如何从我的方程中提取系数：x^3 - 60x^2 + 1100x - 6000 / -6000？

Question

Given an array of integers, I am trying to extract the coefficient in front of each "x^i" , ...., "x^3" , "x^2" , "x" .

Given the equation v(x) = (x-x0)(x-x1)...(xx(i-1)) / (xi-x0)(xi-x1)...(xi-x(i-1))

For example if given array is [30, 20, 10, 0] then the expected result will be:

x^3 - 60x^2 + 1100x - 6000 / -6000

I am nearly there I just need to find a way to obtain 1, -60, 1100, -6000 from the numerator.

I've been trying various split methods but it did not seem to work.

My current code:

from sympy import *

def extract_coeff(array):
    coeff = []

    x=Symbol('x')
    count = 0
    for item in array:
        if item != 0:
            count = count + 1

    total = len(array)
    list = []

    numerator_list = []
    numerator = 1
    denom_list = []
    denom = 1

    for i in range(total):
        list.append(array[i])

    for item in list:
        denom_list.append((list[-1] - item))

    denom_list.pop()

    for item in denom_list:
        denom = denom * item

    # numerator
    for item in array:
        if item != 0:
            numerator = numerator * (x-item)

    numerator = expand(numerator)

    print(numerator)
    numerator = str(numerator)

    # store coefficient
    if numerator[0] == 'x':
        coeff.append(1)

    # trying to split (PLEASE HELP)
    numerator = numerator.replace('+ ', ', ')
    print(numerator.split(', '))

extract_coeff([30,20,10,0])

Answer 1

Say you have an equation

>>> from sympy.abc import x
>>> eq = (x**3 - 60*x**2 + 1100*x - 6000) / -6000

And you want to look at the numerator. If you are sure there are no compound fractions then numer(eq) will work. If there might be more than one term as in x/3 + x then use as_numer_denom()

>>> n, d = eq.as_numer_denom()

Now convert the numerator n to a Poly and ask for all coefficients:

>>> Poly(n).all_coeffs()
[-1, 60, -1100, 6000]

Since the denominator was negative, that negative sign is now in the numerator.