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Fast Cython code to choose a canonical minimal model.
failed to allocate %s * %s bytesE must be an elliptic curvefailed to allocate %s bytes__Pyx_CFunc_object____object____object____int___to_py.<locals>.wrapE must be over Q(sqrt(5))init_memory_functionssage.ext.memorycanonical_modelAttributeErrorEllipticCurvestringsourcediscriminanta_invariantscfunc.to_pyMemoryError__pyx_vtable__base_fieldTypeErrorparent__import__rightidealwrap__test__ra1p__main__leftdiscarg2arg1arg0sa1modgena6pa4pa3pa2pa1pu2u1t2t1opa6a4a3a2a1P3P2D2D1yxutsrdcbaKE;�2d��������T���������<����dD�����������������$���<$���T4���lT���������$����t����4���4D���Lt���d�����4����d���������4���,���������$$���<����\D���|�����d���������D��������$�����$�������T$��������$���44����$����t���d	�����	���
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9	�!H	H08	���o���o���o����o�}!�9�9�9�9::&:6:F:V:f:v:�:�:�:�:�:�:�:�:;;&;6;F;V;f;v;�;�;�;�;�;�;�;�;<<&<6<F<V<f<v<�<�<�<�<�<�<�<�<==&=6=F=V=f=v=�=�=�=�=�=�=�=�=>>&>6>F>V>f>v>�>�>�>�>�>�>�>�>??&?6?F?V?f?v?�?�?�?�?�?�?�?@�!File: sqrt5.pyx (starting at line 401)

    Given the pair (c4,c6) of a global minimal model, canonical_model returns
    a 'cannonical' representation of the curve in terms of (c4,c6).
    
    INPUT:
    
    - ``c4=a+b*\gamma`` -- an element of the ring of integers of `F=Q(\sqrt{5})`
    - ``c6=c+d*\gamma`` -- an element of the ring of integers of `F`
    
    OUTPUT:
    
    A 'cannonical' model of a curve in terms of (c4,c6)
    
    EXAMPLES::
    
        sage: K.<a> = NumberField(x^2-x-1)
        sage: E = EllipticCurve(K,[a,a+1,a+2,a+3,a+4])
        sage: F = E.change_weierstrass_model(a,a+1,a+2,a+3)
        sage: E.c_invariants() == F.c_invariants()
        False
        sage: Ecs = [Integer(i) for i in E.c4()]
        sage: Ecs += [Integer(i) for i in E.c6()]
        sage: Fcs = [Integer(i) for i in F.c4()]
        sage: Fcs += [Integer(i) for i in F.c6()]
        sage: from psage.ellcurve.minmodel.sqrt5 import canonical_model_c_invariants
        sage: canonical_model_c_invariants(Ecs[0],Ecs[1],Ecs[2],Ecs[3])
        (-118, -45, -3001, 116)
        sage: canonical_model_c_invariants(Fcs[0],Fcs[1],Fcs[2],Fcs[3])
        (-118, -45, -3001, 116)
    

    File: sqrt5.pyx (starting at line 345)

    Given a global minimal model E over Q(sqrt5) returns a canonical global
    minimal model.

    EXAMPLES::

      sage: from psage.ellcurve.minmodel.sqrt5 import canonical_model
      sage: K.<a> = NumberField(x**2-x-1)
      sage: E = EllipticCurve(K,[a,a-1,a,-1,-a+1])
      sage: F = canonical_model(E)
      sage: E == F
      False
      sage: E.is_isomorphic(F)
      True
      sage: F == canonical_model(F)
      True
    File: sqrt5.pyx (starting at line 300)

    Computes 'cannonical' representitives for the equivalence relation
        `\lambda / \mu \in U_F^{12},`
    on the ring of integers for `F=Q(\sqrt{5})`.
    
    INPUT:
    
    - ``a+b*\gamma`` -- an element of the ring of integers of `F`
    
    OUTPUT:
    
    A 'cannonical' element `\delta*u^{-12}` of the maximal order of `F` and
    the unit `u`
    
    EXAMPLES::

        sage: from psage.ellcurve.minmodel.sqrt5 import f_map
        sage: K.<a> = NumberField(x^2-x-1)
        sage: E = EllipticCurve(K,[a,a+1,a+2,a+3,a+4])
        sage: olddelta = E.discriminant()
        sage: olddeltapair = (Integer(olddelta[0]),Integer(olddelta[1]))
        sage: temp = f_map(olddeltapair[0],olddeltapair[1])
        sage: temp[0] == olddeltapair[0] and temp[1] == olddeltapair[1]
        True
        sage: F = E.change_weierstrass_model([a^5,0,0,0])
        sage: delta = F.discriminant()
        sage: deltapair = (Integer(delta[0]),Integer(delta[1]))
        sage: temp = f_map(deltapair[0],deltapair[1])
        sage: temp[0] == deltapair[0] and temp[1] == deltapair[1]
        False
        sage: temp[0] == olddeltapair[0] and temp[1] == olddeltapair[1]
        True
        sage: F.change_weierstrass_model([temp[2]+a*temp[3],0,0,0]) == E
        True
    
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