class_docstr: Special functions for solvable quintics
class_docstr_tok: ["Special","functions","for","solvable","quintics"]
code: def f20(self):
      p, q, r, s = self.p, self.q, self.r, self.s
      f20 = (
          q**8
          - 13 * p * q**6 * r
          + p**5 * q**2 * r**2
          + 65 * p**2 * q**4 * r**2
          - 4 * p**6 * r**3
          - 128 * p**3 * q**2 * r**3
          + 17 * q**4 * r**3
          + 48 * p**4 * r**4
          - 16 * p * q**2 * r**4
          - 192 * p**2 * r**5
          + 256 * r**6
          - 4 * p**5 * q**3 * s
          - 12 * p**2 * q**5 * s
          + 18 * p**6 * q * r * s
          + 12 * p**3 * q**3 * r * s
          - 124 * q**5 * r * s
          + 196 * p**4 * q * r**2 * s
          + 590 * p * q**3 * r**2 * s
          - 160 * p**2 * q * r**3 * s
          - 1600 * q * r**4 * s
          - 27 * p**7 * s**2
          - 150 * p**4 * q**2 * s**2
          - 125 * p * q**4 * s**2
          - 99 * p**5 * r * s**2
          - 725 * p**2 * q**2 * r * s**2
          + 1200 * p**3 * r**2 * s**2
          + 3250 * q**2 * r**2 * s**2
          - 2000 * p * r**3 * s**2
          - 1250 * p * q * r * s**3
          + 3125 * p**2 * s**4
          - 9375 * r * s**4
          - (
              2 * p * q**6
              - 19 * p**2 * q**4 * r
              + 51 * p**3 * q**2 * r**2
              - 3 * q**4 * r**2
              - 32 * p**4 * r**3
              - 76 * p * q**2 * r**3
              + 256 * p**2 * r**4
              - 512 * r**5
              + 31 * p**3 * q**3 * s
              + 58 * q**5 * s
              - 117 * p**4 * q * r * s
              - 105 * p * q**3 * r * s
              - 260 * p**2 * q * r**2 * s
              + 2400 * q * r**3 * s
              + 108 * p**5 * s**2
              + 325 * p**2 * q**2 * s**2
              - 525 * p**3 * r * s**2
              - 2750 * q**2 * r * s**2
              + 500 * p * r**2 * s**2
              - 625 * p * q * s**3
              + 3125 * s**4
          )
          * x
          + (
              p**2 * q**4
              - 6 * p**3 * q**2 * r
              - 8 * q**4 * r
              + 9 * p**4 * r**2
              + 76 * p * q**2 * r**2
              - 136 * p**2 * r**3
              + 400 * r**4
              - 50 * p * q**3 * s
              + 90 * p**2 * q * r * s
              - 1400 * q * r**2 * s
              + 625 * q**2 * s**2
              + 500 * p * r * s**2
          )
          * x**2
          - (
              2 * q**4
              - 21 * p * q**2 * r
              + 40 * p**2 * r**2
              - 160 * r**3
              + 15 * p**2 * q * s
              + 400 * q * r * s
              - 125 * p * s**2
          )
          * x**3
          + (2 * p * q**2 - 6 * p**2 * r + 40 * r**2 - 50 * q * s)
          * x**4
          + 8 * r * x**5
          + x**6
      )
      return Poly(f20, x)
  
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 2 for calling the PolyQuintic obj's underlying member method code with example usage: obj.f20() and returns: Poly