class_docstr: Special functions for solvable quintics
class_docstr_tok: ["Special","functions","for","solvable","quintics"]
code: def __init__(self, poly):
      _, _, self.p, self.q, self.r, self.s = poly.all_coeffs()
      self.zeta1 = (
          Rational(-1, 4)
          + (sqrt(5) / 4)
          + I * sqrt((sqrt(5) / 8) + Rational(5, 8))
      )
      self.zeta2 = (
          (-sqrt(5) / 4)
          - Rational(1, 4)
          + I * sqrt((-sqrt(5) / 8) + Rational(5, 8))
      )
      self.zeta3 = (
          (-sqrt(5) / 4)
          - Rational(1, 4)
          - I * sqrt((-sqrt(5) / 8) + Rational(5, 8))
      )
      self.zeta4 = (
          Rational(-1, 4)
          + (sqrt(5) / 4)
          - I * sqrt((sqrt(5) / 8) + Rational(5, 8))
      )
  
file_path: sympy/sympy/polys/polyquinticconst.py
imports: from sympy.core import Symbol
  from sympy.core.evalf import N
  from sympy.core.numbers import I, Rational
  from sympy.functions import sqrt
  from sympy.polys.polytools import Poly
  from sympy.utilities import public
label_desc: Use image node_id 1 to create a new PolyQuintic object  with example: obj = PolyQuintic(poly)