python编程实现广义的多项式Euclid除法代码

请看下面的Python代码：

def polygcd(a,b):
    """
    Calculate the greatest common divisor of polynomials a and b using Euclid's algorithm
    """

    if len(b) > len(a):
        a, b = b, a

    while b:
        q, r = polydiv(a, b)
        a, b = b, r

    return a


def polydiv(a, b):
    """
    Divide polynomials a and b using long division and return quotient and remainder
    """

    quo = [0] * (len(a) - len(b) + 1)
    while len(a) >= len(b):
        # Compute the degree of the quotient
        deg_quo = len(a) - len(b)
        # Compute the leading coefficient of the quotient
        lc_quo = float(a[-1]) / b[-1]
        # Add the term to the quotient
        quo[deg_quo] = lc_quo
        # Subtract the term from the dividend
        a = [round(x - lc_quo * y, 2) for x, y in zip(a, b + [0] * deg_quo)]
        # Remove leading zeros (rounding errors may cause some small coefficients)
        while a and abs(a[-1]) < 1e-10:
            a.pop()
    return [quo, a]

其中，`polygcd(a,b)`函数用于计算多项式 $a$ 和 $b$ 的最大公因式，而`polydiv(a,b)`函数则是单独实现的多项式除法操作。具体实现步骤在代码注释中有说明。