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Call C the list of coefficients, removing immediate repeats.

Unimodality means there is no decrease-then-increase in C.

The package more-itertools (which can be installed with pip) enables an elegant solution:

def is_unimodal(p):
    """
    Return whether this polynomial is unimodal.

    EXAMPLES::

        sage: R.<t> = ZZ[]
        sage: is_unimodal(1 + t + t^2 + 4*t^3 + t^4)
        True
        sage: is_unimodal(1 + t^2 + 4*t^3 + t^4)
        False
    """
    from more_itertools import triplewise, unique_justseen
    return all((a < b) or (b > c)
               for a, b, c in triplewise(unique_justseen(p)))

Call C the list of coefficients, removing immediate repeats.

Unimodality means there is no decrease-then-increase in C.

The package more-itertools (which can be installed with pip) enables an elegant solution:

def is_unimodal(p):
    """
    Return whether this polynomial is unimodal.

    EXAMPLES::

        sage: R.<t> = ZZ[]
        sage: is_unimodal(1 + t + t^2 + 4*t^3 + t^4)
t^4)  # coeffs: 1, 1, 1, 4, 1
        True
        sage: is_unimodal(1 + t^2 + 4*t^3 + t^4)
t^4)  # coeffs: 1, 0, 1, 4, 1
        False
    """
    from more_itertools import triplewise, unique_justseen
    return all((a < b) or (b > c)
               for a, b, c in triplewise(unique_justseen(p)))