How to compute roots of a polynomial in a list?

Question

I'm having some troubles with a homework from my university, so I decided to post here for help

I have to create a list for polynomials. This part is okay:

n = int(input("Degree of polynomial: "))
p = []

for i in range(n+1):
    p.append(float(input("p["+str(i)+"]: ")))
    i += 1

For example, the polynomial:

                                             5x^4+3x^3-2x^2+x-2

Has:

                                                  n = 4

And the list indicated by:

                                             p[] = [5, 3, -2, 1, -2]

Also, I created a list with values that pretend to be roots of a polynomial (listPRoots, the possible roots). This part is also okay:

listPRoots= []

for i in range(int(p[0])): 
    if p[0]%(i+1) == 0:
        listPRoots.append(-(i+1))
        listPRoots.append(i+1)

As the code show, I have a list with the values that can be the roots of my polynomial. I used the rational roots theorem to make this list.

Now, I want to take a polynomial with coeficients in a list (p). With this polynomial, I want to verify every value inside the list (called listPRoots) to find the values of the roots of the polynomial. When I find this value, I want to put they in a new list (called listIntegrerRoots). For this, I tried:

listIntegrerRoots = []
listTestRoots     = []

for i in range(len(listPRoots) - 1):
    flag = len (p) - 1
    while flag > 0:
        root = (listPRoots[i]**(flag)) * p[flag]
        listTestRoots.append(root)
        flag = flag- 1
    if sum(listTestRoots)  + p[0] == 0:
        listIntegrerRoots.append(listPRoots[i])

But, I can't get the list I want. For example:

n = 2
p[0] = 6, p[1] = -5, p[2] = 1

result in:

x^2 - 5x + 6

and:

listPRoots[] = [-1, 1, -2, 2, -3, 3, -6, 6]

I would:

listIntegrerRoots[] = [2, 3]

Because 2 and 3 are the roots of my polynomial. But I get:

listIntegrerRoots[] = []

Can someone help me with this?

Thanks.

Answer 1

Just don't froget to clear your sum buffer listTestRoots every time you test a new possible root value.

Should be something like:

for i in range(len(listPRoots) - 1):
    listTestRoots = []
    ....

And from my point of view, an accumulative sum variable could be a better choice.

-- * Edit * --

In [23]: for i in range(len(listPRoots)):
    ...:     s = 0
    ...:     for j in range(len(p)):
    ...:         s += (listPRoots[i] ** j) * p[j]
    ...:     if s == 0:
    ...:         listIntegerRoots.append(listPRoots[i])
    ...:
    ...:
    ...:

In [24]: listIntegerRoots
Out[24]: [2, 3]