Kummer surfaces over a general ring - Elliptic curves

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# Kummer surfaces over a general ring

class sage.schemes.hyperelliptic_curves.kummer_surface.KummerSurface(J)

  Bases: `AlgebraicScheme_subscheme_projective`

  EXAMPLES:

  Sage

      sage: R.<x> = QQ[]
      sage: f = x^5 + x + 1
      sage: X = HyperellipticCurve(f)
      sage: J = Jacobian(X)
      sage: K = KummerSurface(J); K
      Closed subscheme of Projective Space of dimension 3 over Rational Field defined by:
      X0^4 - 4*X0*X1^3 + 4*X0^2*X1*X2 - 4*X0*X1^2*X2 + 2*X0^2*X2^2 + X2^4 - 4*X0^3*X3 - 2*X0^2*X1*X3 - 2*X1*X2^2*X3 + X1^2*X3^2 - 4*X0*X2*X3^2

  Python

      >>> from sage.all import *
      >>> R = QQ['x']; (x,) = R._first_ngens(1)
      >>> f = x**Integer(5) + x + Integer(1)
      >>> X = HyperellipticCurve(f)
      >>> J = Jacobian(X)
      >>> K = KummerSurface(J); K
      Closed subscheme of Projective Space of dimension 3 over Rational Field defined by:
      X0^4 - 4*X0*X1^3 + 4*X0^2*X1*X2 - 4*X0*X1^2*X2 + 2*X0^2*X2^2 + X2^4 - 4*X0^3*X3 - 2*X0^2*X1*X3 - 2*X1*X2^2*X3 + X1^2*X3^2 - 4*X0*X2*X3^2