How do I show the 5 root polynomials below in python? I want it to show every root.
x = Symbol('x')
det_p = x**5 - 5*x**3 + 5*x + 2
eq1 = Eq(det_p,0)
b_solve = solve(eq1)
print('Energias dos Orbitais: ', [s.evalf() for s in b_solve])
Results: Energias dos Orbitais: [-2.00000000000000, -0.618033988749895, 1.61803398874989]
If you are working with polynomials and want to see all roots in their multiplicity then you can use either roots, which gives a dict showing multiplicity or Poly.all_roots which gives a list of possibly repeated roots:
In [3]: roots(det_p)
Out[3]:
⎧ 1 √5 1 √5 ⎫
⎨-2: 1, ─ - ──: 2, ─ + ──: 2⎬
⎩ 2 2 2 2 ⎭
In [4]: Poly(det_p, x).all_roots()
Out[4]:
⎡ 1 √5 1 √5 1 √5 1 √5⎤
⎢-2, ─ - ──, ─ - ──, ─ + ──, ─ + ──⎥
⎣ 2 2 2 2 2 2 2 2 ⎦
Relevant docs:
https://docs.sympy.org/latest/modules/polys/reference.html#symbolic-root-finding-algorithms
https://docs.sympy.org/latest/modules/polys/reference.html#sympy.polys.polytools.Poly.all_roots