(f, K)
Compute the LMQ lower bound for the positive roots of `f`;
       LMQ (Local Max Quadratic) was developed by Akritas-Strzebonski-Vigklas.

       Reference:
       ==========
       Alkiviadis G. Akritas: "Linear and Quadratic Complexity Bounds on the
           Values of the Positive Roots of Polynomials"
           Journal of Universal Computer Science, Vol. 15, No. 3, 523-537, 2009.
Compute the LMQ lower bound for the positive roots of `f`;
       LMQ (Local Max Quadratic) was developed by Akritas-Strzebonski-Vigklas.
Compute the LMQ lower bound for the positive roots of f ; LMQ ( Local Max Quadratic ) was developed by Akritas - Strzebonski - Vigklas .
def dup_root_lower_bound(f, K):
    """Compute the LMQ lower bound for the positive roots of `f`;
       LMQ (Local Max Quadratic) was developed by Akritas-Strzebonski-Vigklas.

       Reference:
       ==========
       Alkiviadis G. Akritas: "Linear and Quadratic Complexity Bounds on the
           Values of the Positive Roots of Polynomials"
           Journal of Universal Computer Science, Vol. 15, No. 3, 523-537, 2009.
    """
    bound = dup_root_upper_bound(dup_reverse(f), K)

    if bound is not None:
        return 1/bound
    else:
        return None
def dup_root_lower_bound ( f , K ) : bound = dup_root_upper_bound ( dup_reverse ( f ) , K ) if bound is not None : return 1 / bound else : return None