Evaluate polynomials by reading it from a file

I would like to read and evaluate a polynomial from a txt file that is given in the following format,

3x^3-4x^1+5

So the above equation should be evaulated by the program as follows,

Coefficients: [3,0,-4,5]

So far I could able to parse the string and created two different lists that store coefficients and the degrees as follows,

Coefficients: [3,-4,5] --> They are the coeffs of x^3, x^1, and x^0

Degrees: [3,1]

However I could not evaluate (i.e. P(1) = 3(1^3)-4(1^1)+5 = 4) the polynomial with these extracted values. I would like to use numpy, yet the formats do not match.

Can anyone help me how can I obtain the required format for utilizing numpy?

Thanks.

Solution

Assuming you can put the constant term (coefficient of x^0) in your deg list, then you can do this:

coeffs = [3,-4,5]
degs = [3,1,0]
_coeffs = [0]*(max(degs)+1)
for i,deg in enumerate(degs):
    _coeffs[deg] = coeffs[i]

p = np.poly1d(_coeffs[::-1])

Then:

p(1)
4

That is, you just need to create a list of coefficients in which the coefficient appears at the index of the degree.