Python WebNumberField.degree方法代码示例

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
def render_field_webpage(args):
    data = None
    C = base.getDBConnection()
    info = {}
    bread = [('Global Number Fields', url_for(".number_field_render_webpage"))]

    # This function should not be called unless label is set.
    label = clean_input(args['label'])
    nf = WebNumberField(label)
    data = {}
    if nf.is_null():
        bread.append(('Search results', ' '))
        info['err'] = 'There is no field with label %s in the database' % label
        info['label'] = args['label_orig'] if 'label_orig' in args else args['label']
        return search_input_error(info, bread)

    info['wnf'] = nf
    data['degree'] = nf.degree()
    data['class_number'] = nf.class_number()
    t = nf.galois_t()
    n = nf.degree()
    data['is_galois'] = nf.is_galois()
    data['is_abelian'] = nf.is_abelian()
    if nf.is_abelian():
        conductor = nf.conductor()
        data['conductor'] = conductor
        dirichlet_chars = nf.dirichlet_group()
        if len(dirichlet_chars)>0:
            data['dirichlet_group'] = ['<a href = "%s">$\chi_{%s}(%s,&middot;)$</a>' % (url_for('characters.render_Dirichletwebpage',modulus=data['conductor'], number=j), data['conductor'], j) for j in dirichlet_chars]
            data['dirichlet_group'] = r'$\lbrace$' + ', '.join(data['dirichlet_group']) + r'$\rbrace$'
        if data['conductor'].is_prime() or data['conductor'] == 1:
            data['conductor'] = "\(%s\)" % str(data['conductor'])
        else:
            data['conductor'] = "\(%s=%s\)" % (str(data['conductor']), latex(data['conductor'].factor()))
    data['galois_group'] = group_display_knowl(n, t, C)
    data['cclasses'] = cclasses_display_knowl(n, t, C)
    data['character_table'] = character_table_display_knowl(n, t, C)
    data['class_group'] = nf.class_group()
    data['class_group_invs'] = nf.class_group_invariants()
    data['signature'] = nf.signature()
    data['coefficients'] = nf.coeffs()
    nf.make_code_snippets()
    D = nf.disc()
    ram_primes = D.prime_factors()
    data['disc_factor'] = nf.disc_factored_latex()
    if D.abs().is_prime() or D == 1:
        data['discriminant'] = "\(%s\)" % str(D)
    else:
        data['discriminant'] = "\(%s=%s\)" % (str(D), data['disc_factor'])
    npr = len(ram_primes)
    ram_primes = str(ram_primes)[1:-1]
    if ram_primes == '':
        ram_primes = r'\textrm{None}'
    data['frob_data'], data['seeram'] = frobs(nf)
    data['phrase'] = group_phrase(n, t, C)
    zk = nf.zk()
    Ra = PolynomialRing(QQ, 'a')
    zk = [latex(Ra(x)) for x in zk]
    zk = ['$%s$' % x for x in zk]
    zk = ', '.join(zk)
    grh_label = '<small>(<a title="assuming GRH" knowl="nf.assuming_grh">assuming GRH</a>)</small>' if nf.used_grh() else ''
    # Short version for properties
    grh_lab = nf.short_grh_string()
    if 'Not' in str(data['class_number']):
        grh_lab=''
        grh_label=''
    pretty_label = field_pretty(label)
    if label != pretty_label:
        pretty_label = "%s: %s" % (label, pretty_label)

    info.update(data)
    if nf.degree() > 1:
        gpK = nf.gpK()
        rootof1coeff = gpK.nfrootsof1()[2]
        rootofunity = Ra(str(pari("lift(%s)" % gpK.nfbasistoalg(rootof1coeff))).replace('x','a'))
    else:
        rootofunity = Ra('-1')

    info.update({
        'label': pretty_label,
        'label_raw': label,
        'polynomial': web_latex_split_on_pm(nf.poly()),
        'ram_primes': ram_primes,
        'integral_basis': zk,
        'regulator': web_latex(nf.regulator()),
        'unit_rank': nf.unit_rank(),
        'root_of_unity': web_latex(rootofunity),
        'fund_units': nf.units(),
        'grh_label': grh_label
    })

    bread.append(('%s' % info['label_raw'], ' '))
    info['downloads_visible'] = True
    info['downloads'] = [('worksheet', '/')]
    info['friends'] = []
    if nf.can_class_number():
        # hide ones that take a lond time to compute on the fly
        # note that the first degree 4 number field missed the zero of the zeta function
        if abs(D**n) < 50000000:
            info['friends'].append(('L-function', "/L/NumberField/%s" % label))
#.........这里部分代码省略.........

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
def render_hmf_webpage(**args):
    C = getDBConnection()
    if 'data' in args:
        data = args['data']
        label = data['label']
    else:
        label = str(args['label'])
        data = C.hmfs.forms.find_one({'label': label})
    if data is None:
        return "No such form"
    info = {}
    try:
        info['count'] = args['count']
    except KeyError:
        info['count'] = 10

    try:
        numeigs = request.args['numeigs']
        numeigs = int(numeigs)
    except:
        numeigs = 20

    hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
    gen_name = findvar(hmf_field['ideals'])
    nf = WebNumberField(data['field_label'], gen_name=gen_name)
    info['hmf_field'] = hmf_field
    info['field'] = nf
    info['base_galois_group'] = nf.galois_string()
    info['field_degree'] = nf.degree()
    info['field_disc'] = str(nf.disc())
    info['field_poly'] = teXify_pol(str(nf.poly()))

    info.update(data)

    info['downloads'] = [
        ('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
        ('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
        ]
    if hmf_field['narrow_class_no'] == 1 and nf.disc()**2 * data['level_norm'] < 40000:
        info['friends'] = [('L-function',
                            url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
    else:
        info['friends'] = [('L-function not available', "")]
    if data['dimension'] == 1:   # Try to attach associated elliptic curve
        lab = split_class_label(info['label'])
        ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
        if ec_from_hmf == None:
            info['friends'] += [('Elliptic curve not available', "")]
        else:
            info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]

    bread = [('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")), ('%s' % data[
                                                                                         'label'], ' ')]

    t = "Hilbert Cusp Form %s" % info['label']

    forms_space = C.hmfs.forms.search.find(
        {'field_label': data['field_label'], 'level_ideal': data['level_ideal']},{'dimension':True})
    dim_space = 0
    for v in forms_space:
        dim_space += v['dimension']

    info['newspace_dimension'] = dim_space

    eigs = data['hecke_eigenvalues']
    eigs = eigs[:min(len(eigs), numeigs)]

    primes = hmf_field['primes']
    n = min(len(eigs), len(primes))
    info['eigs'] = [{'eigenvalue': teXify_pol(eigs[i]),
                     'prime_ideal': teXify_pol(primes[i]),
                     'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]

    try:
        display_eigs = request.args['display_eigs']
        if display_eigs in ['True', 'true', '1', 'yes']:
            display_eigs = True
        else:
            display_eigs = False
    except KeyError:
        display_eigs = False

    if 'numeigs' in request.args:
        display_eigs = True

    info['hecke_polynomial'] = teXify_pol(info['hecke_polynomial'])

    if 'AL_eigenvalues_fixed' in data:
        if data['AL_eigenvalues_fixed'] == 'done':
            info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
                                'prime_ideal': teXify_pol(al[0]),
                                'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
        else:
            info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
    else:
        info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
    info['AL_eigs_count'] = len(info['AL_eigs']) != 0

    max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
    display_eigs = display_eigs or (max_eig_len<=300)
#.........这里部分代码省略.........

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
    def __init__(self, **args):

        # Check for compulsory arguments
        if not ('label' in args.keys()):
            raise KeyError("You have to supply label for a Hilbert modular form L-function")
        logger.debug(str(args))
        # Initialize default values
        if not args['number']:
            args['number'] = 0     # Default choice of embedding of the coefficients
        args['character'] = 0      # Only trivial character

        # Put the arguments into the object dictionary
        self.__dict__.update(args)
        logger.debug(str(self.character) + str(self.label) + str(self.number))

        # Load form from database
        C = base.getDBConnection()
        f = C.hmfs.forms.find_one({'label': self.label})
        if f is None:
            raise KeyError("There is no Hilbert modular form with that label")
        logger.debug(str(args))

        F = WebNumberField(f['field_label'])
        F_hmf = C.hmfs.fields.find_one({'label': f['field_label']})

        self.character = args['character']
        if self.character > 0:
            raise KeyError("The L-function of a Hilbert modular form with non-trivial character has not been implemented yet.")
        self.number = int(args['number'])

        # It is a Sage int
        self.field_disc = F.disc()
        self.field_degree = int(F.degree())
        try:
            self.weight = int(f['parallel_weight'])
        except KeyError:
            self.weight = int(f['weight'].split(', ')[0][1:])

        self.level = f['level_norm'] * self.field_disc ** 2

        # Extract the L-function information from the elliptic modular form
        self.automorphyexp = float(self.weight - 1) / float(2)
        self.Q_fe = float(sqrt(self.level)) / (2 * math.pi) ** (self.field_degree)

        R = QQ['x']
        (x,) = R._first_ngens(1)
        K = NumberField(R(str(f['hecke_polynomial']).replace('^', '**')), 'e')
        e = K.gens()[0]
        iota = K.complex_embeddings()[self.number]

        if self.level == 1:  # For level 1, the sign is always plus
            self.sign = 1
        else:  # for level not 1, calculate sign from Fricke involution and weight
            AL_signs = [iota(eval(al[1])) for al in f['AL_eigenvalues']]
            self.sign = prod(AL_signs) * (-1) ** (float(self.weight * self.field_degree / 2))
        logger.debug("Sign: " + str(self.sign))

        self.kappa_fe = [1 for i in range(self.field_degree)]
        self.lambda_fe = [self.automorphyexp for i in range(self.field_degree)]
        self.mu_fe = []
        self.nu_fe = [self.automorphyexp for i in range(self.field_degree)]
        self.selfdual = True
        self.langlands = True
        self.primitive = True
        self.degree = 2 * self.field_degree
        self.poles = []
        self.residues = []

        # Compute Dirichlet coefficients
        hecke_eigenvalues = [iota(K(str(ae))) for ae in f['hecke_eigenvalues']]
        primes = [pp_str.split(', ') for pp_str in F_hmf['primes']]
        primes = [[int(pp[0][1:]), int(pp[1])] for pp in primes]
        primes = [[pp[0], pp[1], factor(pp[0])[0][1]] for pp in primes]

        PP = primes[-1][0]
        self.numcoeff = PP  # The number of coefficients is given by the norm of the last prime

        ppmidNN = [c[0] for c in f['AL_eigenvalues']]

        ratl_primes = [p for p in range(primes[-1][0] + 1) if is_prime(p)]
        RCC = CC['T']
        (T,) = RCC._first_ngens(1)
        heckepols = [RCC(1) for p in ratl_primes]
        for l in range(len(hecke_eigenvalues)):
            if F_hmf['primes'][l] in ppmidNN:
                heckepols[ratl_primes.index(primes[l][1])] *= 1 - hecke_eigenvalues[l] / \
                    float(sqrt(primes[l][0])) * (T ** primes[l][2])
            else:
                heckepols[ratl_primes.index(primes[l][1])] *= 1 - hecke_eigenvalues[l] / float(
                    sqrt(primes[l][0])) * (T ** primes[l][2]) + (T ** (2 * primes[l][2]))

        # Compute inverses up to given degree
        heckepolsinv = [heckepols[i].xgcd(T ** ceil(log(PP * 1.0) / log(ratl_primes[i] * 1.0)))[1]
                        for i in range(len(heckepols))]

        dcoeffs = [0, 1]
        for n in range(2, ratl_primes[-1] + 1):
            nfact = factor(n)
            if len(nfact) == 1:
                # prime power
#.........这里部分代码省略.........

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
def render_field_webpage(args):
    data = None
    info = {}
    bread = [('Global Number Fields', url_for(".number_field_render_webpage"))]

    # This function should not be called unless label is set.
    label = clean_input(args['label'])
    nf = WebNumberField(label)
    data = {}
    if nf.is_null():
        bread.append(('Search Results', ' '))
        info['err'] = 'There is no field with label %s in the database' % label
        info['label'] = args['label_orig'] if 'label_orig' in args else args['label']
        return search_input_error(info, bread)

    info['wnf'] = nf
    data['degree'] = nf.degree()
    data['class_number'] = nf.class_number_latex()
    ram_primes = nf.ramified_primes()
    t = nf.galois_t()
    n = nf.degree()
    data['is_galois'] = nf.is_galois()
    data['is_abelian'] = nf.is_abelian()
    if nf.is_abelian():
        conductor = nf.conductor()
        data['conductor'] = conductor
        dirichlet_chars = nf.dirichlet_group()
        if len(dirichlet_chars)>0:
            data['dirichlet_group'] = ['<a href = "%s">$\chi_{%s}(%s,&middot;)$</a>' % (url_for('characters.render_Dirichletwebpage',modulus=data['conductor'], number=j), data['conductor'], j) for j in dirichlet_chars]
            data['dirichlet_group'] = r'$\lbrace$' + ', '.join(data['dirichlet_group']) + r'$\rbrace$'
        if data['conductor'].is_prime() or data['conductor'] == 1:
            data['conductor'] = "\(%s\)" % str(data['conductor'])
        else:
            factored_conductor = factor_base_factor(data['conductor'], ram_primes)
            factored_conductor = factor_base_factorization_latex(factored_conductor)
            data['conductor'] = "\(%s=%s\)" % (str(data['conductor']), factored_conductor)
    data['galois_group'] = group_display_knowl(n, t)
    data['cclasses'] = cclasses_display_knowl(n, t)
    data['character_table'] = character_table_display_knowl(n, t)
    data['class_group'] = nf.class_group()
    data['class_group_invs'] = nf.class_group_invariants()
    data['signature'] = nf.signature()
    data['coefficients'] = nf.coeffs()
    nf.make_code_snippets()
    D = nf.disc()
    data['disc_factor'] = nf.disc_factored_latex()
    if D.abs().is_prime() or D == 1:
        data['discriminant'] = "\(%s\)" % str(D)
    else:
        data['discriminant'] = "\(%s=%s\)" % (str(D), data['disc_factor'])
    data['frob_data'], data['seeram'] = frobs(nf)
    # Bad prime information
    npr = len(ram_primes)
    ramified_algebras_data = nf.ramified_algebras_data()
    if isinstance(ramified_algebras_data,str):
        loc_alg = ''
    else:
        # [label, latex, e, f, c, gal]
        loc_alg = ''
        for j in range(npr):
            if ramified_algebras_data[j] is None:
                loc_alg += '<tr><td>%s<td colspan="7">Data not computed'%str(ram_primes[j])
            else:
                mydat = ramified_algebras_data[j]
                p = ram_primes[j]
                loc_alg += '<tr><td rowspan="%d">$%s$</td>'%(len(mydat),str(p))
                mm = mydat[0]
                myurl = url_for('local_fields.by_label', label=mm[0])
                lab = mm[0]
                if mm[3]*mm[2]==1:
                    lab = r'$\Q_{%s}$'%str(p)
                loc_alg += '<td><a href="%s">%s</a><td>$%s$<td>$%d$<td>$%d$<td>$%d$<td>%s<td>$%s$'%(myurl,lab,mm[1],mm[2],mm[3],mm[4],mm[5],show_slope_content(mm[8],mm[6],mm[7]))
                for mm in mydat[1:]:
                    lab = mm[0]
                    if mm[3]*mm[2]==1:
                        lab = r'$\Q_{%s}$'%str(p)
                    loc_alg += '<tr><td><a href="%s">%s</a><td>$%s$<td>$%d$<td>$%d$<td>$%d$<td>%s<td>$%s$'%(myurl,lab,mm[1],mm[2],mm[3],mm[4],mm[5],show_slope_content(mm[8],mm[6],mm[7]))
        loc_alg += '</tbody></table>'

    ram_primes = str(ram_primes)[1:-1]
    if ram_primes == '':
        ram_primes = r'\textrm{None}'
    data['phrase'] = group_phrase(n, t)
    zk = nf.zk()
    Ra = PolynomialRing(QQ, 'a')
    zk = [latex(Ra(x)) for x in zk]
    zk = ['$%s$' % x for x in zk]
    zk = ', '.join(zk)
    grh_label = '<small>(<a title="assuming GRH" knowl="nf.assuming_grh">assuming GRH</a>)</small>' if nf.used_grh() else ''
    # Short version for properties
    grh_lab = nf.short_grh_string()
    if 'Not' in str(data['class_number']):
        grh_lab=''
        grh_label=''
    pretty_label = field_pretty(label)
    if label != pretty_label:
        pretty_label = "%s: %s" % (label, pretty_label)

    info.update(data)
    if nf.degree() > 1:
#.........这里部分代码省略.........

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
def bmf_field_dim_table(**args):
    argsdict = to_dict(args)
    argsdict.update(to_dict(request.args))
    gl_or_sl = argsdict['gl_or_sl']

    field_label=argsdict['field_label']
    field_label = nf_string_to_label(field_label)

    start = 0
    if 'start' in argsdict:
        start = int(argsdict['start'])

    info={}
    info['gl_or_sl'] = gl_or_sl
    # level_flag controls whether to list all levels ('all'), only
    # those with positive cuspidal dimension ('cusp'), or only those
    # with positive new dimension ('new').  Default is 'cusp'.
    level_flag = argsdict.get('level_flag', 'cusp')
    info['level_flag'] = level_flag
    count = 50
    if 'count' in argsdict:
        count = int(argsdict['count'])

    pretty_field_label = field_pretty(field_label)
    bread = [('Bianchi Modular Forms', url_for(".index")), (
        pretty_field_label, ' ')]
    properties = []
    if gl_or_sl=='gl2_dims':
        info['group'] = 'GL(2)'
        info['bgroup'] = '\GL(2,\mathcal{O}_K)'
    else:
        info['group'] = 'SL(2)'
        info['bgroup'] = '\SL(2,\mathcal{O}_K)'
    t = ' '.join(['Dimensions of spaces of {} Bianchi modular forms over'.format(info['group']), pretty_field_label])
    query = {}
    query['field_label'] = field_label
    query[gl_or_sl] = {'$exists': True}
    data = db_dims().find(query)
    data = data.sort([('level_norm', ASCENDING)])
    info['number'] = nres = data.count()
    if nres > count or start != 0:
        info['report'] = 'Displaying items %s-%s of %s levels,' % (start + 1, min(nres, start + count), nres)
    else:
        info['report'] = 'Displaying all %s levels,' % nres

    # convert data to a list and eliminate levels where all
    # new/cuspidal dimensions are 0.  (This could be done at the
    # search stage, but that requires adding new fields to each
    # record.)
    def filter(dat, flag):
        dat1 = dat[gl_or_sl]
        return any([int(dat1[w][flag])>0 for w in dat1])
    flag = 'cuspidal_dim' if level_flag=='cusp' else 'new_dim'
    data = [dat for dat in data if level_flag == 'all' or filter(dat, flag)]

    data = data[start:start+count]
    info['field'] = field_label
    info['field_pretty'] = pretty_field_label
    nf = WebNumberField(field_label)
    info['base_galois_group'] = nf.galois_string()
    info['field_degree'] = nf.degree()
    info['field_disc'] = str(nf.disc())
    info['field_poly'] = teXify_pol(str(nf.poly()))
    weights = set()
    for dat in data:
        weights = weights.union(set(dat[gl_or_sl].keys()))
    weights = list([int(w) for w in weights])
    weights.sort()
    info['weights'] = weights
    info['nweights'] = len(weights)
    info['count'] = count
    info['start'] = start
    info['more'] = int(start + count < nres)

    data.sort(key = lambda x: [int(y) for y in x['level_label'].split(".")])
    dims = {}
    for dat in data:
        dims[dat['level_label']] = d = {}
        for w in weights:
            sw = str(w)
            if sw in dat[gl_or_sl]:
                d[w] = {'d': dat[gl_or_sl][sw]['cuspidal_dim'],
                        'n': dat[gl_or_sl][sw]['new_dim']}
            else:
                d[w] = {'d': '?', 'n': '?'}
    info['nlevels'] = len(data)
    dimtable = [{'level_label': dat['level_label'],
                 'level_norm': dat['level_norm'],
                 'level_space': url_for(".render_bmf_space_webpage", field_label=field_label, level_label=dat['level_label']) if gl_or_sl=='gl2_dims' else "",
                  'dims': dims[dat['level_label']]} for dat in data]
    info['dimtable'] = dimtable
    return render_template("bmf-field_dim_table.html", info=info, title=t, properties=properties, bread=bread)

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
def render_hmf_webpage(**args):
    if 'data' in args:
        data = args['data']
        label = data['label']
    else:
        label = str(args['label'])
        data = get_hmf(label)
    if data is None:
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid Hilbert modular form label. It must be of the form (number field label) - (level label) - (orbit label) separated by dashes, such as 2.2.5.1-31.1-a" % args['label']), "error")
        return search_input_error()
    info = {}
    try:
        info['count'] = args['count']
    except KeyError:
        info['count'] = 10

    hmf_field = get_hmf_field(data['field_label'])
    gen_name = findvar(hmf_field['ideals'])
    nf = WebNumberField(data['field_label'], gen_name=gen_name)
    info['hmf_field'] = hmf_field
    info['field'] = nf
    info['base_galois_group'] = nf.galois_string()
    info['field_degree'] = nf.degree()
    info['field_disc'] = str(nf.disc())
    info['field_poly'] = teXify_pol(str(nf.poly()))

    info.update(data)

    info['downloads'] = [
        ('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
        ('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
        ]
    if hmf_field['narrow_class_no'] == 1 and nf.disc()**2 * data['level_norm'] < 40000:
        info['friends'] = [('L-function',
                            url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
    else:
        info['friends'] = [('L-function not available', "")]
    if data['dimension'] == 1:   # Try to attach associated elliptic curve
        lab = split_class_label(info['label'])
        ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
        if ec_from_hmf == None:
            info['friends'] += [('Elliptic curve not available', "")]
        else:
            info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]

    bread = [("Modular Forms", url_for('mf.modular_form_main_page')), ('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")),
        ('%s' % data['label'], ' ')]

    t = "Hilbert Cusp Form %s" % info['label']

    forms_space = db_forms().find(
        {'field_label': data['field_label'], 'level_ideal': data['level_ideal']},{'dimension':True})
    dim_space = 0
    for v in forms_space:
        dim_space += v['dimension']

    info['newspace_dimension'] = dim_space

    # Get hecke_polynomial, hecke_eigenvalues and AL_eigenvalues
    try:
        numeigs = request.args['numeigs']
        numeigs = int(numeigs)
    except:
        numeigs = 20
    info['numeigs'] = numeigs

    hecke_pol  = data['hecke_polynomial']
    eigs       = data['hecke_eigenvalues']
    eigs = eigs[:min(len(eigs), numeigs)]
    AL_eigs    = data['AL_eigenvalues']

    primes = hmf_field['primes']
    n = min(len(eigs), len(primes))
    info['eigs'] = [{'eigenvalue': add_space_if_positive(teXify_pol(eigs[i])),
                     'prime_ideal': teXify_pol(primes[i]),
                     'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]

    try:
        display_eigs = request.args['display_eigs']
        if display_eigs in ['True', 'true', '1', 'yes']:
            display_eigs = True
        else:
            display_eigs = False
    except KeyError:
        display_eigs = False

    if 'numeigs' in request.args:
        display_eigs = True

    info['hecke_polynomial'] = web_latex_split_on_pm(teXify_pol(hecke_pol))

    if not AL_eigs: # empty list
        if data['level_norm']==1: # OK, no bad primes
            info['AL_eigs'] = 'none'
        else:                     # not OK, AL eigs are missing
            info['AL_eigs'] = 'missing'
    else:
        info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
                            'prime_ideal': teXify_pol(al[0]),
                            'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
#.........这里部分代码省略.........

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
def render_bmf_space_webpage(field_label, level_label):
    info = {}
    t = "Bianchi modular forms of level %s over %s" % (level_label, field_label)
    credit = bianchi_credit
    bread = [('Bianchi modular forms', url_for(".index")),
             (field_pretty(field_label), url_for(".render_bmf_field_dim_table_gl2", field_label=field_label)),
             (level_label, '')]
    friends = []
    properties2 = []

    if not field_label_regex.match(field_label):
        info['err'] = "%s is not a valid label for an imaginary quadratic field" % field_label
    else:
        pretty_field_label = field_pretty(field_label)
        if not db_dims().find({'field_label': field_label}):
            info['err'] = "no dimension information exists in the database for field %s" % pretty_field_label
        else:
            t = "Bianchi Modular Forms of level %s over %s" % (level_label, pretty_field_label)
            data = db_dims().find({'field_label': field_label, 'level_label': level_label})
            nres = data.count()
            if nres==0:
                info['err'] = "no dimension information exists in the database for level %s and field %s" % (level_label, pretty_field_label)
            else:
                data = data.next()
                info['label'] = data['label']
                nf = WebNumberField(field_label)
                info['base_galois_group'] = nf.galois_string()
                info['field_label'] = field_label
                info['pretty_field_label'] = pretty_field_label
                info['level_label'] = level_label
                info['level_norm'] = data['level_norm']
                info['field_degree'] = nf.degree()
                info['field_classno'] = nf.class_number()
                info['field_disc'] = str(nf.disc())
                info['field_poly'] = teXify_pol(str(nf.poly()))
                info['field_knowl'] = nf_display_knowl(field_label, getDBConnection(), pretty_field_label)
                w = 'i' if nf.disc()==-4 else 'a'
                L = nf.K().change_names(w)
                alpha = L.gen()
                info['field_gen'] = latex(alpha)
                I = ideal_from_label(L,level_label)
                info['level_gen'] = latex(I.gens_reduced()[0])
                info['level_fact'] = latex(I.factor())
                dim_data = data['gl2_dims']
                weights = dim_data.keys()
                weights.sort(key=lambda w: int(w))
                for w in weights:
                    dim_data[w]['dim']=dim_data[w]['cuspidal_dim']
                info['dim_data'] = dim_data
                info['weights'] = weights
                info['nweights'] = len(weights)

                newdim = data['gl2_dims']['2']['new_dim']
                newforms = db_forms().find({'field_label':field_label, 'level_label':level_label}).sort('label_suffix', ASCENDING)
                info['nfdata'] = [{
                    'label': f['short_label'],
                    'url': url_for(".render_bmf_webpage",field_label=f['field_label'], level_label=f['level_label'], label_suffix=f['label_suffix']),
                    'wt': f['weight'],
                    'dim': f['dimension'],
                    'sfe': "+1" if f['sfe']==1 else "-1",
                    'bc': bc_info(f['bc']),
                    'cm': cm_info(f['CM']),
                    } for f in newforms]
                info['nnewforms'] = len(info['nfdata'])
                properties2 = [('Base field', pretty_field_label), ('Level',info['level_label']), ('Norm',str(info['level_norm'])), ('New dimension',str(newdim))]
                friends = [('Newform {}'.format(f['label']), f['url']) for f in info['nfdata'] ]

    return render_template("bmf-space.html", info=info, credit=credit, title=t, bread=bread, properties2=properties2, friends=friends)

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import degree [as 别名]
def bmf_field_dim_table(**args):
    argsdict = to_dict(args)
    argsdict.update(to_dict(request.args))
    gl_or_sl = argsdict['gl_or_sl']

    field_label=argsdict['field_label']
    field_label = nf_string_to_label(field_label)

    start = 0
    if 'start' in argsdict:
        start = int(argsdict['start'])

    info={}
    info['gl_or_sl'] = gl_or_sl
    # level_flag controls whether to list all levels ('all'), only
    # those with positive cuspidal dimension ('cusp'), or only those
    # with positive new dimension ('new').  Default is 'cusp'.
    level_flag = argsdict.get('level_flag', 'cusp')
    info['level_flag'] = level_flag
    count = 50
    if 'count' in argsdict:
        count = int(argsdict['count'])

    pretty_field_label = field_pretty(field_label)
    bread = [('Bianchi Modular Forms', url_for(".index")), (
        pretty_field_label, ' ')]
    properties = []
    if gl_or_sl=='gl2_dims':
        info['group'] = 'GL(2)'
        info['bgroup'] = '\GL(2,\mathcal{O}_K)'
    else:
        info['group'] = 'SL(2)'
        info['bgroup'] = '\SL(2,\mathcal{O}_K)'
    t = ' '.join(['Dimensions of spaces of {} Bianchi modular forms over'.format(info['group']), pretty_field_label])
    query = {}
    query['field_label'] = field_label
    query[gl_or_sl] = {'$exists': True}
    if level_flag != 'all':
        # find which weights are present (TODO: get this from a stats collection)
        wts = list(sum((Set(d.keys()) for d in db_dims().distinct(gl_or_sl)),Set()))
    if level_flag == 'cusp':
        # restrict the query to only return levels where at least one
        # cuspidal dimension is positive:
        query.update(
            {'$or':[{gl_or_sl+'.{}.cuspidal_dim'.format(w):{'$gt':0}} for w in wts]}
        )
    if level_flag == 'new':
        # restrict the query to only return levels where at least one
        # new dimension is positive:
        query.update(
            {'$or':[{gl_or_sl+'.{}.new_dim'.format(w):{'$gt':0}} for w in wts]}
        )
    data = db_dims().find(query)
    data = data.sort([('level_norm', ASCENDING)])
    info['number'] = nres = data.count()
    if nres > count or start != 0:
        info['report'] = 'Displaying items %s-%s of %s levels,' % (start + 1, min(nres, start + count), nres)
    else:
        info['report'] = 'Displaying all %s levels,' % nres

    data = list(data.skip(start).limit(count))
    info['field'] = field_label
    info['field_pretty'] = pretty_field_label
    nf = WebNumberField(field_label)
    info['base_galois_group'] = nf.galois_string()
    info['field_degree'] = nf.degree()
    info['field_disc'] = str(nf.disc())
    info['field_poly'] = teXify_pol(str(nf.poly()))
    weights = set()
    for dat in data:
        weights = weights.union(set(dat[gl_or_sl].keys()))
    weights = list([int(w) for w in weights])
    weights.sort()
    info['weights'] = weights
    info['nweights'] = len(weights)
    info['count'] = count
    info['start'] = start
    info['more'] = int(start + count < nres)

    dims = {}
    for dat in data:
        dims[dat['level_label']] = d = {}
        for w in weights:
            sw = str(w)
            if sw in dat[gl_or_sl]:
                d[w] = {'d': dat[gl_or_sl][sw]['cuspidal_dim'],
                        'n': dat[gl_or_sl][sw]['new_dim']}
            else:
                d[w] = {'d': '?', 'n': '?'}
    info['nlevels'] = len(data)
    dimtable = [{'level_label': dat['level_label'],
                 'level_norm': dat['level_norm'],
                 'level_space': url_for(".render_bmf_space_webpage", field_label=field_label, level_label=dat['level_label']) if gl_or_sl=='gl2_dims' else "",
                  'dims': dims[dat['level_label']]} for dat in data]
    print("Length of dimtable = {}".format(len(dimtable)))
    info['dimtable'] = dimtable
    return render_template("bmf-field_dim_table.html", info=info, title=t, properties=properties, bread=bread)