, mid, end));
 }
 /// <summary>
 /// Check that the endpoints specify an interval.
 /// </summary>
 /// <param name="lower">Lower endpoint.</param>
 /// <param name="upper">Upper endpoint.</param>
 /// <exception cref="NumberIsTooLargeException"> if <c>lower >= upper</c></exception>
 protected void verifyInterval(double lower, double upper)
 {
     UnivariateSolverUtils.verifyInterval(lower, upper);
 }
 /// <summary>
 /// Check whether the function takes opposite signs at the endpoints.
 /// </summary>
 /// <param name="lower">Lower endpoint.</param>
 /// <param name="upper">Upper endpoint.</param>
 /// <returns><c>true</c> if the function values have opposite signs at the
 /// given points.</returns>
 protected Boolean isBracketing(double lower, double upper)
 {
     return(UnivariateSolverUtils.isBracketing(function, lower, upper));
 }