Exemplo n.º 1
0
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' % label2
        info['label'] = args['label_orig'] if 'label_orig' in args else args['label']
        return search_input_error(info, bread)

    info['wnf'] = nf
    from lmfdb.WebNumberField import nf_display_knowl
    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.K())
    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)
    info.update({
        'label': pretty_label,
        'label_raw': label,
        'polynomial': web_latex_split_on_pm(nf.K().defining_polynomial()),
        'ram_primes': ram_primes,
        'integral_basis': zk,
        'regulator': web_latex(nf.regulator()),
        'unit_rank': nf.unit_rank(),
        'root_of_unity': web_latex(nf.K().primitive_root_of_unity()),
        '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))
    info['friends'].append(('Galois group', "/GaloisGroup/%dT%d" % (n, t)))
    if 'dirichlet_group' in info:
        info['friends'].append(('Dirichlet group', url_for("characters.dirichlet_group_table",
                                                           modulus=int(conductor),
                                                           char_number_list=','.join(
                                                               [str(a) for a in dirichlet_chars]),
                                                           poly=info['polynomial'])))
    info['learnmore'] = [('Global number field labels', url_for(
        ".render_labels_page")), 
        (Completename, url_for(".render_discriminants_page")),
        ('How data was computed', url_for(".how_computed_page"))]
    if info['signature'] == [0,1]:
        info['learnmore'].append(('Quadratic imaginary class groups', url_for(".render_class_group_data")))
    # With Galois group labels, probably not needed here
    # info['learnmore'] = [('Global number field labels',
    # url_for(".render_labels_page")), ('Galois group
    # labels',url_for(".render_groups_page")),
    # (Completename,url_for(".render_discriminants_page"))]
    title = "Global Number Field %s" % info['label']

    if npr == 1:
        primes = 'prime'
    else:
        primes = 'primes'

    properties2 = [('Degree:', '%s' % data['degree']),
                   ('Signature:', '$%s$' % data['signature']),
                   ('Discriminant:', '$%s$' % data['disc_factor']),
                   ('Ramified ' + primes + ':', '$%s$' % ram_primes),
                   ('Class number:', '%s %s' % (data['class_number'], grh_lab)),
                   ('Class group:', '%s %s' % (data['class_group_invs'], grh_lab)),
                   ('Galois Group:', group_display_short(data['degree'], t, C))
                   ]
    from lmfdb.math_classes import NumberFieldGaloisGroup
    try:
        info["tim_number_field"] = NumberFieldGaloisGroup(nf._data['coeffs'])
        v = nf.factor_perm_repn(info["tim_number_field"])
        def dopow(m):
            if m==0: return ''
            if m==1: return '*'
            return '*<sup>%d</sup>'% m

        info["mydecomp"] = [dopow(x) for x in v]
    except AttributeError:
        pass
#    del info['_id']
    return render_template("number_field.html", properties2=properties2, credit=NF_credit, title=title, bread=bread, friends=info.pop('friends'), learnmore=info.pop('learnmore'), info=info)
Exemplo n.º 2
0
def render_field_webpage(args):
    data = None
    C = base.getDBConnection()
    info = {}
    bread = [('Global Number Fields', url_for(".number_field_render_webpage"))]

    if 'label' in args:
        label = clean_input(args['label'])
        nf = WebNumberField(label)
        data = {}
    if nf.is_null():
        bread.append(('Search results', ' '))
        label2 = re.sub(r'[<>]', '', args['label'])
        if 'You need to enter a field' in label2:
            info['err'] = label2
        else:
            info['err'] = 'No such field: %s in the database' % label2
        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()
        data['dirichlet_group'] = ['<a href = "%s">$\chi_{%s}(%s,&middot;)$</a>' % (url_for("render_Character", arg1=data['conductor'], arg2=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()
    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.K())
    data['phrase'] = group_phrase(n, t, C)
    zk = pari(nf.K()).nf_subst('a')
    zk = list(zk.nf_get_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()
    pretty_label = field_pretty(label)
    if label != pretty_label:
        pretty_label = "%s: %s" % (label, pretty_label)

    info.update(data)
    info.update({
        'label': pretty_label,
        'label_raw': label,
        'polynomial': web_latex_split_on_pm(nf.K().defining_polynomial()),
        'ram_primes': ram_primes,
        'integral_basis': zk,
        'regulator': web_latex(nf.regulator()),
        'unit_rank': nf.unit_rank(),
        'root_of_unity': web_latex(nf.K().primitive_root_of_unity()),
        '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():
        info['friends'].append(('L-function', "/L/NumberField/%s" % label))
    info['friends'].append(('Galois group', "/GaloisGroup/%dT%d" % (n, t)))
    if 'dirichlet_group' in info:
        info['friends'].append(('Dirichlet group', url_for("dirichlet_group_table",
                                                           modulus=int(conductor),
                                                           char_number_list=','.join(
                                                               [str(a) for a in dirichlet_chars]),
                                                           poly=info['polynomial'])))
    info['learnmore'] = [('Global number field labels', url_for(
        ".render_labels_page")), (Completename, url_for(".render_discriminants_page"))]
    # With Galois group labels, probably not needed here
    # info['learnmore'] = [('Global number field labels',
    # url_for(".render_labels_page")), ('Galois group
    # labels',url_for(".render_groups_page")),
    # (Completename,url_for(".render_discriminants_page"))]
    title = "Global Number Field %s" % info['label']

    if npr == 1:
        primes = 'prime'
    else:
        primes = 'primes'

    properties2 = [('Degree:', '%s' % data['degree']),
                   ('Signature:', '$%s$' % data['signature']),
                   ('Discriminant:', '$%s$' % data['disc_factor']),
                   ('Ramified ' + primes + ':', '$%s$' % ram_primes),
                   ('Class number:', '%s %s' % (data['class_number'], grh_lab)),
                   ('Class group:', '%s %s' % (data['class_group_invs'], grh_lab)),
                   ('Galois Group:', group_display_short(data['degree'], t, C))
                   ]
    from lmfdb.math_classes import NumberFieldGaloisGroup
    try:
        info["tim_number_field"] = NumberFieldGaloisGroup.find_one({"label": label})
        v = nf.factor_perm_repn(info["tim_number_field"])
        info["mydecomp"] = ['*' if x>0 else '' for x in v]
    except AttributeError:
        pass
#    del info['_id']
    return render_template("number_field.html", properties2=properties2, credit=NF_credit, title=title, bread=bread, friends=info.pop('friends'), learnmore=info.pop('learnmore'), info=info)