在Python中分解二次多项式

Question

因为我脑子里能很快地把二次方程拆解开来，这种能力从我学会它的时候就有了。那么我该如何开始用Python写一个能拆解二次方程的程序呢？

Answer 1

我试着按照hugomg的方法来做。我从网上抄了“gcd”（最大公约数）和“简化分数”的函数。下面是我这个不太严谨的方法：

from math import sqrt

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def simplify_fraction(numer, denom):
    if denom == 0:
        return "Division by 0 - result undefined"

    # Remove greatest common divisor:
    common_divisor = gcd(numer, denom)
    (reduced_num, reduced_den) = (numer / common_divisor, denom / common_divisor)
    # Note that reduced_den > 0 as documented in the gcd function.

    if common_divisor == 1:
        return (numer, denom)
    else:
        # Bunch of nonsense to make sure denominator is negative if possible
        if (reduced_den > denom):
            if (reduced_den * reduced_num < 0):
                return(-reduced_num, -reduced_den)
            else:
                return (reduced_num, reduced_den)
        else:
            return (reduced_num, reduced_den)

def quadratic_function(a,b,c):
    if (b**2-4*a*c >= 0):
        x1 = (-b+sqrt(b**2-4*a*c))/(2*a)
        x2 = (-b-sqrt(b**2-4*a*c))/(2*a)
        # Added a "-" to these next 2 values because they would be moved to the other side of the equation
        mult1 = -x1 * a
        mult2 = -x2 * a
        (num1,den1) = simplify_fraction(a,mult1)
        (num2,den2) = simplify_fraction(a,mult2)
        if ((num1 > a) or (num2 > a)):
            # simplify fraction will make too large of num and denom to try to make a sqrt work
            print("No factorization")
        else:
            # Getting ready to make the print look nice
            if (den1 > 0):
                sign1 = "+"
            else:
                sign1 = ""
            if (den2 > 0):
                sign2 = "+"
            else:
                sign2 = ""
            print("({}x{}{})({}x{}{})".format(int(num1),sign1,int(den1),int(num2),sign2,int(den2)))
    else:
        # if the part under the sqrt is negative, you have a solution with i
        print("Solutions are imaginary")
    return

# This function takes in a, b, and c from the equation:
# ax^2 + bx + c
# and prints out the factorization if there is one

quadratic_function(7,27,-4)

如果我运行这个代码，我得到的输出是：

(7x-1)(1x+4)

Answer 2

使用二次公式。

Answer 3

改进Keith的回答：

首先，从一个多项式开始，形如 P(x) = a*x^2 + b*x + c。

接下来，使用二次公式（或者你喜欢的其他方法）来找到方程 P(x) = 0 的根，也就是 r1 和 r2。

现在你可以把这个多项式分解成 a*(x-r1)(x-r2) 的形式。

如果你的因式是 (3x - 4)(x - 9)，那么解会是 3*(x - 4/3)(x - 9)。

你可能想找个方法把3乘到因式里，这样就可以去掉分数，让结果看起来更整齐。在这种情况下，使用分数运算而不是浮点数运算可能会更好，这样你能更清楚地知道分母是什么。

在Python中分解二次多项式

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