Python QQ.factor方法代码示例

# 需要导入模块: from sage.all import QQ [as 别名]
# 或者: from sage.all.QQ import factor [as 别名]
def render_curve_webpage_by_label(label):
    C = lmfdb.base.getDBConnection()
    data = C.elliptic_curves.curves.find_one({'lmfdb_label': label})
    if data is None:
        return elliptic_curve_jump_error(label, {})
    info = {}
    ainvs = [int(a) for a in data['ainvs']]
    E = EllipticCurve(ainvs)
    cremona_label = data['label']
    lmfdb_label = data['lmfdb_label']
    N = ZZ(data['conductor'])
    cremona_iso_class = data['iso']  # eg '37a'
    lmfdb_iso_class = data['lmfdb_iso']  # eg '37.a'
    rank = data['rank']
    try:
        j_invariant = QQ(str(data['jinv']))
    except KeyError:
        j_invariant = E.j_invariant()
    if j_invariant == 0:
        j_inv_factored = latex(0)
    else:
        j_inv_factored = latex(j_invariant.factor())
    jinv = unicode(str(j_invariant))
    CMD = 0
    CM = "no"
    EndE = "\(\Z\)"
    if E.has_cm():
        CMD = E.cm_discriminant()
        CM = "yes (\(%s\))"%CMD
        if CMD%4==0:
            d4 = ZZ(CMD)//4
            # r = d4.squarefree_part()
            # f = (d4//r).isqrt()
            # f="" if f==1 else str(f)
            # EndE = "\(\Z[%s\sqrt{%s}]\)"%(f,r)
            EndE = "\(\Z[\sqrt{%s}]\)"%(d4)
        else:            
            EndE = "\(\Z[(1+\sqrt{%s})/2]\)"%CMD

    # plot=E.plot()
    discriminant = E.discriminant()
    xintpoints_projective = [E.lift_x(x) for x in xintegral_point(data['x-coordinates_of_integral_points'])]
    xintpoints = proj_to_aff(xintpoints_projective)
    if 'degree' in data:
        modular_degree = data['degree']
    else:
        try:
            modular_degree = E.modular_degree()
        except RuntimeError:
            modular_degree = 0  # invalid, will be displayed nicely

    G = E.torsion_subgroup().gens()
    minq = E.minimal_quadratic_twist()[0]
    if E == minq:
        minq_label = lmfdb_label
    else:
        minq_ainvs = [str(c) for c in minq.ainvs()]
        minq_label = C.elliptic_curves.curves.find_one({'ainvs': minq_ainvs})['lmfdb_label']
# We do not just do the following, as Sage's installed database
# might not have all the curves in the LMFDB database.
# minq_label = E.minimal_quadratic_twist()[0].label()

    if 'gens' in data:
        generator = parse_gens(data['gens'])
    if len(G) == 0:
        tor_struct = '\mathrm{Trivial}'
        tor_group = '\mathrm{Trivial}'
    else:
        tor_group = ' \\times '.join(['\Z/{%s}\Z' % a.order() for a in G])
    if 'torsion_structure' in data:
        info['tor_structure'] = ' \\times '.join(['\Z/{%s}\Z' % int(a) for a in data['torsion_structure']])
    else:
        info['tor_structure'] = tor_group

    info.update(data)
    if rank >= 2:
        lder_tex = "L%s(E,1)" % ("^{(" + str(rank) + ")}")
    elif rank == 1:
        lder_tex = "L%s(E,1)" % ("'" * rank)
    else:
        assert rank == 0
        lder_tex = "L(E,1)"
    info['Gamma0optimal'] = (
        cremona_label[-1] == '1' if cremona_iso_class != '990h' else cremona_label[-1] == '3')
    info['modular_degree'] = modular_degree
    p_adic_data_exists = (C.elliptic_curves.padic_db.find(
        {'lmfdb_iso': lmfdb_iso_class}).count()) > 0 and info['Gamma0optimal']

    # Local data
    local_data = []
    for p in N.prime_factors():
        local_info = E.local_data(p)
        local_data.append({'p': p,
                           'tamagawa_number': local_info.tamagawa_number(),
                           'kodaira_symbol': web_latex(local_info.kodaira_symbol()).replace('$', ''),
                           'reduction_type': local_info.bad_reduction_type()
                           })

    mod_form_iso = lmfdb_label_regex.match(lmfdb_iso_class).groups()[1]

#.........这里部分代码省略.........

# 需要导入模块: from sage.all import QQ [as 别名]
# 或者: from sage.all.QQ import factor [as 别名]
def render_curve_webpage_by_label(label):
    C = lmfdb.base.getDBConnection()
    data = C.elliptic_curves.curves.find_one({"lmfdb_label": label})
    if data is None:
        return elliptic_curve_jump_error(label, {})
    info = {}
    ainvs = [int(a) for a in data["ainvs"]]
    E = EllipticCurve(ainvs)
    cremona_label = data["label"]
    lmfdb_label = data["lmfdb_label"]
    N = ZZ(data["conductor"])
    cremona_iso_class = data["iso"]  # eg '37a'
    lmfdb_iso_class = data["lmfdb_iso"]  # eg '37.a'
    rank = data["rank"]
    try:
        j_invariant = QQ(str(data["jinv"]))
    except KeyError:
        j_invariant = E.j_invariant()
    if j_invariant == 0:
        j_inv_factored = latex(0)
    else:
        j_inv_factored = latex(j_invariant.factor())
    jinv = unicode(str(j_invariant))
    CMD = 0
    CM = "no"
    EndE = "\(\Z\)"
    if E.has_cm():
        CMD = E.cm_discriminant()
        CM = "yes (\(%s\))" % CMD
        if CMD % 4 == 0:
            d4 = ZZ(CMD) // 4
            # r = d4.squarefree_part()
            # f = (d4//r).isqrt()
            # f="" if f==1 else str(f)
            # EndE = "\(\Z[%s\sqrt{%s}]\)"%(f,r)
            EndE = "\(\Z[\sqrt{%s}]\)" % (d4)
        else:
            EndE = "\(\Z[(1+\sqrt{%s})/2]\)" % CMD

    # plot=E.plot()
    discriminant = E.discriminant()
    xintpoints_projective = [E.lift_x(x) for x in xintegral_point(data["x-coordinates_of_integral_points"])]
    xintpoints = proj_to_aff(xintpoints_projective)
    if "degree" in data:
        modular_degree = data["degree"]
    else:
        try:
            modular_degree = E.modular_degree()
        except RuntimeError:
            modular_degree = 0  # invalid, will be displayed nicely

    G = E.torsion_subgroup().gens()
    E_pari = E.pari_curve(prec=200)
    from sage.libs.pari.all import PariError

    try:
        minq = E.minimal_quadratic_twist()[0]
    except PariError:  # this does occur with 164411a1
        print "PariError computing minimal quadratic twist of elliptic curve %s" % lmfdb_label
        minq = E
    if E == minq:
        minq_label = lmfdb_label
    else:
        minq_ainvs = [str(c) for c in minq.ainvs()]
        minq_label = C.elliptic_curves.curves.find_one({"ainvs": minq_ainvs})["lmfdb_label"]
    # We do not just do the following, as Sage's installed database
    # might not have all the curves in the LMFDB database.
    # minq_label = E.minimal_quadratic_twist()[0].label()

    if "gens" in data:
        generator = parse_gens(data["gens"])
    if len(G) == 0:
        tor_struct = "\mathrm{Trivial}"
        tor_group = "\mathrm{Trivial}"
    else:
        tor_group = " \\times ".join(["\Z/{%s}\Z" % a.order() for a in G])
    if "torsion_structure" in data:
        info["tor_structure"] = " \\times ".join(["\Z/{%s}\Z" % int(a) for a in data["torsion_structure"]])
    else:
        info["tor_structure"] = tor_group

    info.update(data)
    if rank >= 2:
        lder_tex = "L%s(E,1)" % ("^{(" + str(rank) + ")}")
    elif rank == 1:
        lder_tex = "L%s(E,1)" % ("'" * rank)
    else:
        assert rank == 0
        lder_tex = "L(E,1)"
    info["Gamma0optimal"] = cremona_label[-1] == "1" if cremona_iso_class != "990h" else cremona_label[-1] == "3"
    info["modular_degree"] = modular_degree
    p_adic_data_exists = (C.elliptic_curves.padic_db.find({"lmfdb_iso": lmfdb_iso_class}).count()) > 0 and info[
        "Gamma0optimal"
    ]

    # Local data
    local_data = []
    for p in N.prime_factors():
        local_info = E.local_data(p, algorithm="generic")
        local_data.append(
#.........这里部分代码省略.........