class Polynomial:
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def __init__(self, *argv: float):
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if len(argv) < 1:
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raise ValueError("A Polynomial has at least one coefficient.")
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if argv[-1] == 0:
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raise ValueError("The coefficient at the highest degree must not be zero.")
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self.__coefficients = tuple(argv)
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self.__order = len(argv)
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def evaluate(self, x: float) -> tuple[float, list[float]]:
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p = self.__coefficients[-1]
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c = [p]
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for ak in self.__coefficients[-2::-1]:
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p = ak + (p * x)
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c.insert(0, p)
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return c[0], c[1:]
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def order(self):
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return self.__order
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def __add__(self, other: "Polynomial") -> "Polynomial":
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if not isinstance(other, Polynomial):
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raise ValueError("Operator + is only applicable for Polynomial.")
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coefficients = []
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if self.__order > other.__order:
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low_order = other.__order
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heigh_order = self.__order
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higher_coefficients = self.__coefficients
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else:
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low_order = self.__order
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heigh_order = other.__order
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higher_coefficients = other.__coefficients
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for i in range(0, low_order):
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coefficients.append(self.__coefficients[i] + other.__coefficients[i])
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for j in range(i+1, heigh_order):
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coefficients.append(higher_coefficients[j])
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return Polynomial(*coefficients)
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def __getitem__(self, key):
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return self.__coefficients[key]
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def __repr__(self) -> str:
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coe = []
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for c in self.__coefficients:
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coe.append(f'{c}')
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return ' '.join(coe)
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