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# Rational point sets on a Jacobian

EXAMPLES:

    sage: x = QQ['x'].0
    sage: f = x^5 + x + 1
    sage: C = HyperellipticCurve(f); C
    Hyperelliptic Curve over Rational Field defined by y^2 = x^5 + x + 1
    sage: C(QQ)
    Set of rational points of Hyperelliptic Curve over Rational Field defined by y^2 = x^5 + x + 1
    sage: P = C([0,1,1])
    sage: J = C.jacobian(); J
    Jacobian of Hyperelliptic Curve over Rational Field defined by y^2 = x^5 + x + 1
    sage: Q = J(QQ)(P); Q
    (x, y - 1)
    sage: Q + Q
    (x^2, y - 1/2*x - 1)
    sage: Q*3
    (x^2 - 1/64*x + 1/8, y + 255/512*x + 65/64)

    sage: F.<a> = GF(3)
    sage: R.<x> = F[]
    sage: f = x^5-1
    sage: C = HyperellipticCurve(f)
    sage: J = C.jacobian()
    sage: X = J(F)
    sage: a = x^2-x+1
    sage: b = -x +1
    sage: c = x-1
    sage: d = 0
    sage: D1 = X([a,b])
    sage: D1
    (x^2 + 2*x + 1, y + x + 2)
    sage: D2 = X([c,d])
    sage: D2
    (x + 2, y)
    sage: D1+D2
    (x^2 + 2*x + 2, y + 2*x + 1)

class `sage.schemes.hyperelliptic_curves.jacobian_homset.``JacobianHomset_divisor_classes`(Y, X, **kwds)

  Bases: `sage.schemes.generic.homset.SchemeHomset_points`

  `base_extend`(R)

    x.__init__(...) initializes x; see help(type(x)) for signature

  `curve`()

    x.__init__(...) initializes x; see help(type(x)) for signature

  `value_ring`()

    Returns S for a homset X(T) where T = Spec(S).

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