Python WebNumberField.is_null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 is_null [as 别名]
def render_Heckewebpage(number_field=None, modulus=None, number=None):
    #args = request.args
    #temp_args = to_dict(args)

    args = {}
    args['type'] = 'Hecke'
    args['number_field'] = number_field
    args['modulus'] = modulus
    args['number'] = number

    if number_field == None:
        info = WebHeckeExamples(**args).to_dict()
        return render_template('Hecke.html', **info)
    else:
        WNF = WebNumberField(number_field)
        if WNF.is_null():
            return flask.abort(404, "Number field %s not found."%number_field)

    if modulus == None:
        try:
            info = WebHeckeFamily(**args).to_dict()
        except (ValueError,KeyError,TypeError) as err:
            return flask.abort(404,err.args)
        return render_template('CharFamily.html', **info)
    elif number == None:
        try:
            info = WebHeckeGroup(**args).to_dict()
        except (ValueError,KeyError,TypeError) as err:
            # Typical failure case is a GP error inside bnrinit which we don't really want to display
            return flask.abort(404,'Unable to construct modulus %s for number field %s'%(modulus,number_field))
        m = info['modlabel']
        info['bread'] = [('Characters', url_for(".render_characterNavigation")),
                         ('Hecke', url_for(".render_Heckewebpage")),
                         ('Number Field %s'%number_field, url_for(".render_Heckewebpage", number_field=number_field)),
                         ('%s'%m,  url_for(".render_Heckewebpage", number_field=number_field, modulus=m))]
        info['code'] = dict([(k[4:],info[k]) for k in info if k[0:4] == "code"])
        info['code']['show'] = { lang:'' for lang in info['codelangs'] } # use default show names
        return render_template('CharGroup.html', **info)
    else:
        try:
            X = WebHeckeCharacter(**args)
        except (ValueError,KeyError,TypeError) as err:
            return flask.abort(404, 'Unable to construct Hecke character %s modulo %s in number field %s.'%(number,modulus,number_field))
        info = X.to_dict()
        info['bread'] = [('Characters',url_for(".render_characterNavigation")),
                         ('Hecke',  url_for(".render_Heckewebpage")),
                         ('Number Field %s'%number_field,url_for(".render_Heckewebpage", number_field=number_field)),
                         ('%s'%X.modulus, url_for(".render_Heckewebpage", number_field=number_field, modulus=X.modlabel)),
                         ('%s'%X.number2label(X.number), '')]
        info['code'] = dict([(k[4:],info[k]) for k in info if k[0:4] == "code"])
        info['code']['show'] = { lang:'' for lang in info['codelangs'] } # use default show names
        return render_template('Character.html', **info)

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import is_null [as 别名]
def av_data(label):
    abvar = db.av_fqisog.lookup(label)
    wnf = WebNumberField(abvar['nf'])
    inf = '<div>Dimension: ' + str(abvar['g']) + '<br />'
    if not wnf.is_null():
        inf += 'Number field: ' + nf_display_knowl(abvar['nf'], name = abvar['nf']) + '<br />'
        inf += 'Galois group: ' + group_display_knowl(abvar['gal']['n'],abvar['gal']['t']) + '<br />'
    inf += '$p$-rank: ' + str(abvar['p_rank']) + '</div>'
    inf += '<div align="right">'
    g, q, iso = split_label(label)
    url = url_for("abvarfq.abelian_varieties_by_gqi", g = g, q = q, iso = iso)
    inf += '<a href="%s">%s home page</a>' % (url, label)
    inf += '</div>'
    return inf

# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import is_null [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 is_null [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.........