code: def dispersion(p, q=None, *gens, **args):
      r"""Compute the *dispersion* of polynomials.
  
      For two polynomials `f(x)` and `g(x)` with `\deg f > 0`
      and `\deg g > 0` the dispersion `\operatorname{dis}(f, g)` is defined as:
  
      .. math::
          \operatorname{dis}(f, g)
          & := \max\{ J(f,g) \cup \{0\} \} \\
          &  = \max\{ \{a \in \mathbb{N} | \gcd(f(x), g(x+a)) \neq 1\} \cup \{0\} \}
  
      and for a single polynomial `\operatorname{dis}(f) := \operatorname{dis}(f, f)`.
      Note that we make the definition `\max\{\} := -\infty`.
  
      Examples
      ========
  
      >>> from sympy import poly
      >>> from sympy.polys.dispersion import dispersion, dispersionset
      >>> from sympy.abc import x
  
      Dispersion set and dispersion of a simple polynomial:
  
      >>> fp = poly((x - 3)*(x + 3), x)
      >>> sorted(dispersionset(fp))
      [0, 6]
      >>> dispersion(fp)
      6
  
      Note that the definition of the dispersion is not symmetric:
  
      >>> fp = poly(x**4 - 3*x**2 + 1, x)
      >>> gp = fp.shift(-3)
      >>> sorted(dispersionset(fp, gp))
      [2, 3, 4]
      >>> dispersion(fp, gp)
      4
      >>> sorted(dispersionset(gp, fp))
      []
      >>> dispersion(gp, fp)
      -oo
  
      The maximum of an empty set is defined to be `-\infty`
      as seen in this example.
  
      Computing the dispersion also works over field extensions:
  
      >>> from sympy import sqrt
      >>> fp = poly(x**2 + sqrt(5)*x - 1, x, domain='QQ<sqrt(5)>')
      >>> gp = poly(x**2 + (2 + sqrt(5))*x + sqrt(5), x, domain='QQ<sqrt(5)>')
      >>> sorted(dispersionset(fp, gp))
      [2]
      >>> sorted(dispersionset(gp, fp))
      [1, 4]
  
      We can even perform the computations for polynomials
      having symbolic coefficients:
  
      >>> from sympy.abc import a
      >>> fp = poly(4*x**4 + (4*a + 8)*x**3 + (a**2 + 6*a + 4)*x**2 + (a**2 + 2*a)*x, x)
      >>> sorted(dispersionset(fp))
      [0, 1]
  
      See Also
      ========
  
      dispersionset
  
      References
      ==========
  
      .. [1] [ManWright94]_
      .. [2] [Koepf98]_
      .. [3] [Abramov71]_
      .. [4] [Man93]_
      """
      J = dispersionset(p, q, *gens, **args)
      if not J:
          # Definition for maximum of empty set
          j = S.NegativeInfinity
      else:
          j = max(J)
      return j
  
imports: from sympy.core import S
  from sympy.polys import Poly
label_desc: Use image node_id 2 for calling a global function with example usage: dispersion(p, q) and returns: j