# HG changeset patch # User Nick Alexander # Date 1242107581 25200 # Node ID 87edc42e682b66e1236459ad8a76b375862c855a # Parent 268d1efbf60f6c24ad9c49cb9c91ff0437e42340 [mq]: take2.patch diff -r 268d1efbf60f -r 87edc42e682b sage/schemes/hyperelliptic_curves/all.py --- a/sage/schemes/hyperelliptic_curves/all.py Tue May 05 23:19:43 2009 -0700 +++ b/sage/schemes/hyperelliptic_curves/all.py Mon May 11 22:53:01 2009 -0700 @@ -1,4 +1,7 @@ from constructor import HyperellipticCurve from hyperelliptic_generic import is_HyperellipticCurve from kummer_surface import KummerSurface - +from invariants import (igusa_clebsch_invariants, + absolute_igusa_invariants_kohel, + absolute_igusa_invariants_wamelen, + clebsch_invariants) diff -r 268d1efbf60f -r 87edc42e682b sage/schemes/hyperelliptic_curves/hyperelliptic_g2_generic.py --- a/sage/schemes/hyperelliptic_curves/hyperelliptic_g2_generic.py Tue May 05 23:19:43 2009 -0700 +++ b/sage/schemes/hyperelliptic_curves/hyperelliptic_g2_generic.py Mon May 11 22:53:01 2009 -0700 @@ -7,12 +7,11 @@ import hyperelliptic_generic import jacobian_g2 +import invariants + from sage.schemes.generic.projective_space import ProjectiveSpace class HyperellipticCurve_g2_generic(hyperelliptic_generic.HyperellipticCurve_generic): - def igusa_invariants(self): - raise NotImplementedError - def is_odd_degree(self): """ Returns True if the curve is an odd degree model. @@ -26,7 +25,7 @@ else: a0 = f.leading_coefficient() c0 = h.leading_coefficient() - return (c0^2 + 4*a0) == 0 + return (c0**2 + 4*a0) == 0 def jacobian(self): return jacobian_g2.HyperellipticJacobian_g2(self) @@ -47,3 +46,111 @@ J = self.jacobian() K = J.kummer_surface() return self._kummer_morphism + + def clebsch_invariants(self): + r""" + Return the Clebsch invariants `(A, B, C, D)` of Mestre, p 317, [M]_. + + SEEALSO:: + + .. sage.schemes.hyperelliptic_curves.invariants + + EXAMPLES:: + + sage: R. = QQ[] + sage: f = x^5 - x^4 + 3 + sage: HyperellipticCurve(f).clebsch_invariants() + (0, -2048/375, -4096/25, -4881645568/84375) + sage: HyperellipticCurve(f(2*x)).clebsch_invariants() + (0, -8388608/375, -1073741824/25, -5241627016305836032/84375) + + sage: HyperellipticCurve(f, x).clebsch_invariants() + (-8/15, 17504/5625, -23162896/140625, -420832861216768/7119140625) + sage: HyperellipticCurve(f(2*x), 2*x).clebsch_invariants() + (-512/15, 71696384/5625, -6072014209024/140625, -451865844002031331704832/7119140625) + + TESTS:: + + sage: magma(HyperellipticCurve(f)).ClebschInvariants() # optional - magma + [ 0, -2048/375, -4096/25, -4881645568/84375 ] + sage: magma(HyperellipticCurve(f(2*x))).ClebschInvariants() # optional - magma + [ 0, -8388608/375, -1073741824/25, -5241627016305836032/84375 ] + sage: magma(HyperellipticCurve(f, x)).ClebschInvariants() # optional - magma + [ -8/15, 17504/5625, -23162896/140625, -420832861216768/7119140625 ] + sage: magma(HyperellipticCurve(f(2*x), 2*x)).ClebschInvariants() # optional - magma + [ -512/15, 71696384/5625, -6072014209024/140625, -451865844002031331704832/7119140625 ] + """ + f, h = self.hyperelliptic_polynomials() + return invariants.clebsch_invariants(4*f + h**2) + + def igusa_clebsch_invariants(self): + r""" + Return the Igusa-Clebsch invariants `I_2, I_4, I_6, I_{10}` of Igusa and Clebsch [I]_. + + SEEALSO:: + + .. sage.schemes.hyperelliptic_curves.invariants + + EXAMPLES:: + + sage: R. = QQ[] + sage: f = x^5 - x + 2 + sage: HyperellipticCurve(f).igusa_clebsch_invariants() + (-640, -20480, 1310720, 52160364544) + sage: HyperellipticCurve(f(2*x)).igusa_clebsch_invariants() + (-40960, -83886080, 343597383680, 56006764965979488256) + + sage: HyperellipticCurve(f, x).igusa_clebsch_invariants() + (-640, 17920, -1966656, 52409511936) + sage: HyperellipticCurve(f(2*x), 2*x).igusa_clebsch_invariants() + (-40960, 73400320, -515547070464, 56274284941110411264) + + TESTS:: + + sage: magma(HyperellipticCurve(f)).IgusaClebschInvariants() # optional - magma + [ 0, -2048/375, -4096/25, -4881645568/84375 ] + sage: magma(HyperellipticCurve(f(2*x))).IgusaClebschInvariants() # optional - magma + [ 0, -8388608/375, -1073741824/25, -5241627016305836032/84375 ] + sage: magma(HyperellipticCurve(f, x)).IgusaClebschInvariants() # optional - magma + [ -8/15, 17504/5625, -23162896/140625, -420832861216768/7119140625 ] + sage: magma(HyperellipticCurve(f(2*x), 2*x)).IgusaClebschInvariants() # optional - magma + [ -512/15, 71696384/5625, -6072014209024/140625, -451865844002031331704832/7119140625 ] + """ + f, h = self.hyperelliptic_polynomials() + return invariants.igusa_clebsch_invariants(4*f + h**2) + + def absolute_igusa_invariants_wamelen(self): + r""" + Return the three absolute Igusa invariants used by van Wamelen [W]_. + + EXAMPLES:: + + sage: R. = QQ[] + sage: HyperellipticCurve(x^5 - 1).absolute_igusa_invariants_wamelen() + (0, 0, 0) + sage: HyperellipticCurve((x^5 - 1)(x - 2), (x^2)(x - 2)).absolute_igusa_invariants_wamelen() + (0, 0, 0) + """ + f, h = self.hyperelliptic_polynomials() + return invariants.absolute_igusa_invariants_wamelen(4*f + h**2) + + def absolute_igusa_invariants_kohel(self): + r""" + Return the three absolute Igusa invariants used by Kohel [K]_. + + SEEALSO:: + + .. sage.schemes.hyperelliptic_curves.invariants + + EXAMPLES:: + + sage: R. = QQ[] + sage: HyperellipticCurve(x^5 - 1).absolute_igusa_invariants_kohel() + (0, 0, 0) + sage: HyperellipticCurve(x^5 - x + 1, x^2).absolute_igusa_invariants_kohel() + (-1030567/178769, 259686400/178769, 20806400/178769) + sage: HyperellipticCurve((x^5 - x + 1)(3*x + 1), (x^2)(3*x + 1)).absolute_igusa_invariants_kohel() + (-1030567/178769, 259686400/178769, 20806400/178769) + """ + f, h = self.hyperelliptic_polynomials() + return invariants.absolute_igusa_invariants_kohel(4*f + h**2) diff -r 268d1efbf60f -r 87edc42e682b sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py --- a/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py Tue May 05 23:19:43 2009 -0700 +++ b/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py Mon May 11 22:53:01 2009 -0700 @@ -63,8 +63,10 @@ names = ["x","y"] elif isinstance(names,str): names = names.split(",") + self._names = names P1 = PolynomialRing(R,name=names[0]) P2 = PolynomialRing(P1,name=names[1]) + self._PP = PP self._printing_ring = P2 self._hyperelliptic_polynomials = (f,h) self._genus = genus