Ejemplo n.º 1
0
def parse_artin_label(label):
    label = clean_input(label)
    if re.compile(r'^\d+\.\d+e\d+(_\d+e\d+)*\.\d+t\d\.\d+c\d+$').match(label):
        return label
    else:
        raise ValueError(
            "Error parsing input %s.  It is not in a valid form for an Artin representation label, such as 9.2e12_587e3.10t32.1c1"
            % label)
Ejemplo n.º 2
0
Archivo: main.py Proyecto: koffie/lmfdb
def parse_artin_label(label):
    label = clean_input(label)
    if LABEL_RE.match(label):
        return label
    else:
        raise ValueError(
            "Error parsing input %s.  It is not in a valid form for an Artin representation label, such as 9.2e12_587e3.10t32.1c1"
            % label)
Ejemplo n.º 3
0
def hgm_jump(info):
    label = clean_input(info['jump_to'])
    if HGM_LABEL_RE.match(label):
        return render_hgm_webpage(normalize_motive(label))
    if HGM_FAMILY_LABEL_RE.match(label):
        return render_hgm_family_webpage(normalize_family(label))
    flash_error('%s is not a valid label for a hypergeometric motive or family of hypergeometric motives', label)
    return redirect(url_for(".index"))
Ejemplo n.º 4
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def parse_artin_label(label):
    label = clean_input(label)
    if re.compile(r"^\d+\.\d+e\d+(_\d+e\d+)*\.\d+t\d\.\d+c\d+$").match(label):
        return label
    else:
        raise ValueError(
            "Error parsing input %s.  It is not in a valid form for an Artin representation label, such as 9.2e12_587e3.10t32.1c1"
            % label
        )
Ejemplo n.º 5
0
def render_hgm_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        data = C.hgm.motives.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info['err'] = "Motive " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Hypergeometric Motive:' + label
        A = data['A']
        B = data['B']
        tn,td = data['t']
        t = latex(QQ(str(tn)+'/'+str(td)))
        primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
        locinfo = data['locinfo']
        for j in range(len(locinfo)):
            locinfo[j] = [primes[j]] + locinfo[j]
            locinfo[j][2] = poly_with_factored_coeffs(locinfo[j][2], primes[j])
        hodge = data['hodge']
        prop2 = [
            ('Degree', '\(%s\)' % data['degree']),
            ('Weight',  '\(%s\)' % data['weight']),
            ('Conductor', '\(%s\)' % data['cond']),
        ]
        # Now add factorization of conductor
        Cond = ZZ(data['cond'])
        if not (Cond.abs().is_prime() or Cond == 1):
            data['cond'] = "%s=%s" % (str(Cond), factorint(data['cond']))

        info.update({
                    'A': A,
                    'B': B,
                    't': t,
                    'degree': data['degree'],
                    'weight': data['weight'],
                    'sign': data['sign'],
                    'sig': data['sig'],
                    'hodge': hodge,
                    'cond': data['cond'],
                    'req': data['req'],
                    'locinfo': locinfo
                    })
        AB_data, t_data = data["label"].split("_t")
        #AB_data = data["label"].split("_t")[0]
        friends = [("Motive family "+AB_data.replace("_"," "), url_for(".by_family_label", label = AB_data))]
        friends.append(('L-function', url_for("l_functions.l_function_hgm_page", label=AB_data, t='t'+t_data)))
#        if rffriend != '':
#            friends.append(('Discriminant root field', rffriend))


        bread = get_bread([(label, ' ')])
        return render_template("hgm-show-motive.html", credit=HGM_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends)
Ejemplo n.º 6
0
def by_label(label):
    try:
        nflabel = nf_string_to_label(clean_input(label))
        if label != nflabel:
            return redirect(url_for(".by_label", label=nflabel), 301)
        return render_field_webpage({'label': nf_string_to_label(label)})
    except ValueError as err:
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid number field. %s" % (label,err)), "error")
        bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search Results', ' ')]
        return search_input_error({'err':''}, bread)
Ejemplo n.º 7
0
def by_label(label):
    try:
        nflabel = nf_string_to_label(clean_input(label))
        if label != nflabel:
            return redirect(url_for(".by_label", label=nflabel), 301)
        return render_field_webpage({'label': nf_string_to_label(label)})
    except ValueError as err:
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid number field. %s" % (label,err)), "error")
        bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search Results', ' ')]
        return search_input_error({'err':''}, bread)
Ejemplo n.º 8
0
def render_hgm_family_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        data = C.hgm.families.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info['err'] = "Family of hypergeometric motives " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Hypergeometric Motive Family:' + label
        A = data['A']
        B = data['B']
        hodge = data['hodge']
        prop2 = [
            ('Degree', '\(%s\)' % data['degree']),
            ('Weight',  '\(%s\)' % data['weight'])
        ]
        info.update({
                    'A': A,
                    'B': B,
                    'degree': data['degree'],
                    'weight': data['weight'],
                    'hodge': hodge,
                    'gal2': data['gal2'],
                    'gal3': data['gal3'],
                    'gal5': data['gal5'],
                    'gal7': data['gal7'],
                    })
        friends = [('Motives in the family', url_for('hypergm.index')+"?A=%s&B=%s" % (str(A), str(B)))]
#        if unramfriend != '':
#            friends.append(('Unramified subfield', unramfriend))
#        if rffriend != '':
#            friends.append(('Discriminant root field', rffriend))

        info.update({"plotcircle":  url_for(".hgm_family_circle_image", AB  =  "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
        info.update({"plotlinear": url_for(".hgm_family_linear_image", AB  = "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
        info.update({"plotconstant": url_for(".hgm_family_constant_image", AB  = "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
        bread = get_bread([(label, ' ')])
        return render_template("hgm-show-family.html", credit=HGM_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends)
Ejemplo n.º 9
0
Archivo: main.py Proyecto: koffie/lmfdb
def render_hecke_algebras_webpage_l_adic(**args):
    data = None
    if 'orbit_label' in args and 'prime' in args:
        lab = clean_input(args.get('orbit_label'))
        if lab != args.get('orbit_label'):
            base_lab=".".join([split(lab)[i] for i in [0,1,2]])
            return redirect(url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        try:
            ell = int(args.get('prime'))
        except ValueError:
            base_lab=".".join([split(lab)[i] for i in [0,1,2]])
            return redirect(url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        data = db.hecke_ladic.lucky({'orbit_label': lab , 'ell': ell})
    if data is None:
        t = "Hecke Algebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for the &#x2113;-adic information for an Hecke Algebra orbit in the database." % (lab)),"error")
        return render_template("hecke_algebras-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
    info = {}
    info.update(data)

    proj = ['index','orbit_label','ell','idempotent','field','structure','properties','operators']
    res = list(db.hecke_ladic.search({'level': data['level'],'weight': data['weight'],'orbit_label': data['orbit_label'], 'ell': data['ell']}, proj))

    for f in res:
        if f['idempotent'] != "":
            dim = len(sage_eval(f['idempotent']))
            l_max = sage_eval(f['idempotent'])[0][0].ndigits()
            if dim > 4 or l_max > 5:
                f['idempotent_display'] = []
            elif dim == 1:
                f['idempotent_display'] = sage_eval(f['idempotent'])[0][0]
            else:
                f['idempotent_display'] = latex(matrix(sage_eval(f['idempotent'])))
        else:
            f['idempotent_display']=latex(matrix([[1]]))
        del f['idempotent']
        f['download_id'] = [(i, url_for(".render_hecke_algebras_webpage_ell_download", orbit_label=f['orbit_label'], index=f['index'], prime=f['ell'], lang=i, obj='idempotents')) for i in ['magma','sage']]  # for 'gp' the code does not work, since p-adics are not implemented
        field = f.pop('field')
        if field is not None:
            f['deg'] = field[1]
            f['field_poly'] = field[2]
        structure = f.pop('structure')
        if structure is not None:
            f['dim'] = structure[0]
            f['num_gen'] = structure[1]
            s2 = sage_eval(structure[2])
            f['gens'] = [[int(s2.index(i)+1), str(i)] for i in s2]
            f['rel'] = sage_eval(structure[3])
        properties = f.pop('properties')
        if properties is not None:
            f['grading'] = properties[0]
            f['gorenstein_def'] = properties[1]
            f['gorenstein'] = "yes" if properties[1] == 0 else "no"
        operators = f.pop('operators')
        if operators is not None:
            f['operators_mod_l'] = operators
            f['num_hecke_op'] = len(operators)
            f['size_op'] = size = sqrt(len(operators[0]))
            if size > 4:
                f['operators_mod_l_display'] = []
            elif size == 1:
                f['operators_mod_l_display'] = [[i+1, operators[i][0]] for i in range(10)]
            else:
                f['operators_mod_l_display'] = [[i+1, latex(matrix(size,size,operators[i]))] for i in range(5)]
            f['download_op'] = [(lang, url_for(".render_hecke_algebras_webpage_ell_download", orbit_label=f['orbit_label'], index=f['index'], prime=f['ell'], lang=lang, obj='operators')) for lang in ['magma','sage']]  # for 'gp' the code does not work

    info['num_l_adic_orbits'] = len(res)
    info['l_adic_orbits'] = res
    info['level']=int(data['level'])
    info['weight']= int(data['weight'])
    info['base_lab']=".".join([split(data['orbit_label'])[i] for i in [0,1,2]])
    info['orbit_label']= str(data['orbit_label'])
    info['ell']=int(data['ell'])

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")), ('%s' % info['base_lab'], url_for('.render_hecke_algebras_webpage', label=info['base_lab'])), ('%s' % info['ell'], ' ')]
    credit = hecke_algebras_credit
    info['properties'] = [
        ('Level', '%s' %info['level']),
        ('Weight', '%s' %info['weight']),
        ('Characteristic', '%s' %info['ell']),
        ('Orbit label', '%s' %info['orbit_label'])]
    info['friends'] = [('Modular form ' + info['base_lab'], url_for("cmf.by_url_space_label", level=info['level'], weight=info['weight'], char_orbit_label='a'))]

    t = "%s-adic and mod %s Data for the Hecke Algebra Orbit %s" % (info['ell'], info['ell'], info['orbit_label'])
    return render_template("hecke_algebras_l_adic-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list(), friends=info['friends'])
Ejemplo n.º 10
0
def render_hgcwa_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        data = C.curve_automorphisms.families.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info[
                'err'] = "Higher Genus Curve with Automorphism " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        g = data['genus']
        GG = data['trangplabel']
        gn = GG[0]
        gt = GG[1]

        group = groupid_to_meaningful(data['group'])
        title = 'Family of genus ' + str(
            g) + ' curves with automorphism group $' + group + '$'

        sign = data['signature']

        prop2 = [('Genus', '\(%d\)' % g),
                 ('Group', group_display_short(gn, gt, C)),
                 ('Signature', '\(%s\)' % sign)]
        info.update({
            'genus': data['genus'],
            'genvecs': perm_display(data['gen_vectors']),
            'sign': data['signature'],
            'group': groupid_to_meaningful(data['group']),
            'g0': data['g0'],
            'dim': data['r'] - 3,
            'r': data['r'],
            'ishyp': tfTOyn(data['hyperelliptic']),
            'deg': data['degree'],
            'trgroup': group_display_short(gn, gt, C)
        })

        if 'hyp_eqn' in data:
            info.update({'eqn': data['hyp_eqn']})

        gg = "/GaloisGroup/"

        if 'full_auto' in data:
            info.update({
                'fullauto': groupid_to_meaningful(data['full_auto']),
                'signH': data['signH'],
                'higgenlabel': data['full_label']
            })
            higgenstrg = "/HigherGenus/C/aut/" + data['full_label']
            friends = [('Automorphism group', gg),
                       ('Family of full automorphism', higgenstrg)]
        else:
            friends = [('Automorphism group', gg)]

        bread = get_bread([(label, ' ')])
        learnmore = [('Completeness of the data',
                      url_for(".completeness_page")),
                     ('Source of the data', url_for(".how_computed_page")),
                     ('Labeling convension', url_for(".labels_page"))]

        downloads = [('Download this example', '.')]

        return render_template("hgcwa-show-curve.html",
                               credit=HGCwA_credit,
                               title=title,
                               bread=bread,
                               info=info,
                               properties2=prop2,
                               friends=friends,
                               learnmore=learnmore,
                               downloads=downloads)
Ejemplo n.º 11
0
def render_artin_representation_webpage(label):
    if re.compile(r'^\d+$').match(label):
        return artin_representation_search(**{'dimension': label})

    bread = get_bread([(label, ' ')])

    # label=dim.cond.nTt.indexcj, c is literal, j is index in conj class
    # Should we have a big try around this to catch bad labels?
    label = clean_input(label)
    try:
        the_rep = ArtinRepresentation(label)
    except:
        flash(
            Markup(
                "Error: <span style='color:black'>%s</span> is not the label of an Artin representation in the database."
                % (label)), "error")
        return search_input_error({'err': ''}, bread)

    extra_data = {}  # for testing?
    C = getDBConnection()
    extra_data['galois_knowl'] = group_display_knowl(5, 3, C)  # for testing?
    #artin_logger.info("Found %s" % (the_rep._data))

    title = "Artin representation %s" % label
    the_nf = the_rep.number_field_galois_group()
    from lmfdb.number_field_galois_groups import nfgg_page
    from lmfdb.number_field_galois_groups.main import by_data
    if the_rep.sign() == 0:
        processed_root_number = "not computed"
    else:
        processed_root_number = str(the_rep.sign())
    properties = [
        ("Dimension", str(the_rep.dimension())),
        ("Group", the_rep.group()),
        #("Conductor", str(the_rep.conductor())),
        ("Conductor", "$" + the_rep.factored_conductor_latex() + "$"),
        #("Bad primes", str(the_rep.bad_primes())),
        ("Root number", processed_root_number),
        ("Frobenius-Schur indicator", str(the_rep.indicator()))
    ]

    friends = []
    nf_url = the_nf.url_for()
    if nf_url:
        friends.append(("Artin Field", nf_url))
    cc = the_rep.central_character()
    if cc is not None:
        if cc.modulus <= 100000:
            if the_rep.dimension() == 1:
                friends.append(("Corresponding Dirichlet character",
                                url_for("characters.render_Dirichletwebpage",
                                        modulus=cc.modulus,
                                        number=cc.number)))
            else:
                friends.append(("Determinant character",
                                url_for("characters.render_Dirichletwebpage",
                                        modulus=cc.modulus,
                                        number=cc.number)))

    # once the L-functions are in the database, the link can always be shown
    if the_rep.dimension() <= 6:
        friends.append(("L-function",
                        url_for("l_functions.l_function_artin_page",
                                label=the_rep.label())))
    info = {}
    #mychar = the_rep.central_char()
    #info['pol2']= str([((j+1),mychar(j+1, 2*the_rep.character_field())) for j in range(50)])
    #info['pol3']=str(the_rep.central_character())
    #info['pol3']=str(the_rep.central_char(3))
    #info['pol5']=str(the_rep.central_char(5))
    #info['pol7']=str(the_rep.central_char(7))
    #info['pol11']=str(the_rep.central_char(11))

    return render_template("artin-representation-show.html",
                           credit=tim_credit,
                           support=support_credit,
                           title=title,
                           bread=bread,
                           friends=friends,
                           object=the_rep,
                           properties2=properties,
                           extra_data=extra_data,
                           info=info)
Ejemplo n.º 12
0
Archivo: main.py Proyecto: 370417/lmfdb
def render_family(args):
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        dataz = C.curve_automorphisms.passports.find({'label': label}).sort('cc.0', pymongo.ASCENDING)
        
        if dataz.count() is 0:
            flash_error( "No family with label %s was found in the database.", label)
            return redirect(url_for(".index"))

        data=dataz[0]

        g = data['genus']
        GG = ast.literal_eval(data['group'])
        gn = GG[0]
        gt = GG[1]

        gp_string=str(gn) + '.' + str(gt)
        pretty_group=sg_pretty(gp_string)

        if gp_string == pretty_group:
            spname=False
        else:
            spname=True
        title = 'Family of Genus ' + str(g) + ' Curves with Automorphism Group $' + pretty_group +'$'
        smallgroup="[" + str(gn) + "," +str(gt) +"]"

        prop2 = [
            ('Genus', '\(%d\)' % g),
            ('Group', '\(%s\)' %  pretty_group),
            ('Signature', '\(%s\)' % sign_display(ast.literal_eval(data['signature'])))
        ]
        info.update({'genus': data['genus'],
                    'sign': sign_display(ast.literal_eval(data['signature'])),
                     'group': pretty_group,
                    'g0':data['g0'],
                    'dim':data['dim'],
                    'r':data['r'],
                    'gpid': smallgroup
                   })

        if spname:
            info.update({'specialname': True})

        Lcc=[]
        Lall=[]
        Ltopo_rep=[] #List of topological representatives
        Lelements=[] #List of lists of equivalence classes    
        for dat in dataz:
            if ast.literal_eval(dat['con']) not in Lcc:
                urlstrng=dat['passport_label']
                Lcc.append(ast.literal_eval(dat['con']))
                Lall.append([cc_display(ast.literal_eval(dat['con'])),dat['passport_label'],
                             urlstrng])
                
            #Topological equivalence
            if 'topological' in dat:
                if dat['topological'] == dat['cc']:
                    x1=[] #A list of permutations of generating vectors of topo_rep
                    for perm in dat['gen_vectors']:
                        x1.append(sep.join(split_perm(Permutation(perm).cycle_string())))
                    Ltopo_rep.append([dat['passport_label'], dat['total_label'], x1])

                    topo_class = C.curve_automorphisms.passports.find({'label': dat['label'], 'topological': dat['cc']}).sort('cc.0', pymongo.ASCENDING)
                    elements=[] #An equivalence class
                    for element in topo_class:
                        elements.append((element['passport_label'], element['total_label']))
                    Lelements.append(elements)    

        Ltopo_class = zip(Ltopo_rep, Lelements)
        topo_length = len(Ltopo_rep)
        #Add topological equivalence to info
        info.update({'topological_rep': Ltopo_rep})
        info.update({'topological_class': Ltopo_class})
        info.update({'topological_num': topo_length})
        
        info.update({'passport': Lall})
        info.update({'passport_num': len(Lall)})

        
        g2List = ['[2,1]','[4,2]','[8,3]','[10,2]','[12,4]','[24,8]','[48,29]']
        if g  == 2 and data['group'] in g2List:
            g2url = "/Genus2Curve/Q/?geom_aut_grp_id=" + data['group']
            friends = [("Genus 2 curves over $\Q$", g2url ) ]
        else:
            friends = [ ]

        br_g, br_gp, br_sign = split_family_label(label)

        bread_sign = label_to_breadcrumbs(br_sign)
        bread_gp = label_to_breadcrumbs(br_gp)

        bread = get_bread([(br_g, './?genus='+br_g),('$'+pretty_group+'$','./?genus='+br_g + '&group='+bread_gp), (bread_sign,' ')])
        learnmore =[('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Labeling convention', url_for(".labels_page"))]
        if topo_length == 0:
            downloads = [('Download Magma code', url_for(".hgcwa_code_download",  label=label, download_type='magma')),
                             ('Download Gap code', url_for(".hgcwa_code_download", label=label, download_type='gap'))]
        else:
            downloads = [('Magma code', None),
                             (u'\u2003 All vectors', url_for(".hgcwa_code_download",  label=label, download_type='magma')),
                             (u'\u2003 Up to topological equivalence', url_for(".hgcwa_code_download", label=label, download_type='topo_magma')),
                             ('Gap code', None),
                             (u'\u2003 All vectors', url_for(".hgcwa_code_download", label=label, download_type='gap')),
                             (u'\u2003 Up to topological equivalence', url_for(".hgcwa_code_download", label=label, download_type='topo_gap'))] 

        return render_template("hgcwa-show-family.html",
                               title=title, bread=bread, info=info,
                               properties2=prop2, friends=friends,
                               learnmore=learnmore, downloads=downloads, credit=credit)
Ejemplo n.º 13
0
def render_hecke_algebras_webpage(**args):
    data = None
    if 'label' in args:
        lab = clean_input(args.get('label'))
        if lab != args.get('label'):
            return redirect(url_for('.render_hecke_algebras_webpage', label=lab), 301)
        data = hecke_db().find_one({'label': lab })
    if data is None:
        t = "Hecke Agebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for a Hecke Algebras in the database." % (lab)),"error")
        return render_template("hecke_algebras-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
    info = {}
    info.update(data)

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")), ('%s' % data['label'], ' ')]
    credit = hecke_algebras_credit
    f = hecke_db().find_one({'level': data['level'],'weight': data['weight'],'num_orbits': data['num_orbits']})
    info['level']=int(f['level'])
    info['weight']= int(f['weight'])
    info['num_orbits']= int(f['num_orbits'])
    dim_count = "not available"

    orb = hecke_orbits_db().find({'parent_label': f['label']}).sort([('orbit', ASC)])
    if orb.count()!=0:
        #consistency check
        if orb.count()!= int(f['num_orbits']):
            return search_input_error(info)

        dim_count=0
        res_clean = []
        for v in orb:
            v_clean = {}
            v_clean['orbit_label'] = v['orbit_label']
            v_clean['hecke_op'] = v['hecke_op']
            v_clean['gen'] = v['gen']
            v_clean['dim'] = int(matrix(sage_eval(v_clean['hecke_op'])[0]).dimensions()[0])
            dim_count = dim_count + v_clean['dim']
            if v_clean['dim']>4:
                v_clean['hecke_op_display'] = []
            elif v_clean['dim']==1:
                v_clean['hecke_op_display'] = [[i+1, (sage_eval(v_clean['hecke_op'])[i])[0][0]] for i in range(0,10)]
            else:
                v_clean['hecke_op_display'] = [[i+1, latex(matrix(sage_eval(v_clean['hecke_op'])[i]))] for i in range(0,5)]
            v_clean['num_hecke_op'] = v['num_hecke_op']
            v_clean['download_op'] = [(i, url_for(".render_hecke_algebras_webpage_download", orbit_label=v_clean['orbit_label'], lang=i, obj='operators')) for i in ['gp', 'magma','sage']]
            if 'Zbasis' in v.keys():
                v_clean['Zbasis'] = [[int(i) for i in j] for j in v['Zbasis']]
                if v_clean['dim']>4:
                    v_clean['gen_display'] = []
                elif v_clean['dim']==1:
                    v_clean['gen_display'] = [v_clean['Zbasis'][0][0]]
                else:
                    v_clean['gen_display'] = [latex(matrix(v_clean['dim'],v_clean['dim'], v_clean['Zbasis'][i])) for i in range(0,v_clean['dim'])]
                v_clean['discriminant'] = int(v['discriminant'])
                v_clean['disc_fac'] = [[int(i) for i in j] for j in v['disc_fac']]
                v_clean['Qbasis'] = [int(i) for i in v['Qbasis']]
                v_clean['Qalg_gen'] = [int(i) for i in v['Qalg_gen']]
                if 'inner_twists' in v.keys():
                    v_clean['inner_twists'] = [str(i) for i in v['inner_twists']]
                else:
                    v_clean['inner_twists'] = "not available"
                v_clean['download_gen'] = [(i, url_for(".render_hecke_algebras_webpage_download", orbit_label=v_clean['orbit_label'], lang=i, obj='gen')) for i in ['gp', 'magma','sage']]
            res_clean.append(v_clean)

        info['orbits'] = res_clean

    info['dim_alg'] = dim_count
    info['l_adic'] = l_range
    info['properties'] = [
        ('Label', '%s' %info['label']),
        ('Level', '%s' %info['level']),
        ('Weight', '%s' %info['weight'])]
    if info['num_orbits']!=0:      
        info['friends'] = [('Newforms space ' + info['label'], url_for("emf.render_elliptic_modular_forms", level=info['level'], weight=info['weight'], character=1))]
    else:
        info['friends'] = []    
    t = "Hecke Algebra %s" % info['label']
    return render_template("hecke_algebras-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list(), friends=info['friends'])
Ejemplo n.º 14
0
def render_family(args):
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        dataz = C.curve_automorphisms.passports.find({'label': label})
        if dataz.count() is 0:
            flash_error("No family with label %s was found in the database.",
                        label)
            return redirect(url_for(".index"))
        data = dataz[0]
        g = data['genus']
        GG = ast.literal_eval(data['group'])
        gn = GG[0]
        gt = GG[1]

        gp_string = str(gn) + '.' + str(gt)
        pretty_group = sg_pretty(gp_string)

        if gp_string == pretty_group:
            spname = False
        else:
            spname = True
        title = 'Family of genus ' + str(
            g) + ' curves with automorphism group $' + pretty_group + '$'
        smallgroup = "[" + str(gn) + "," + str(gt) + "]"

        prop2 = [('Genus', '\(%d\)' % g), ('Group', '\(%s\)' % pretty_group),
                 ('Signature',
                  '\(%s\)' % sign_display(ast.literal_eval(data['signature'])))
                 ]
        info.update({
            'genus': data['genus'],
            'sign': sign_display(ast.literal_eval(data['signature'])),
            'group': pretty_group,
            'g0': data['g0'],
            'dim': data['dim'],
            'r': data['r'],
            'gpid': smallgroup
        })

        if spname:
            info.update({'specialname': True})

        Lcc = []
        Lall = []
        i = 1
        for dat in dataz:
            if ast.literal_eval(dat['con']) not in Lcc:
                urlstrng = dat['passport_label']
                Lcc.append(ast.literal_eval(dat['con']))
                Lall.append([
                    cc_display(ast.literal_eval(dat['con'])),
                    dat['passport_label'], urlstrng
                ])
                i = i + 1

        info.update({'passport': Lall})

        g2List = [
            '[2,1]', '[4,2]', '[8,3]', '[10,2]', '[12,4]', '[24,8]', '[48,29]'
        ]
        if g == 2 and data['group'] in g2List:
            g2url = "/Genus2Curve/Q/?geom_aut_grp_id=" + data['group']
            friends = [("Genus 2 curves over $\Q$", g2url)]
        else:
            friends = []

        br_g, br_gp, br_sign = split_family_label(label)

        bread_sign = label_to_breadcrumbs(br_sign)
        bread_gp = label_to_breadcrumbs(br_gp)

        bread = get_bread([(br_g, './?genus=' + br_g),
                           ('$' + pretty_group + '$',
                            './?genus=' + br_g + '&group=' + bread_gp),
                           (bread_sign, ' ')])
        learnmore = [('Completeness of the data',
                      url_for(".completeness_page")),
                     ('Source of the data', url_for(".how_computed_page")),
                     ('Labeling convention', url_for(".labels_page"))]

        downloads = [('Download Magma code',
                      url_for(".hgcwa_code_download",
                              label=label,
                              download_type='magma')),
                     ('Download Gap code',
                      url_for(".hgcwa_code_download",
                              label=label,
                              download_type='gap'))]

        return render_template("hgcwa-show-family.html",
                               title=title,
                               bread=bread,
                               info=info,
                               properties2=prop2,
                               friends=friends,
                               learnmore=learnmore,
                               downloads=downloads,
                               credit=credit)
Ejemplo n.º 15
0
def number_field_search(info):

    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")),
        ('Quadratic imaginary class groups',
         url_for(".render_class_group_data"))
    ]
    t = 'Global Number Field search results'
    bread = [('Global Number Fields', url_for(".number_field_render_webpage")),
             ('Search results', ' ')]

    if 'natural' in info:
        query = {'label_orig': info['natural']}
        try:
            parse_nf_string(info,
                            query,
                            'natural',
                            name="Label",
                            qfield='label')
            return redirect(
                url_for(".by_label", label=clean_input(query['label_orig'])))
        except ValueError:
            query['err'] = info['err']
            return search_input_error(query, bread)

    if 'algebra' in info:
        fields = info['algebra'].split('_')
        fields2 = [WebNumberField.from_coeffs(a) for a in fields]
        for j in range(len(fields)):
            if fields2[j] is None:
                fields2[j] = WebNumberField.fakenf(fields[j])
        t = 'Number field algebra'
        info = {}
        info = {'fields': fields2}
        return render_template("number_field_algebra.html",
                               info=info,
                               title=t,
                               bread=bread)

    query = {}
    try:
        parse_galgrp(info, query, qfield='galois')
        parse_ints(info, query, 'degree')
        parse_bracketed_posints(info,
                                query,
                                'signature',
                                split=False,
                                exactlength=2)
        parse_signed_ints(info,
                          query,
                          'discriminant',
                          qfield=('disc_sign', 'disc_abs_key'),
                          parse_one=make_disc_key)
        parse_ints(info, query, 'class_number')
        parse_bracketed_posints(info,
                                query,
                                'class_group',
                                split=False,
                                check_divisibility='increasing')
        parse_primes(info,
                     query,
                     'ur_primes',
                     name='Unramified primes',
                     qfield='ramps',
                     mode='complement',
                     to_string=True)
        # modes are now contained (in), exactly, include
        if 'ram_quantifier' in info and str(
                info['ram_quantifier']) == 'include':
            mode = 'append'
            parse_primes(info,
                         query,
                         'ram_primes',
                         'ramified primes',
                         'ramps',
                         mode,
                         to_string=True)
        elif 'ram_quantifier' in info and str(
                info['ram_quantifier']) == 'contained':
            parse_primes(info,
                         query,
                         'ram_primes',
                         'ramified primes',
                         'ramps_all',
                         'subsets',
                         to_string=False)
            pass  # build list
        else:
            mode = 'liststring'
            parse_primes(info, query, 'ram_primes', 'ramified primes',
                         'ramps_all', mode)
    except ValueError:
        return search_input_error(info, bread)
    count = parse_count(info)
    start = parse_start(info)

    # nf_logger.debug(query)
    info['query'] = dict(query)
    if 'lucky' in info:
        one = nfdb().find_one(query)
        if one:
            label = one['label']
            return redirect(url_for(".by_label", label=clean_input(label)))

    fields = nfdb()

    res = fields.find(query)
    res = res.sort([('degree', ASC), ('disc_abs_key', ASC),
                    ('disc_sign', ASC)])

    if 'download' in info and info['download'] != '0':
        return download_search(info, res)

    nres = res.count()
    res = res.skip(start).limit(count)

    if (start >= nres):
        start -= (1 + (start - nres) / count) * count
    if (start < 0):
        start = 0

    info['fields'] = res
    info['number'] = nres
    info['start'] = start
    if nres == 1:
        info['report'] = 'unique match'
    else:
        if nres > count or start != 0:
            info['report'] = 'displaying matches %s-%s of %s' % (
                start + 1, min(nres, start + count), nres)
        else:
            info['report'] = 'displaying all %s matches' % nres

    info['wnf'] = WebNumberField.from_data
    return render_template("number_field_search.html",
                           info=info,
                           title=t,
                           bread=bread)
Ejemplo n.º 16
0
def by_label(label):
    clean_label = clean_input(label)
    if clean_label != label:
        return redirect(url_for('.by_label', label=clean_label), 301)
    return search_by_label(label)
Ejemplo n.º 17
0
def render_hgcwa_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        data = C.curve_automorphisms.families.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info['err'] = "Higher Genus Curve with Automorphism " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        g = data['genus']
        GG = data['group']
        gn = GG[0]
        gt = GG[1]
    

        group = groupid_to_meaningful(data['group'])
        if group == str(GG) or group == "[" + str(gn)+","+str(gt)+"]":
            spname=False
        else:
            spname=True
        title = 'Family of genus ' + str(g) + ' curves with automorphism group $' + group +'$'
        smallgroup="(" + str(gn) + "," +str(gt) +")"   

        prop2 = [
            ('Genus', '\(%d\)' % g),
            ('Small Group', '\(%s\)' %  smallgroup),
            ('Signature', '\(%s\)' % sign_display(data['signature']))
        ]
        info.update({'genus': data['genus'],
                    'genvecs': data['gen_vectors'],
                    'sign': sign_display(data['signature']),   
                    'group': groupid_to_meaningful(data['group']),
                    'g0':data['g0'],
                    'dim':data['dim'],
                     'r':data['r'],
                     'gpid': smallgroup
                   })

        if spname:
            info.update({'specialname': True})
        		   
        if 'eqn' in data:
            info.update({'eqn': data['eqn']})

        if 'hyperelliptic' in data:
            info.update({'ishyp':  tfTOyn(data['hyperelliptic'])})
            
        if 'hyp_involution' in data:
            info.update({'hypinv': data['hyp_involution']})
            
        gg = "/GaloisGroup/" + str(gn) + "T" + str(gt)
            
        if 'full_auto' in data:
            info.update({'fullauto': groupid_to_meaningful(data['full_auto']),
                         'signH':sign_display(data['signH']),
                         'higgenlabel' : data['full_label'] })
            higgenstrg = "/HigherGenus/C/aut/" + data['full_label']
            friends = [('Family of full automorphisms',  higgenstrg  )]
        else:
            friends = [ ]
        

        
        bread = get_bread([(label, ' ')])
        learnmore =[('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Labeling convention', url_for(".labels_page"))]

        downloads = [('Download this example', '.')]
            
        return render_template("hgcwa-show-curve.html", credit=HGCwA_credit,
                               title=title, bread=bread, info=info,
                               properties2=prop2, friends=friends,
                               learnmore=learnmore, downloads=downloads)
Ejemplo n.º 18
0
def render_group_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        label = label.replace('t', 'T')
        data = db.gps_transitive.lookup(label)
        if data is None:
            bread = get_bread([("Search Error", ' ')])
            info['err'] = "Group " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        data['label_raw'] = label.lower()
        title = 'Galois Group: ' + label
        wgg = WebGaloisGroup.from_data(data)
        n = data['n']
        t = data['t']
        data['yesno'] = yesno
        order = data['order']
        data['orderfac'] = latex(ZZ(order).factor())
        orderfac = latex(ZZ(order).factor())
        data['ordermsg'] = "$%s=%s$" % (order, latex(orderfac))
        if order == 1:
            data['ordermsg'] = "$1$"
        if ZZ(order).is_prime():
            data['ordermsg'] = "$%s$ (is prime)" % order
        pgroup = len(ZZ(order).prime_factors()) < 2
        if n == 1:
            G = gap.SmallGroup(n, t)
        else:
            G = gap.TransitiveGroup(n, t)
        if ZZ(order) < ZZ('10000000000'):
            ctable = chartable(n, t)
        else:
            ctable = 'Group too large'
        data['gens'] = generators(n, t)
        if n == 1 and t == 1:
            data['gens'] = 'None needed'
        data['chartable'] = ctable
        data['parity'] = "$%s$" % data['parity']
        data['cclasses'] = conjclasses(G, n)
        data['subinfo'] = subfield_display(n, data['subs'])
        data['resolve'] = resolve_display(data['resolve'])
        if data['gapid'] == 0:
            data['gapid'] = "Data not available"
        else:
            data['gapid'] = small_group_display_knowl(int(data['order']),
                                                      int(data['gapid']),
                                                      str([int(data['order']), int(data['gapid'])]))
        data['otherreps'] = wgg.otherrep_list()
        ae = wgg.arith_equivalent()
        if ae>0:
            if ae>1:
                data['arith_equiv'] = r'A number field with this Galois group has %d <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.'% ae
            else:
                data['arith_equiv'] = r'A number field with this Galois group has exactly one <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> field.'
        else:
            data['arith_equiv'] = r'A number field with this Galois group has no <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.'
        if len(data['otherreps']) == 0:
            data['otherreps']="There is no other low degree representation."
        intreps = list(db.gps_gmodules.search({'n': n, 't': t}))
        if len(intreps) > 0:
            data['int_rep_classes'] = [str(z[0]) for z in intreps[0]['gens']]
            for onerep in intreps:
                onerep['gens']=[list_to_latex_matrix(z[1]) for z in onerep['gens']]
            data['int_reps'] = intreps
            data['int_reps_complete'] = int_reps_are_complete(intreps)
            dcq = data['moddecompuniq']
            if dcq[0] == 0:
                data['decompunique'] = 0
            else:
                data['decompunique'] = dcq[0]
                data['isoms'] = [[mult2mult(z[0]), mult2mult(z[1])] for z in dcq[1]]
                data['isoms'] = [[modules2string(n,t,z[0]), modules2string(n,t,z[1])] for z in data['isoms']]
                #print dcq[1]
                #print data['isoms']

        friends = []
        if db.nf_fields.exists({'degree': n, 'galt': t}):
            friends.append(('Number fields with this Galois group', url_for('number_fields.number_field_render_webpage')+"?galois_group=%dT%d" % (n, t) ))
        prop2 = [('Label', label),
            ('Order', '\(%s\)' % order),
            ('n', '\(%s\)' % data['n']),
            ('Cyclic', yesno(data['cyc'])),
            ('Abelian', yesno(data['ab'])),
            ('Solvable', yesno(data['solv'])),
            ('Primitive', yesno(data['prim'])),
            ('$p$-group', yesno(pgroup)),
        ]
        pretty = group_display_pretty(n,t)
        if len(pretty)>0:
            prop2.extend([('Group:', pretty)])
            info['pretty_name'] = pretty
        data['name'] = re.sub(r'_(\d+)',r'_{\1}',data['name'])
        data['name'] = re.sub(r'\^(\d+)',r'^{\1}',data['name'])
        info.update(data)

        bread = get_bread([(label, ' ')])
        return render_template("gg-show-group.html", credit=GG_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends)
Ejemplo n.º 19
0
def render_field_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        data = lfdb().find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", ' ')])
            info['err'] = "Field " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Local Number Field ' + label
        polynomial = coeff_to_poly(string2list(data['coeffs']))
        p = data['p']
        e = data['e']
        f = data['f']
        cc = data['c']
        GG = data['gal']
        gn = GG[0]
        gt = GG[1]
        the_gal = WebGaloisGroup.from_nt(gn,gt)
        isgal = ' Galois' if the_gal.order() == gn else ' not Galois'
        abelian = ' and abelian' if the_gal.is_abelian() else ''
        galphrase = 'This field is'+isgal+abelian+' over $\Q_{%d}$.'%p
        autstring = r'\Gal' if the_gal.order() == gn else r'\Aut'
        prop2 = [
            ('Label', label),
            ('Base', '\(\Q_{%s}\)' % p),
            ('Degree', '\(%s\)' % data['n']),
            ('e', '\(%s\)' % e),
            ('f', '\(%s\)' % f),
            ('c', '\(%s\)' % cc),
            ('Galois group', group_display_short(gn, gt, db())),
        ]
        Pt = PolynomialRing(QQ, 't')
        Pyt = PolynomialRing(Pt, 'y')
        eisenp = Pyt(str(data['eisen']))
        unramp = Pyt(str(data['unram']))
        # Look up the unram poly so we can link to it
        unramdata = lfdb().find_one({'p': p, 'n': f, 'c': 0})
        if unramdata is not None:
            unramfriend = "/LocalNumberField/%s" % unramdata['label']
        else:
            logger.fatal("Cannot find unramified field!")
            unramfriend = ''
        rfdata = lfdb().find_one({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']})
        if rfdata is None:
            logger.fatal("Cannot find discriminant root field!")
            rffriend = ''
        else:
            rffriend = "/LocalNumberField/%s" % rfdata['label']
        gsm = data['gsm']
        if gsm == '0':
            gsm = 'Not computed'
        elif gsm == '-1':
            gsm = 'Does not exist'
        else:
            gsm = web_latex(coeff_to_poly(string2list(gsm)))


        info.update({
                    'polynomial': web_latex(polynomial),
                    'n': data['n'],
                    'p': p,
                    'c': data['c'],
                    'e': data['e'],
                    'f': data['f'],
                    't': data['t'],
                    'u': data['u'],
                    'rf': printquad(data['rf'], p),
                    'hw': data['hw'],
                    'slopes': show_slopes(data['slopes']),
                    'gal': group_display_knowl(gn, gt, db()),
                    'gt': gt,
                    'inertia': group_display_inertia(data['inertia'], db()),
                    'unram': web_latex(unramp),
                    'eisen': web_latex(eisenp),
                    'gms': data['gms'],
                    'gsm': gsm,
                    'galphrase': galphrase,
                    'autstring': autstring,
                    'subfields': format_subfields(data['subfields'],p),
                    'aut': data['aut'],
                    })
        friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
        if unramfriend != '':
            friends.append(('Unramified subfield', unramfriend))
        if rffriend != '':
            friends.append(('Discriminant root field', rffriend))

        bread = get_bread([(label, ' ')])
        learnmore = [('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Local field labels', url_for(".labels_page"))]
        return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
Ejemplo n.º 20
0
def render_hecke_algebras_webpage_l_adic(**args):
    data = None
    if 'orbit_label' in args and 'prime' in args:
        lab = clean_input(args.get('orbit_label'))
        if lab != args.get('orbit_label'):
            base_lab = ".".join([split(lab)[i] for i in [0, 1, 2]])
            return redirect(
                url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        try:
            ell = int(args.get('prime'))
        except ValueError:
            base_lab = ".".join([split(lab)[i] for i in [0, 1, 2]])
            return redirect(
                url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        data = db.hecke_ladic.lucky({'orbit_label': lab, 'ell': ell})
    if data is None:
        t = "Hecke Algebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(
            Markup(
                "Error: <span style='color:black'>%s</span> is not a valid label for the &#x2113;-adic information for an Hecke Algebra orbit in the database."
                % (lab)), "error")
        return render_template("hecke_algebras-error.html",
                               title=t,
                               properties=[],
                               bread=bread,
                               learnmore=learnmore_list())
    info = {}
    info.update(data)

    proj = [
        'index', 'orbit_label', 'ell', 'idempotent', 'field', 'structure',
        'properties', 'operators'
    ]
    res = list(
        db.hecke_ladic.search(
            {
                'level': data['level'],
                'weight': data['weight'],
                'orbit_label': data['orbit_label'],
                'ell': data['ell']
            }, proj))

    for f in res:
        if f['idempotent'] != "":
            dim = len(sage_eval(f['idempotent']))
            l_max = sage_eval(f['idempotent'])[0][0].ndigits()
            if dim > 4 or l_max > 5:
                f['idempotent_display'] = []
            elif dim == 1:
                f['idempotent_display'] = sage_eval(f['idempotent'])[0][0]
            else:
                f['idempotent_display'] = latex(
                    matrix(sage_eval(f['idempotent'])))
        else:
            f['idempotent_display'] = latex(matrix([[1]]))
        del f['idempotent']
        f['download_id'] = [
            (i,
             url_for(".render_hecke_algebras_webpage_ell_download",
                     orbit_label=f['orbit_label'],
                     index=f['index'],
                     prime=f['ell'],
                     lang=i,
                     obj='idempotents')) for i in ['magma', 'sage']
        ]  # for 'gp' the code does not work, since p-adics are not implemented
        field = f.pop('field')
        if field is not None:
            f['deg'] = field[1]
            f['field_poly'] = field[2]
        structure = f.pop('structure')
        if structure is not None:
            f['dim'] = structure[0]
            f['num_gen'] = structure[1]
            s2 = sage_eval(structure[2])
            f['gens'] = [[int(s2.index(i) + 1), str(i)] for i in s2]
            f['rel'] = sage_eval(structure[3])
        properties = f.pop('properties')
        if properties is not None:
            f['grading'] = properties[0]
            f['gorenstein_def'] = properties[1]
            f['gorenstein'] = "yes" if properties[1] == 0 else "no"
        operators = f.pop('operators')
        if operators is not None:
            f['operators_mod_l'] = operators
            f['num_hecke_op'] = len(operators)
            f['size_op'] = size = sqrt(len(operators[0]))
            if size > 4:
                f['operators_mod_l_display'] = []
            elif size == 1:
                f['operators_mod_l_display'] = [[i + 1, operators[i][0]]
                                                for i in range(10)]
            else:
                f['operators_mod_l_display'] = [[
                    i + 1, latex(matrix(size, size, operators[i]))
                ] for i in range(5)]
            f['download_op'] = [
                (lang,
                 url_for(".render_hecke_algebras_webpage_ell_download",
                         orbit_label=f['orbit_label'],
                         index=f['index'],
                         prime=f['ell'],
                         lang=lang,
                         obj='operators')) for lang in ['magma', 'sage']
            ]  # for 'gp' the code does not work

    info['num_l_adic_orbits'] = len(res)
    info['l_adic_orbits'] = res
    info['level'] = int(data['level'])
    info['weight'] = int(data['weight'])
    info['base_lab'] = ".".join(
        [split(data['orbit_label'])[i] for i in [0, 1, 2]])
    info['orbit_label'] = str(data['orbit_label'])
    info['ell'] = int(data['ell'])

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")),
             ('%s' % info['base_lab'],
              url_for('.render_hecke_algebras_webpage',
                      label=info['base_lab'])), ('%s' % info['ell'], ' ')]
    credit = hecke_algebras_credit
    info['properties'] = [('Level', '%s' % info['level']),
                          ('Weight', '%s' % info['weight']),
                          ('Characteristic', '%s' % info['ell']),
                          ('Orbit label', '%s' % info['orbit_label'])]
    info['friends'] = [('Modular form ' + info['base_lab'],
                        url_for("emf.render_elliptic_modular_forms",
                                level=info['level'],
                                weight=info['weight'],
                                character=1))]

    t = "%s-adic and mod %s Data for the Hecke Algebra Orbit %s" % (
        info['ell'], info['ell'], info['orbit_label'])
    return render_template("hecke_algebras_l_adic-single.html",
                           info=info,
                           credit=credit,
                           title=t,
                           bread=bread,
                           properties2=info['properties'],
                           learnmore=learnmore_list(),
                           friends=info['friends'])
Ejemplo n.º 21
0
def render_hecke_algebras_webpage(**args):
    data = None
    if 'label' in args:
        lab = clean_input(args.get('label'))
        if lab != args.get('label'):
            return redirect(
                url_for('.render_hecke_algebras_webpage', label=lab), 301)
        data = db.hecke_algebras.lookup(lab)
    if data is None:
        t = "Hecke Algebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(
            Markup(
                "Error: <span style='color:black'>%s</span> is not a valid label for a Hecke Algebras in the database."
                % (lab)), "error")
        return render_template("hecke_algebras-error.html",
                               title=t,
                               properties=[],
                               bread=bread,
                               learnmore=learnmore_list())
    info = {}
    info.update(data)

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")),
             ('%s' % data['label'], ' ')]
    credit = hecke_algebras_credit
    info['level'] = int(data['level'])
    info['weight'] = int(data['weight'])
    info['num_orbits'] = int(data['num_orbits'])
    dim_count = "not available"

    proj = [
        'orbit_label', 'hecke_op', 'num_hecke_op', 'Zbasis', 'discriminant',
        'disc_fac', 'Qbasis', 'Qalg_gen'
    ]
    orb = list(db.hecke_orbits.search({'parent_label': data['label']}, proj))
    if orb:
        #consistency check
        if len(orb) != int(data['num_orbits']):
            return search_input_error(info)

        dim_count = 0
        for v in orb:
            ops = sage_eval(v['hecke_op'])
            dim = int(matrix(ops[0]).nrows())
            dim_count += dim
            if dim > 4:
                v['hecke_op_display'] = []
            elif dim == 1:
                v['hecke_op_display'] = [[i + 1, ops[i][0][0]]
                                         for i in range(10)]
            else:
                v['hecke_op_display'] = [[i + 1, latex(matrix(ops[i]))]
                                         for i in range(5)]
            v['download_op'] = [
                (lang,
                 url_for(".render_hecke_algebras_webpage_download",
                         orbit_label=v['orbit_label'],
                         lang=lang,
                         obj='operators')) for lang in ['gp', 'magma', 'sage']
            ]
            if v['Zbasis'] is None:
                for key in [
                        'Zbasis', 'discriminant', 'disc_fac', 'Qbasis',
                        'Qalg_gen'
                ]:
                    del v[key]
            else:
                v['Zbasis'] = [[int(i) for i in j] for j in v['Zbasis']
                               ]  # getDBConnection grep make ints in database
                v['disc_fac'] = [[int(i) for i in j] for j in v['disc_fac']
                                 ]  # make ints in database
                if dim > 4:
                    v['gen_display'] = []
                elif dim == 1:
                    v['gen_display'] = [v['Zbasis'][0][0]]
                else:
                    v['gen_display'] = [
                        latex(matrix(dim, dim, v['Zbasis'][i]))
                        for i in range(dim)
                    ]
                v['inner_twists'] = "not available"  # not yet in the database
                v['download_gen'] = [
                    (lang,
                     url_for(".render_hecke_algebras_webpage_download",
                             orbit_label=v['orbit_label'],
                             lang=lang,
                             obj='gen')) for lang in ['gp', 'magma', 'sage']
                ]
        info['orbits'] = orb

    info['dim_alg'] = dim_count
    info['l_adic'] = l_range
    info['properties'] = [('Label', '%s' % info['label']),
                          ('Level', '%s' % info['level']),
                          ('Weight', '%s' % info['weight'])]
    if info['num_orbits'] != 0:
        info['friends'] = [('Newforms space ' + info['label'],
                            url_for("emf.render_elliptic_modular_forms",
                                    level=info['level'],
                                    weight=info['weight'],
                                    character=1))]
    else:
        info['friends'] = []
    t = "Hecke Algebra %s" % info['label']
    return render_template("hecke_algebras-single.html",
                           info=info,
                           credit=credit,
                           title=t,
                           bread=bread,
                           properties2=info['properties'],
                           learnmore=learnmore_list(),
                           friends=info['friends'])
Ejemplo n.º 22
0
Archivo: main.py Proyecto: koffie/lmfdb
def render_artin_representation_webpage(label):
    if re.compile(r'^\d+$').match(label):
        return artin_representation_search(**{'dimension': label})

    bread = get_bread([(label, ' ')])

    # label=dim.cond.nTt.indexcj, c is literal, j is index in conj class
    # Should we have a big try around this to catch bad labels?
    clean_label = clean_input(label)
    if clean_label != label:
        return redirect(
            url_for('.render_artin_representation_webpage', label=clean_label),
            301)
    try:
        the_rep = ArtinRepresentation(label)
    except:
        flash(
            Markup(
                "Error: <span style='color:black'>%s</span> is not the label of an Artin representation in the database."
                % (label)), "error")
        return search_input_error({'err': ''}, bread)

    extra_data = {}  # for testing?
    extra_data['galois_knowl'] = group_display_knowl(5, 3)  # for testing?
    #artin_logger.info("Found %s" % (the_rep._data))

    title = "Artin Representation %s" % label
    the_nf = the_rep.number_field_galois_group()
    if the_rep.sign() == 0:
        processed_root_number = "not computed"
    else:
        processed_root_number = str(the_rep.sign())
    properties = [
        ("Label", label),
        ("Dimension", str(the_rep.dimension())),
        ("Group", the_rep.group()),
        #("Conductor", str(the_rep.conductor())),
        ("Conductor", "$" + the_rep.factored_conductor_latex() + "$"),
        #("Bad primes", str(the_rep.bad_primes())),
        ("Root number", processed_root_number),
        ("Frobenius-Schur indicator", str(the_rep.indicator()))
    ]

    friends = []
    nf_url = the_nf.url_for()
    if nf_url:
        friends.append(("Artin Field", nf_url))
    cc = the_rep.central_character()
    if cc is not None:
        if the_rep.dimension() == 1:
            if cc.order == 2:
                cc_name = cc.symbol
            else:
                cc_name = cc.texname
            friends.append(("Dirichlet character " + cc_name,
                            url_for("characters.render_Dirichletwebpage",
                                    modulus=cc.modulus,
                                    number=cc.number)))
        else:
            detrep = the_rep.central_character_as_artin_rep()
            friends.append(("Determinant representation " + detrep.label(),
                            detrep.url_for()))

    # once the L-functions are in the database, the link can always be shown
    #if the_rep.dimension() <= 6:
    if the_rep.dimension() == 1:
        # Zeta is loaded differently
        if cc.modulus == 1 and cc.number == 1:
            friends.append(("L-function",
                            url_for("l_functions.l_function_dirichlet_page",
                                    modulus=cc.modulus,
                                    number=cc.number)))
        else:
            # looking for Lhash dirichlet_L_modulus.number
            mylhash = 'dirichlet_L_%d.%d' % (cc.modulus, cc.number)
            lres = db.lfunc_instances.lucky({'Lhash': mylhash})
            if lres is not None:
                friends.append(
                    ("L-function",
                     url_for("l_functions.l_function_dirichlet_page",
                             modulus=cc.modulus,
                             number=cc.number)))

    # Dimension > 1
    elif int(the_rep.conductor())**the_rep.dimension() <= 729000000000000:
        friends.append(("L-function",
                        url_for("l_functions.l_function_artin_page",
                                label=the_rep.label())))
    info = {}
    #mychar = the_rep.central_char()
    #info['pol2']= str([((j+1),mychar(j+1, 2*the_rep.character_field())) for j in range(50)])
    #info['pol3']=str(the_rep.central_character())
    #info['pol3']=str(the_rep.central_char(3))
    #info['pol5']=str(the_rep.central_char(5))
    #info['pol7']=str(the_rep.central_char(7))
    #info['pol11']=str(the_rep.central_char(11))
    learnmore = [('Artin representations labels', url_for(".labels_page"))]

    return render_template("artin-representation-show.html",
                           credit=tim_credit,
                           support=support_credit,
                           title=title,
                           bread=bread,
                           friends=friends,
                           object=the_rep,
                           properties2=properties,
                           extra_data=extra_data,
                           info=info,
                           learnmore=learnmore)
Ejemplo n.º 23
0
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:
        gpK = nf.gpK()
        rootof1coeff = gpK.nfrootsof1()
        rootofunityorder = int(rootof1coeff[1])
        rootof1coeff = rootof1coeff[2]
        rootofunity = web_latex(Ra(str(pari("lift(%s)" % gpK.nfbasistoalg(rootof1coeff))).replace('x','a'))) 
        rootofunity += ' (order $%d$)' % rootofunityorder
    else:
        rootofunity = web_latex(Ra('-1'))+ ' (order $2$)'

    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': rootofunity,
        'fund_units': nf.units(),
        'grh_label': grh_label,
        'loc_alg': loc_alg
    })

    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 character group', url_for("characters.dirichlet_group_table",
                                                           modulus=int(conductor),
                                                           char_number_list=','.join(
                                                               [str(a) for a in dirichlet_chars]),
                                                           poly=info['polynomial'])))
    resinfo=[]
    galois_closure = nf.galois_closure()
    if galois_closure[0]>0:
        if len(galois_closure[1])>0:
            resinfo.append(('gc', galois_closure[1]))
            if len(galois_closure[2]) > 0:
                info['friends'].append(('Galois closure',url_for(".by_label", label=galois_closure[2][0])))
        else:
            resinfo.append(('gc', [dnc]))

    sextic_twins = nf.sextic_twin()
    if sextic_twins[0]>0:
        if len(sextic_twins[1])>0:
            resinfo.append(('sex', r' $\times$ '.join(sextic_twins[1])))
        else:
            resinfo.append(('sex', dnc))

    siblings = nf.siblings()
    # [degsib list, label list]
    # first is list of [deg, num expected, list of knowls]
    if len(siblings[0])>0:
        for sibdeg in siblings[0]:
            if len(sibdeg[2]) ==0:
                sibdeg[2] = dnc
            else:
                sibdeg[2] = ', '.join(sibdeg[2])
                if len(sibdeg[2])<sibdeg[1]:
                    sibdeg[2] += ', some '+dnc
                
        resinfo.append(('sib', siblings[0]))
        for lab in siblings[1]:
            if lab != '':
                labparts = lab.split('.')
                info['friends'].append(("Degree %s sibling"%labparts[0] ,url_for(".by_label", label=lab)))

    arith_equiv = nf.arith_equiv()
    if arith_equiv[0]>0:
        if len(arith_equiv[1])>0:
            resinfo.append(('ae', ', '.join(arith_equiv[1]), len(arith_equiv[1])))
            for aelab in arith_equiv[2]:
                info['friends'].append(('Arithmetically equivalent sibling',url_for(".by_label", label=aelab)))
        else:
            resinfo.append(('ae', dnc, len(arith_equiv[1])))

    info['resinfo'] = resinfo
    learnmore = learnmore_list()
    #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 = [('Label', label),
                   ('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))
                   ]
    downloads = []
    for lang in [["Magma","magma"], ["SageMath","sage"], ["Pari/GP", "gp"]]:
        downloads.append(('Download {} code'.format(lang[0]),
                          url_for(".nf_code_download", nf=label, download_type=lang[1])))
    from lmfdb.artin_representations.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
    return render_template("number_field.html", properties2=properties2, credit=NF_credit, title=title, bread=bread, code=nf.code, friends=info.pop('friends'), downloads=downloads, learnmore=learnmore, info=info)
Ejemplo n.º 24
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,
    )
Ejemplo n.º 25
0
def by_label(label):
    clean_label = clean_input(label)
    if clean_label != label:
        return redirect(url_for('.by_label', label=clean_label), 301)
    return search_by_label(label)
Ejemplo n.º 26
0
def number_field_search(**args):
    info = to_dict(args)

    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")),
        ("Quadratic imaginary class groups", url_for(".render_class_group_data")),
    ]
    t = "Global Number Field search results"
    bread = [("Global Number Fields", url_for(".number_field_render_webpage")), ("Search results", " ")]

    # for k in info.keys():
    #  nf_logger.debug(str(k) + ' ---> ' + str(info[k]))
    # nf_logger.debug('******************* '+ str(info['search']))

    if "natural" in info:
        query = {"label_orig": info["natural"]}
        try:
            parse_nf_string(info, query, "natural", name="Label", qfield="label")
            return redirect(url_for(".by_label", label=clean_input(query["label"])))
        except ValueError:
            query["err"] = info["err"]
            return search_input_error(query, bread)

    query = {}
    try:
        parse_galgrp(info, query, qfield="galois")
        parse_ints(info, query, "degree")
        parse_bracketed_posints(info, query, "signature", split=False, exactlength=2)
        parse_signed_ints(info, query, "discriminant", qfield=("disc_sign", "disc_abs_key"), parse_one=make_disc_key)
        parse_ints(info, query, "class_number")
        parse_bracketed_posints(info, query, "class_group", split=False, check_divisibility="increasing")
        parse_primes(
            info, query, "ur_primes", name="Unramified primes", qfield="ramps", mode="complement", to_string=True
        )
        if "ram_quantifier" in info and str(info["ram_quantifier"]) == "some":
            mode = "append"
        else:
            mode = "exact"
        parse_primes(info, query, "ram_primes", "ramified primes", "ramps", mode, to_string=True)
    except ValueError:
        return search_input_error(info, bread)
    count = parse_count(info)
    start = parse_start(info)

    if info.get("paging"):
        try:
            paging = int(info["paging"])
            if paging == 0:
                start = 0
        except:
            pass

    C = base.getDBConnection()
    # nf_logger.debug(query)
    info["query"] = dict(query)
    if "lucky" in args:
        one = C.numberfields.fields.find_one(query)
        if one:
            label = one["label"]
            return redirect(url_for(".by_label", clean_input(label)))

    fields = C.numberfields.fields

    res = fields.find(query)

    if "download" in info and info["download"] != "0":
        return download_search(info, res)

    res = res.sort([("degree", ASC), ("disc_abs_key", ASC), ("disc_sign", ASC)])
    nres = res.count()
    res = res.skip(start).limit(count)

    if start >= nres:
        start -= (1 + (start - nres) / count) * count
    if start < 0:
        start = 0

    info["fields"] = res
    info["number"] = nres
    info["start"] = start
    if nres == 1:
        info["report"] = "unique match"
    else:
        if nres > count or start != 0:
            info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
        else:
            info["report"] = "displaying all %s matches" % nres

    info["wnf"] = WebNumberField.from_data
    return render_template("number_field_search.html", info=info, title=t, bread=bread)
Ejemplo n.º 27
0
def number_field_search(info):

    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")), ('Quadratic imaginary class groups', url_for(".render_class_group_data"))]
    t = 'Global Number Field search results'
    bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search Results', ' ')]

    if 'natural' in info:
        query = {'label_orig': info['natural']}
        try:
            parse_nf_string(info,query,'natural',name="Label",qfield='label')
            return redirect(url_for(".by_label", label=query['label']))
        except ValueError:
            query['err'] = info['err']
            return search_input_error(query, bread)

    if 'algebra' in info:
        fields=info['algebra'].split('_')
        fields2=[WebNumberField.from_coeffs(a) for a in fields]
        for j in range(len(fields)):
            if fields2[j] is None:
                fields2[j] = WebNumberField.fakenf(fields[j])
        t = 'Number field algebra'
        info = {}
        info = {'fields': fields2}
        return render_template("number_field_algebra.html", info=info, title=t, bread=bread)



    query = {}
    try:
        parse_galgrp(info,query, qfield='galois')
        parse_ints(info,query,'degree')
        parse_bracketed_posints(info,query,'signature',split=False,exactlength=2)
        parse_signed_ints(info,query,'discriminant',qfield=('disc_sign','disc_abs_key'),parse_one=make_disc_key)
        parse_ints(info,query,'class_number')
        parse_bracketed_posints(info,query,'class_group',split=False,check_divisibility='increasing')
        parse_primes(info,query,'ur_primes',name='Unramified primes',qfield='ramps',mode='complement',to_string=True)
        # modes are now contained (in), exactly, include
        if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'include':
            mode = 'append'
            parse_primes(info,query,'ram_primes','ramified primes','ramps',mode,to_string=True)
        elif 'ram_quantifier' in info and str(info['ram_quantifier']) == 'contained':
            parse_primes(info,query,'ram_primes','ramified primes','ramps_all','subsets',to_string=False)
            pass # build list
        else:
            mode = 'liststring'
            parse_primes(info,query,'ram_primes','ramified primes','ramps_all',mode)
    except ValueError:
        return search_input_error(info, bread)
    count = parse_count(info)
    start = parse_start(info)

    # nf_logger.debug(query)
    info['query'] = dict(query)
    if 'lucky' in info:
        one = nfdb().find_one(query)
        if one:
            label = one['label']
            return redirect(url_for(".by_label", label=clean_input(label)))

    fields = nfdb()

    res = fields.find(query)
    res = res.sort([('degree', ASC), ('disc_abs_key', ASC),('disc_sign', ASC)])

    if 'download' in info and info['download'] != '0':
        return download_search(info, res)

    # equivalent to
    # nres = res.count()
    #if(start >= nres):
    #    start -= (1 + (start - nres) / count) * count
    #if(start < 0):
    #    start = 0
    # res = res.skip(start).limit(count)
    try:
        start, nres, res = search_cursor_timeout_decorator(res, start, count);
    except ValueError as err:
        info['err'] = err;
        return search_input_error(info, bread)


    info['fields'] = res
    info['number'] = nres
    info['start'] = start
    if nres == 1:
        info['report'] = 'unique match'
    else:
        if nres > count or start != 0:
            info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
        else:
            info['report'] = 'displaying all %s matches' % nres

    info['wnf'] = WebNumberField.from_data
    return render_template("number_field_search.html", info=info, title=t, bread=bread)
Ejemplo n.º 28
0
def hgm_search(**args):
    info = to_dict(args)
    bread = get_bread([("Search results", url_for('.search'))])
    C = base.getDBConnection()
    query = {}
    if 'jump_to' in info:
        return render_hgm_webpage({'label': info['jump_to']})

    family_search = False
    if info.get('Submit Family') or info.get('family'):
        family_search = True

    # generic, irreducible not in DB yet
    for param in ['A', 'B', 'hodge', 'a2', 'b2', 'a3', 'b3', 'a5', 'b5', 'a7', 'b7']:
        if info.get(param):
            info[param] = clean_input(info[param])
            if IF_RE.match(info[param]):
                query[param] = split_list(info[param])
                query[param].sort()
            else:
                name = param
                if field == 'hodge':
                    name = 'Hodge vector'
                info['err'] = 'Error parsing input for %s.  It needs to be a list of integers in square brackets, such as [2,3] or [1,1,1]' % name
                return search_input_error(info, bread)

    if info.get('t') and not family_search:
        info['t'] = clean_input(info['t'])
        try:
            tsage = QQ(str(info['t']))
            tlist = [int(tsage.numerator()), int(tsage.denominator())]
            query['t'] = tlist
        except:
            info['err'] = 'Error parsing input for t.  It needs to be a rational number, such as 2/3 or -3'

    # sign can only be 1, -1, +1
    if info.get('sign') and not family_search:
        sign = info['sign']
        sign = re.sub(r'\s','',sign)
        sign = clean_input(sign)
        if sign == '+1':
            sign = '1'
        if not (sign == '1' or sign == '-1'):
            info['err'] = 'Error parsing input %s for sign.  It needs to be 1 or -1' % sign
            return search_input_error(info, bread)
        query['sign'] = int(sign)


    for param in ['degree','weight','conductor']:
        # We don't look at conductor in family searches
        if info.get(param) and not (param=='conductor' and family_search):
            if param=='conductor':
                cond = info['conductor']
                try:
                    cond = re.sub(r'(\d)\s+(\d)', r'\1 * \2', cond) # implicit multiplication of numbers
                    cond = cond.replace(r'..', r'-') # all ranges use -
                    cond = re.sub(r'[a..zA..Z]', '', cond)
                    cond = clean_input(cond)
                    tmp = parse_range2(cond, 'cond', myZZ)
                except:
                    info['err'] = 'Error parsing input for conductor.  It needs to be an integer (e.g., 8), a range of integers (e.g. 10-100), or a list of such (e.g., 5,7,8,10-100).  Integers may be given in factored form (e.g. 2^5 3^2) %s' % cond
                    return search_input_error(info, bread)
            else: # not conductor
                info[param] = clean_input(info[param])
                ran = info[param]
                ran = ran.replace(r'..', r'-')
                if LIST_RE.match(ran):
                    tmp = parse_range2(ran, param)
                else:
                    names = {'weight': 'weight', 'degree': 'degree'}
                    info['err'] = 'Error parsing input for the %s.  It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 2,3,8 or 3-5, 7, 8-11).' % names[param]
                    return search_input_error(info, bread)
            # work around syntax for $or
            # we have to foil out multiple or conditions
            if tmp[0] == '$or' and '$or' in query:
                newors = []
                for y in tmp[1]:
                    oldors = [dict.copy(x) for x in query['$or']]
                    for x in oldors:
                        x.update(y)
                    newors.extend(oldors)
                tmp[1] = newors
            query[tmp[0]] = tmp[1]

    #print query
    count_default = 20
    if info.get('count'):
        try:
            count = int(info['count'])
        except:
            count = count_default
    else:
        count = count_default
    info['count'] = count

    start_default = 0
    if info.get('start'):
        try:
            start = int(info['start'])
            if(start < 0):
                start += (1 - (start + 1) / count) * count
        except:
            start = start_default
    else:
        start = start_default
    if info.get('paging'):
        try:
            paging = int(info['paging'])
            if paging == 0:
                start = 0
        except:
            pass

    # logger.debug(query)
    if family_search:
        res = C.hgm.families.find(query).sort([('label', pymongo.ASCENDING)])
    else:
        res = C.hgm.motives.find(query).sort([('cond', pymongo.ASCENDING), ('label', pymongo.ASCENDING)])
    nres = res.count()
    res = res.skip(start).limit(count)

    if(start >= nres):
        start -= (1 + (start - nres) / count) * count
    if(start < 0):
        start = 0

    info['motives'] = res
    info['number'] = nres
    info['start'] = start
    if nres == 1:
        info['report'] = 'unique match'
    else:
        if nres > count or start != 0:
            info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
        else:
            info['report'] = 'displaying all %s matches' % nres
    info['make_label'] = make_abt_label
    info['make_t_label'] = make_t_label
    info['ab_label'] = ab_label
    info['display_t'] = display_t
    info['family'] = family_search
    info['factorint'] = factorint

    if family_search:
        return render_template("hgm-search.html", info=info, title="Hypergeometric Family over $\Q$ Search Result", bread=bread, credit=HGM_credit)
    else:
        return render_template("hgm-search.html", info=info, title="Hypergeometric Motive over $\Q$ Search Result", bread=bread, credit=HGM_credit)
Ejemplo n.º 29
0
def render_hecke_algebras_webpage_l_adic(**args):
    data = None
    if 'orbit_label' in args and 'prime' in args:
        lab = clean_input(args.get('orbit_label'))
        if lab != args.get('orbit_label'):
            base_lab=".".join([split(lab)[i] for i in [0,1,2]])
            return redirect(url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        try:
            ell = int(args.get('prime'))
        except ValueError:
            base_lab=".".join([split(lab)[i] for i in [0,1,2]])
            return redirect(url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        data = hecke_l_adic_db().find_one({'orbit_label': lab , 'ell': ell})
    if data is None:
        t = "Hecke Algebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for the &#x2113;-adic information for an Hecke Algebra orbit in the database." % (lab)),"error")
        return render_template("hecke_algebras-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
    info = {}
    info.update(data)
    res = hecke_l_adic_db().find({'level': data['level'],'weight': data['weight'],'orbit_label': data['orbit_label'], 'ell': data['ell']})

    info['num_l_adic_orbits']=res.count()
    res_clean = []
    for f in res:
        f_clean = {}
        f_clean['index']=int(f['index'])
        f_clean['orbit_label']=str(f['orbit_label'])
        f_clean['ell']=int(f['ell'])
        if f['idempotent'] != "":
            f['dim']=len(sage_eval(f['idempotent']))
            l_max= sage_eval(f['idempotent'])[0][0].ndigits()
            if f['dim']>4 or l_max>5:
                f_clean['idempotent_display']=[]
            elif f['dim']==1:
                f_clean['idempotent_display']=sage_eval(f['idempotent'])[0][0]
            else:
                f_clean['idempotent_display']=latex(matrix(sage_eval(f['idempotent'])))
        else:
            f_clean['idempotent_display']=latex(matrix([[1]]))
        f_clean['download_id'] = [(i, url_for(".render_hecke_algebras_webpage_ell_download", orbit_label=f_clean['orbit_label'], index=f_clean['index'], prime=f_clean['ell'], lang=i, obj='idempotents')) for i in ['magma','sage']]  # for 'gp' the code does not work, since p-adics are not implemented


        try:
            f_clean['deg']=int(f['field'][1])
            f_clean['field_poly']=str(f['field'][2])
            f_clean['dim']=int(f['structure'][0])
            f_clean['num_gen']=int(f['structure'][1])
            f_clean['gens']=[[int(sage_eval(f['structure'][2]).index(i)+1), str(i)] for i in sage_eval(f['structure'][2])]
            f_clean['rel']=sage_eval(f['structure'][3])
            f_clean['grading']=[int(i) for i in f['properties'][0]]
            f_clean['gorenstein_def']=int(f['properties'][1])
            if f_clean['gorenstein_def']==0:
                f_clean['gorenstein']="yes"
            else:
                f_clean['gorenstein']="no"
            f_clean['operators_mod_l']=[[int(i) for i in j] for j in f['operators']]
            f_clean['num_hecke_op']=len(f_clean['operators_mod_l'])
            f_clean['download_op'] = [(i, url_for(".render_hecke_algebras_webpage_ell_download", orbit_label=f_clean['orbit_label'], index=f_clean['index'], prime=f_clean['ell'], lang=i, obj='operators')) for i in ['magma','sage']]  # for 'gp' the code does not work
            f_clean['size_op']=sqrt(len(f_clean['operators_mod_l'][0]))
            if f_clean['size_op']>4:
                f_clean['operators_mod_l_display']=[]
            elif f_clean['size_op']==1:
                f_clean['operators_mod_l_display']=[[i+1, f_clean['operators_mod_l'][i][0]] for i in range(0,10)]
            else:
                f_clean['operators_mod_l_display']=[[i+1,latex(matrix(f_clean['size_op'],f_clean['size_op'], f_clean['operators_mod_l'][i]))] for i in range(0,5)]
            res_clean.append(f_clean)
        except KeyError:
            pass    

    info['l_adic_orbits']=res_clean

    info['level']=int(data['level'])
    info['weight']= int(data['weight'])
    info['base_lab']=".".join([split(data['orbit_label'])[i] for i in [0,1,2]])
    info['orbit_label']= str(data['orbit_label'])
    info['ell']=int(data['ell'])

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")), ('%s' % info['base_lab'], url_for('.render_hecke_algebras_webpage', label=info['base_lab'])), ('%s' % info['ell'], ' ')]
    credit = hecke_algebras_credit
    info['properties'] = [
        ('Level', '%s' %info['level']),
        ('Weight', '%s' %info['weight']),
        ('Characteristic', '%s' %info['ell']),
        ('Orbit label', '%s' %info['orbit_label'])]    
    info['friends'] = [('Modular form ' + info['base_lab'], url_for("emf.render_elliptic_modular_forms", level=info['level'], weight=info['weight'], character=1))]

    t = "%s-adic and mod %s Data for the Hecke Algebra Orbit %s" % (info['ell'], info['ell'], info['orbit_label'])
    return render_template("hecke_algebras_l_adic-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list(), friends=info['friends'])
Ejemplo n.º 30
0
def hgm_search(info):
    #info = to_dict(args)
    bread = get_bread([("Search Results", '')])
    query = {}
    queryab = {}
    queryabrev = {}
    if 'jump_to' in info:
        label = clean_input(info['jump_to'])
        if HGM_LABEL_RE.match(label):
            return render_hgm_webpage(normalize_motive(label))
        if HGM_FAMILY_LABEL_RE.match(label):
            return render_hgm_family_webpage(normalize_family(label))
        flash_error(
            '%s is not a valid label for a hypergeometric motive or family of hypergeometric motives',
            label)
        return redirect(url_for(".index"))

    family_search = False
    if info.get('Submit Family') or info.get('family'):
        family_search = True

    # generic, irreducible not in DB yet

    try:
        parse_ints(info, query, 'degree')
        parse_ints(info, query, 'weight')
        parse_bracketed_posints(info,
                                query,
                                'famhodge',
                                'family Hodge vector',
                                split=False)
        parse_restricted(info,
                         query,
                         'sign',
                         allowed=['+1', 1, -1],
                         process=int)
        for param in [
                'A', 'B', 'A2', 'B2', 'A3', 'B3', 'A5', 'B5', 'A7', 'B7',
                'Au2', 'Bu2', 'Au3', 'Bu3', 'Au5', 'Bu5', 'Au7', 'Bu7'
        ]:
            parse_bracketed_posints(
                info,
                queryab,
                param,
                split=False,
                listprocess=lambda a: sorted(a, reverse=True))
        # Make a version to search reversed way
        if not family_search:
            parse_ints(info, query, 'conductor', 'Conductor', 'cond')
            parse_rational(info, query, 't')
            parse_bracketed_posints(info, query, 'hodge', 'Hodge vector')
    except ValueError:
        if family_search:
            return render_template(
                "hgm-search.html",
                info=info,
                title="Hypergeometric Family over $\Q$ Search Result",
                bread=bread,
                credit=HGM_credit,
                learnmore=learnmore_list())
        return render_template(
            "hgm-search.html",
            info=info,
            title="Hypergeometric Motive over $\Q$ Search Result",
            bread=bread,
            credit=HGM_credit,
            learnmore=learnmore_list())

    # Now combine the parts of the query if there are A,B parts
    if queryab != {}:
        for k in queryab.keys():
            queryabrev[k + 'rev'] = queryab[k]
        queryab.update(query)
        queryabrev.update(query)
        query = {'$or': [queryab, queryabrev]}
    print query
    count_default = 20
    if info.get('count'):
        try:
            count = int(info['count'])
        except:
            count = count_default
    else:
        count = count_default
    info['count'] = count

    start_default = 0
    if info.get('start'):
        try:
            start = int(info['start'])
            if (start < 0):
                start += (1 - (start + 1) / count) * count
        except:
            start = start_default
    else:
        start = start_default
    if info.get('paging'):
        try:
            paging = int(info['paging'])
            if paging == 0:
                start = 0
        except:
            pass

    # logger.debug(query)
    if family_search:
        #query['leader'] = '1'
        res = familydb().find(query).sort([('label', pymongo.ASCENDING)])
    else:
        res = motivedb().find(query).sort([('cond', pymongo.ASCENDING),
                                           ('label', pymongo.ASCENDING)])
    nres = res.count()
    res = res.skip(start).limit(count)

    if (start >= nres):
        start -= (1 + (start - nres) / count) * count
    if (start < 0):
        start = 0

    info['motives'] = res
    info['number'] = nres
    info['start'] = start
    if nres == 1:
        info['report'] = 'unique match'
    else:
        if nres > count or start != 0:
            info['report'] = 'displaying matches %s-%s of %s' % (
                start + 1, min(nres, start + count), nres)
        else:
            info['report'] = 'displaying all %s matches' % nres
    info['make_label'] = make_abt_label
    info['make_t_label'] = make_t_label
    info['ab_label'] = ab_label
    info['display_t'] = display_t
    info['family'] = family_search
    info['factorint'] = factorint

    if family_search:
        return render_template(
            "hgm-search.html",
            info=info,
            title="Hypergeometric Family over $\Q$ Search Result",
            bread=bread,
            credit=HGM_credit,
            learnmore=learnmore_list())
    else:
        return render_template(
            "hgm-search.html",
            info=info,
            title="Hypergeometric Motive over $\Q$ Search Result",
            bread=bread,
            credit=HGM_credit,
            learnmore=learnmore_list())
Ejemplo n.º 31
0
def render_artin_representation_webpage(label):
    if re.compile(r'^\d+$').match(label):
        return artin_representation_search(**{'dimension': label})

    bread = get_bread([(label, ' ')])

    # label=dim.cond.nTt.indexcj, c is literal, j is index in conj class
    # Should we have a big try around this to catch bad labels?
    clean_label = clean_input(label)
    if clean_label != label:
        return redirect(url_for('.render_artin_representation_webpage', label=clean_label), 301)
    try:
        the_rep = ArtinRepresentation(label)
    except:
        flash(Markup("Error: <span style='color:black'>%s</span> is not the label of an Artin representation in the database." % (label)), "error")
        return search_input_error({'err':''}, bread)

    extra_data = {} # for testing?
    extra_data['galois_knowl'] = group_display_knowl(5,3) # for testing?
    #artin_logger.info("Found %s" % (the_rep._data))


    title = "Artin Representation %s" % label
    the_nf = the_rep.number_field_galois_group()
    if the_rep.sign() == 0:
        processed_root_number = "not computed"
    else:
        processed_root_number = str(the_rep.sign())
    properties = [("Label", label),
                  ("Dimension", str(the_rep.dimension())),
                  ("Group", the_rep.group()),
                  #("Conductor", str(the_rep.conductor())),
                  ("Conductor", "$" + the_rep.factored_conductor_latex() + "$"),
                  #("Bad primes", str(the_rep.bad_primes())),
                  ("Root number", processed_root_number),
                  ("Frobenius-Schur indicator", str(the_rep.indicator()))
                  ]

    friends = []
    nf_url = the_nf.url_for()
    if nf_url:
        friends.append(("Artin Field", nf_url))
    cc = the_rep.central_character()
    if cc is not None:
        if the_rep.dimension()==1:
            if cc.order == 2:
                cc_name = cc.symbol
            else:
                cc_name = cc.texname
            friends.append(("Dirichlet character "+cc_name, url_for("characters.render_Dirichletwebpage", modulus=cc.modulus, number=cc.number)))
        else:
            detrep = the_rep.central_character_as_artin_rep()
            friends.append(("Determinant representation "+detrep.label(), detrep.url_for()))

    # once the L-functions are in the database, the link can always be shown
    #if the_rep.dimension() <= 6:
    if the_rep.dimension() == 1:
        # Zeta is loaded differently
        if cc.modulus == 1 and cc.number == 1:
            friends.append(("L-function", url_for("l_functions.l_function_dirichlet_page", modulus=cc.modulus, number=cc.number)))
        else:
            # looking for Lhash dirichlet_L_modulus.number
            mylhash = 'dirichlet_L_%d.%d'%(cc.modulus,cc.number)
            lres = db.lfunc_instances.lucky({'Lhash': mylhash})
            if lres is not None:
                friends.append(("L-function", url_for("l_functions.l_function_dirichlet_page", modulus=cc.modulus, number=cc.number)))

    # Dimension > 1
    elif int(the_rep.conductor())**the_rep.dimension() <= 729000000000000:
        friends.append(("L-function", url_for("l_functions.l_function_artin_page",
                                          label=the_rep.label())))
    info={}
    #mychar = the_rep.central_char()
    #info['pol2']= str([((j+1),mychar(j+1, 2*the_rep.character_field())) for j in range(50)])
    #info['pol3']=str(the_rep.central_character())
    #info['pol3']=str(the_rep.central_char(3))
    #info['pol5']=str(the_rep.central_char(5))
    #info['pol7']=str(the_rep.central_char(7))
    #info['pol11']=str(the_rep.central_char(11))
    learnmore=[('Artin representations labels', url_for(".labels_page"))]

    return render_template("artin-representation-show.html", credit=tim_credit, support=support_credit, title=title, bread=bread, friends=friends, object=the_rep, properties2=properties, extra_data=extra_data, info=info, learnmore=learnmore)
Ejemplo n.º 32
0
def by_label(label):
    clean_label = clean_input(label)
    if clean_label != label:
        return redirect(url_for('.by_label', label=clean_label), 301)
    return render_group_webpage({'label': label})
Ejemplo n.º 33
0
def hgm_search(info):
    #info = to_dict(args)
    bread = get_bread([("Search Results", '')])
    query = {}
    queryab = {}
    queryabrev = {}
    if 'jump_to' in info:
        label = clean_input(info['jump_to'])
        if HGM_LABEL_RE.match(label):
            return render_hgm_webpage(normalize_motive(label))
        if HGM_FAMILY_LABEL_RE.match(label):
            return render_hgm_family_webpage(normalize_family(label))
        flash_error('%s is not a valid label for a hypergeometric motive or family of hypergeometric motives', label)
        return redirect(url_for(".index"))

    family_search = False
    if info.get('Submit Family') or info.get('family'):
        family_search = True

    # generic, irreducible not in DB yet

    try:
        parse_ints(info, query, 'degree')
        parse_ints(info, query, 'weight')
        parse_bracketed_posints(info, query, 'famhodge', 'family Hodge vector',split=False)
        parse_restricted(info, query, 'sign', allowed=['+1',1,-1], process=int)
        for param in ['A', 'B', 'A2', 'B2', 'A3', 'B3', 'A5', 'B5', 'A7', 'B7',
            'Au2', 'Bu2', 'Au3', 'Bu3', 'Au5', 'Bu5', 'Au7', 'Bu7']:
            parse_bracketed_posints(info, queryab, param, split=False,
                listprocess=lambda a: sorted(a, reverse=True))
        # Make a version to search reversed way
        if not family_search:
            parse_ints(info, query, 'conductor', 'Conductor' , 'cond')
            parse_rational(info, query, 't')
            parse_bracketed_posints(info, query, 'hodge', 'Hodge vector')
    except ValueError:
        if family_search:
            return render_template("hgm-search.html", info=info, title="Hypergeometric Family over $\Q$ Search Result", bread=bread, credit=HGM_credit, learnmore=learnmore_list())
        return render_template("hgm-search.html", info=info, title="Hypergeometric Motive over $\Q$ Search Result", bread=bread, credit=HGM_credit, learnmore=learnmore_list())

    # Now combine the parts of the query if there are A,B parts
    if queryab != {}:
        for k in queryab.keys():
            queryabrev[k+'rev'] = queryab[k]
        queryab.update(query)
        queryabrev.update(query)
        query = {'$or':[queryab, queryabrev]}
    print query
    count_default = 20
    if info.get('count'):
        try:
            count = int(info['count'])
        except:
            count = count_default
    else:
        count = count_default
    info['count'] = count

    start_default = 0
    if info.get('start'):
        try:
            start = int(info['start'])
            if(start < 0):
                start += (1 - (start + 1) / count) * count
        except:
            start = start_default
    else:
        start = start_default
    if info.get('paging'):
        try:
            paging = int(info['paging'])
            if paging == 0:
                start = 0
        except:
            pass

    # logger.debug(query)
    if family_search:
        #query['leader'] = '1'
        res = familydb().find(query).sort([('label', pymongo.ASCENDING)])
    else:
        res = motivedb().find(query).sort([('cond', pymongo.ASCENDING), ('label', pymongo.ASCENDING)])
    nres = res.count()
    res = res.skip(start).limit(count)

    if(start >= nres):
        start -= (1 + (start - nres) / count) * count
    if(start < 0):
        start = 0

    info['motives'] = res
    info['number'] = nres
    info['start'] = start
    if nres == 1:
        info['report'] = 'unique match'
    else:
        if nres > count or start != 0:
            info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
        else:
            info['report'] = 'displaying all %s matches' % nres
    info['make_label'] = make_abt_label
    info['make_t_label'] = make_t_label
    info['ab_label'] = ab_label
    info['display_t'] = display_t
    info['family'] = family_search
    info['factorint'] = factorint

    if family_search:
        return render_template("hgm-search.html", info=info, title="Hypergeometric Family over $\Q$ Search Result", bread=bread, credit=HGM_credit, learnmore=learnmore_list())
    else:
        return render_template("hgm-search.html", info=info, title="Hypergeometric Motive over $\Q$ Search Result", bread=bread, credit=HGM_credit, learnmore=learnmore_list())
Ejemplo n.º 34
0
def render_artin_representation_webpage(label):
    if re.compile(r'^\d+$').match(label):
        return artin_representation_search(**{'dimension': label})

    bread = get_bread([(label, ' ')])

    # label=dim.cond.nTt.indexcj, c is literal, j is index in conj class
    # Should we have a big try around this to catch bad labels?
    label = clean_input(label)
    try:
        the_rep = ArtinRepresentation(label)
    except:
        flash(Markup("Error: <span style='color:black'>%s</span> is not the label of an Artin representation in the database." % (label)), "error")
        return search_input_error({'err':''}, bread)
              

    extra_data = {} # for testing?
    C = getDBConnection()
    extra_data['galois_knowl'] = group_display_knowl(5,3,C) # for testing?
    #artin_logger.info("Found %s" % (the_rep._data))


    title = "Artin representation %s" % label
    the_nf = the_rep.number_field_galois_group()
    from lmfdb.number_field_galois_groups import nfgg_page
    from lmfdb.number_field_galois_groups.main import by_data
    if the_rep.sign() == 0:
        processed_root_number = "not computed"
    else:
        processed_root_number = str(the_rep.sign())
    properties = [("Dimension", str(the_rep.dimension())),
                  ("Group", the_rep.group()),
                  #("Conductor", str(the_rep.conductor())),
                  ("Conductor", "$" + the_rep.factored_conductor_latex() + "$"),
                  #("Bad primes", str(the_rep.bad_primes())),
                  ("Root number", processed_root_number),
                  ("Frobenius-Schur indicator", str(the_rep.indicator()))
                  ]

    friends = []
    nf_url = the_nf.url_for()
    if nf_url:
    	friends.append(("Artin Field", nf_url))
    cc = the_rep.central_character()
    if cc is not None:
        if cc.modulus <= 100000: 
            if the_rep.dimension()==1:
                friends.append(("Corresponding Dirichlet character", url_for("characters.render_Dirichletwebpage", modulus=cc.modulus, number=cc.number)))
            else:
                friends.append(("Determinant character", url_for("characters.render_Dirichletwebpage", modulus=cc.modulus, number=cc.number)))

    # once the L-functions are in the database, the link can always be shown
    if the_rep.dimension() <= 6:
        friends.append(("L-function", url_for("l_functions.l_function_artin_page",
                                          label=the_rep.label())))
    info={}
    #mychar = the_rep.central_char()
    #info['pol2']= str([((j+1),mychar(j+1, 2*the_rep.character_field())) for j in range(50)])
    #info['pol3']=str(the_rep.central_character())
    #info['pol3']=str(the_rep.central_char(3))
    #info['pol5']=str(the_rep.central_char(5))
    #info['pol7']=str(the_rep.central_char(7))
    #info['pol11']=str(the_rep.central_char(11))

    return render_template("artin-representation-show.html", credit=tim_credit, support=support_credit, title=title, bread=bread, friends=friends, object=the_rep, properties2=properties, extra_data=extra_data, info=info)
Ejemplo n.º 35
0
def render_group_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        label = label.replace('t', 'T')
        C = base.getDBConnection()
        data = C.transitivegroups.groups.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search Error", ' ')])
            info['err'] = "Group " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        data['label_raw'] = label.lower()
        title = 'Galois Group: ' + label
        wgg = WebGaloisGroup.from_data(data)
        n = data['n']
        t = data['t']
        data['yesno'] = yesno
        order = data['order']
        data['orderfac'] = latex(ZZ(order).factor())
        orderfac = latex(ZZ(order).factor())
        data['ordermsg'] = "$%s=%s$" % (order, latex(orderfac))
        if order == 1:
            data['ordermsg'] = "$1$"
        if ZZ(order).is_prime():
            data['ordermsg'] = "$%s$ (is prime)" % order
        pgroup = len(ZZ(order).prime_factors()) < 2
        if n == 1:
            G = gap.SmallGroup(n, t)
        else:
            G = gap.TransitiveGroup(n, t)
        if ZZ(order) < ZZ('10000000000'):
            ctable = chartable(n, t)
        else:
            ctable = 'Group too large'
        data['gens'] = generators(n, t)
        if n == 1 and t == 1:
            data['gens'] = 'None needed'
        data['chartable'] = ctable
        data['parity'] = "$%s$" % data['parity']
        data['cclasses'] = conjclasses(G, n)
        data['subinfo'] = subfield_display(C, n, data['subs'])
        data['resolve'] = resolve_display(C, data['resolve'])
        if data['gapid'] == 0:
            data['gapid'] = "Data not available"
        else:
            data['gapid'] = small_group_display_knowl(int(data['order']),int(data['gapid']),C, str([int(data['order']),int(data['gapid'])]))
        data['otherreps'] = wgg.otherrep_list()
        ae = wgg.arith_equivalent()
        if ae>0:
            if ae>1:
                data['arith_equiv'] = r'A number field with this Galois group has %d <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.'% ae
            else:
                data['arith_equiv'] = r'A number field with this Galois group has exactly one <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> field.'
        else:
            data['arith_equiv'] = r'A number field with this Galois group has no <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.'
        if len(data['otherreps']) == 0:
            data['otherreps']="There is no other low degree representation."
        query={'galois': bson.SON([('n', n), ('t', t)])}
        C = base.getDBConnection()
        intreps = C.transitivegroups.Gmodules.find({'n': n, 't': t}).sort('index', pymongo.ASCENDING)
        # turn cursor into a list
        intreps = [z for z in intreps]
        if len(intreps) > 0:
            data['int_rep_classes'] = [str(z[0]) for z in intreps[0]['gens']]
            for onerep in intreps:
                onerep['gens']=[list_to_latex_matrix(z[1]) for z in onerep['gens']]
            data['int_reps'] = intreps
            data['int_reps_complete'] = int_reps_are_complete(intreps)
            dcq = data['moddecompuniq']
            if dcq[0] == 0:
                data['decompunique'] = 0
            else:
                data['decompunique'] = dcq[0]
                data['isoms'] = [[mult2mult(z[0]), mult2mult(z[1])] for z in dcq[1]]
                data['isoms'] = [[modules2string(n,t,z[0]), modules2string(n,t,z[1])] for z in data['isoms']]
                #print dcq[1]
                #print data['isoms']

        friends = []
        one = C.numberfields.fields.find_one(query)
        if one:
            friends.append(('Number fields with this Galois group', url_for('number_fields.number_field_render_webpage')+"?galois_group=%dT%d" % (n, t) )) 
        prop2 = [('Label', label),
            ('Order', '\(%s\)' % order),
            ('n', '\(%s\)' % data['n']),
            ('Cyclic', yesno(data['cyc'])),
            ('Abelian', yesno(data['ab'])),
            ('Solvable', yesno(data['solv'])),
            ('Primitive', yesno(data['prim'])),
            ('$p$-group', yesno(pgroup)),
        ]
        pretty = group_display_pretty(n,t,C)
        if len(pretty)>0:
            prop2.extend([('Group:', pretty)])
            info['pretty_name'] = pretty
        data['name'] = re.sub(r'_(\d+)',r'_{\1}',data['name'])
        data['name'] = re.sub(r'\^(\d+)',r'^{\1}',data['name'])
        info.update(data)

        bread = get_bread([(label, ' ')])
        return render_template("gg-show-group.html", credit=GG_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends)
Ejemplo n.º 36
0
Archivo: main.py Proyecto: koffie/lmfdb
def render_hecke_algebras_webpage(**args):
    data = None
    if 'label' in args:
        lab = clean_input(args.get('label'))
        if lab != args.get('label'):
            return redirect(url_for('.render_hecke_algebras_webpage', label=lab), 301)
        data = db.hecke_algebras.lookup(lab)
    if data is None:
        t = "Hecke Algebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for a Hecke Algebras in the database." % (lab)),"error")
        return render_template("hecke_algebras-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
    info = {}
    info.update(data)

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")), ('%s' % data['label'], ' ')]
    credit = hecke_algebras_credit
    info['level']=int(data['level'])
    info['weight']= int(data['weight'])
    info['num_orbits']= int(data['num_orbits'])
    dim_count = "not available"

    proj = ['orbit_label','hecke_op','num_hecke_op','Zbasis','discriminant','disc_fac','Qbasis','Qalg_gen']
    orb = list(db.hecke_orbits.search({'parent_label': data['label']}, proj))
    if orb:
        #consistency check
        if len(orb) != int(data['num_orbits']):
            return search_input_error(info)

        dim_count=0
        for v in orb:
            ops = sage_eval(v['hecke_op'])
            dim = int(matrix(ops[0]).nrows())
            dim_count += dim
            if dim > 4:
                v['hecke_op_display'] = []
            elif dim == 1:
                v['hecke_op_display'] = [[i+1, ops[i][0][0]] for i in range(10)]
            else:
                v['hecke_op_display'] = [[i+1, latex(matrix(ops[i]))] for i in range(5)]
            v['download_op'] = [(lang, url_for(".render_hecke_algebras_webpage_download", orbit_label=v['orbit_label'], lang=lang, obj='operators')) for lang in ['gp', 'magma','sage']]
            if v['Zbasis'] is None:
                for key in ['Zbasis','discriminant','disc_fac','Qbasis','Qalg_gen']:
                    del v[key]
            else:
                v['Zbasis'] = [[int(i) for i in j] for j in v['Zbasis']]
                v['disc_fac'] = [[int(i) for i in j] for j in v['disc_fac']]
                if dim > 4:
                    v['gen_display'] = []
                elif dim == 1:
                    v['gen_display'] = [v['Zbasis'][0][0]]
                else:
                    v['gen_display'] = [latex(matrix(dim,dim,v['Zbasis'][i])) for i in range(dim)]
                v['inner_twists'] = "not available" # not yet in the database
                v['download_gen'] = [(lang, url_for(".render_hecke_algebras_webpage_download", orbit_label=v['orbit_label'], lang=lang, obj='gen')) for lang in ['gp', 'magma','sage']]
        info['orbits'] = orb

    info['dim_alg'] = dim_count
    info['l_adic'] = l_range
    info['properties'] = [
        ('Label', '%s' %info['label']),
        ('Level', '%s' %info['level']),
        ('Weight', '%s' %info['weight'])]
    if info['num_orbits']!=0:
        info['friends'] = [('Newforms space ' + info['label'], url_for("cmf.by_url_space_label", level=info['level'], weight=info['weight'], char_orbit_label='a'))]
    else:
        info['friends'] = []
    t = "Hecke Algebra %s" % info['label']
    return render_template("hecke_algebras-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list(), friends=info['friends'])
Ejemplo n.º 37
0
def render_field_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        data = C.localfields.fields.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info['err'] = "Field " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Local Number Field:' + label
        polynomial = coeff_to_poly(data['coeffs'])
        p = data['p']
        e = data['e']
        f = data['f']
        cc = data['c']
        GG = data['gal']
        gn = GG[0]
        gt = GG[1]
        prop2 = [
            ('Base', '\(\Q_{%s}\)' % p),
            ('Degree', '\(%s\)' % data['n']),
            ('e', '\(%s\)' % e),
            ('f', '\(%s\)' % f),
            ('c', '\(%s\)' % cc),
            ('Galois group', group_display_short(gn, gt, C)),
        ]
        Pt = PolynomialRing(QQ, 't')
        Pyt = PolynomialRing(Pt, 'y')
        eisenp = Pyt(str(data['eisen']))
        unramp = Pyt(str(data['unram']))
        # Look up the unram poly so we can link to it
        unramdata = C.localfields.fields.find_one({'p': p, 'n': f, 'c': 0})
        if len(unramdata) > 0:
            unramfriend = "/LocalNumberField/%s" % unramdata['label']
        else:
            logger.fatal("Cannot find unramified field!")
            unramfriend = ''
        rfdata = C.localfields.fields.find_one({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']})
        if rfdata is None:
            logger.fatal("Cannot find discriminant root field!")
            rffriend = ''
        else:
            rffriend = "/LocalNumberField/%s" % rfdata['label']

        info.update({
                    'polynomial': web_latex(polynomial),
                    'n': data['n'],
                    'p': data['p'],
                    'c': data['c'],
                    'e': data['e'],
                    'f': data['f'],
                    't': data['t'],
                    'u': data['u'],
                    'rf': printquad(data['rf'], p),
                    'hw': data['hw'],
                    'slopes': show_slopes(data['slopes']),
                    'gal': group_display_knowl(gn, gt, C),
                    'gt': gt,
                    'inertia': group_display_inertia(data['inertia'], C),
                    'unram': web_latex(unramp),
                    'eisen': web_latex(eisenp),
                    'gms': data['gms'],
                    'aut': data['aut'],
                    })
        friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
        if unramfriend != '':
            friends.append(('Unramified subfield', unramfriend))
        if rffriend != '':
            friends.append(('Discriminant root field', rffriend))

        bread = get_bread([(label, ' ')])
        learnmore = [('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Local field labels', url_for(".labels_page"))]
        return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
Ejemplo n.º 38
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)
Ejemplo n.º 39
0
def render_field_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        C = base.getDBConnection()
        data = C.localfields.fields.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", ' ')])
            info['err'] = "Field " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Local Number Field:' + label
        polynomial = coeff_to_poly(data['coeffs'])
        p = data['p']
        e = data['e']
        f = data['f']
        cc = data['c']
        GG = data['gal']
        gn = GG[0]
        gt = GG[1]
        prop2 = [
            ('Label', label),
            ('Base', '\(\Q_{%s}\)' % p),
            ('Degree', '\(%s\)' % data['n']),
            ('e', '\(%s\)' % e),
            ('f', '\(%s\)' % f),
            ('c', '\(%s\)' % cc),
            ('Galois group', group_display_short(gn, gt, C)),
        ]
        Pt = PolynomialRing(QQ, 't')
        Pyt = PolynomialRing(Pt, 'y')
        eisenp = Pyt(str(data['eisen']))
        unramp = Pyt(str(data['unram']))
        # Look up the unram poly so we can link to it
        unramdata = C.localfields.fields.find_one({'p': p, 'n': f, 'c': 0})
        if len(unramdata) > 0:
            unramfriend = "/LocalNumberField/%s" % unramdata['label']
        else:
            logger.fatal("Cannot find unramified field!")
            unramfriend = ''
        rfdata = C.localfields.fields.find_one({
            'p': p,
            'n': {
                '$in': [1, 2]
            },
            'rf': data['rf']
        })
        if rfdata is None:
            logger.fatal("Cannot find discriminant root field!")
            rffriend = ''
        else:
            rffriend = "/LocalNumberField/%s" % rfdata['label']

        info.update({
            'polynomial': web_latex(polynomial),
            'n': data['n'],
            'p': data['p'],
            'c': data['c'],
            'e': data['e'],
            'f': data['f'],
            't': data['t'],
            'u': data['u'],
            'rf': printquad(data['rf'], p),
            'hw': data['hw'],
            'slopes': show_slopes(data['slopes']),
            'gal': group_display_knowl(gn, gt, C),
            'gt': gt,
            'inertia': group_display_inertia(data['inertia'], C),
            'unram': web_latex(unramp),
            'eisen': web_latex(eisenp),
            'gms': data['gms'],
            'aut': data['aut'],
        })
        friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
        if unramfriend != '':
            friends.append(('Unramified subfield', unramfriend))
        if rffriend != '':
            friends.append(('Discriminant root field', rffriend))

        bread = get_bread([(label, ' ')])
        learnmore = [('Completeness of the data',
                      url_for(".completeness_page")),
                     ('Source of the data', url_for(".how_computed_page")),
                     ('Local field labels', url_for(".labels_page"))]
        return render_template("lf-show-field.html",
                               credit=LF_credit,
                               title=title,
                               bread=bread,
                               info=info,
                               properties2=prop2,
                               friends=friends,
                               learnmore=learnmore)
Ejemplo n.º 40
0
def number_field_search(**args):
    info = to_dict(args)

    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")), ('Quadratic imaginary class groups', url_for(".render_class_group_data"))]
    t = 'Global Number Field search results'
    bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search results', ' ')]

    # for k in info.keys():
    #  nf_logger.debug(str(k) + ' ---> ' + str(info[k]))
    # nf_logger.debug('******************* '+ str(info['search']))

    if 'natural' in info:
        query = {'label_orig': info['natural']}
        try:
            parse_nf_string(info,query,'natural',name="Label",qfield='label')
            return redirect(url_for(".by_label", label= clean_input(query['label'])))
        except ValueError:
            query['err'] = info['err']
            return search_input_error(query, bread)

    query = {}
    try:
        parse_galgrp(info,query, qfield='galois')
        parse_ints(info,query,'degree')
        parse_bracketed_posints(info,query,'signature',split=False,exactlength=2)
        parse_signed_ints(info,query,'discriminant',qfield=('disc_sign','disc_abs_key'),parse_one=make_disc_key)
        parse_ints(info,query,'class_number')
        parse_bracketed_posints(info,query,'class_group',split=False,check_divisibility='increasing')
        parse_primes(info,query,'ur_primes',name='Unramified primes',qfield='ramps',mode='complement',to_string=True)
        if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'some':
            mode = 'append'
        else:
            mode = 'exact'
        parse_primes(info,query,'ram_primes','ramified primes','ramps',mode,to_string=True)
    except ValueError:
        return search_input_error(info, bread)
    count = parse_count(info)
    start = parse_start(info)

    if info.get('paging'):
        try:
            paging = int(info['paging'])
            if paging == 0:
                start = 0
        except:
            pass

    C = base.getDBConnection()
    # nf_logger.debug(query)
    info['query'] = dict(query)
    if 'lucky' in args:
        one = C.numberfields.fields.find_one(query)
        if one:
            label = one['label']
            return redirect(url_for(".by_label", clean_input(label)))

    fields = C.numberfields.fields

    res = fields.find(query)

    if 'download' in info and info['download'] != '0':
        return download_search(info, res)

    res = res.sort([('degree', ASC), ('disc_abs_key', ASC),('disc_sign', ASC)])
    nres = res.count()
    res = res.skip(start).limit(count)

    if(start >= nres):
        start -= (1 + (start - nres) / count) * count
    if(start < 0):
        start = 0

    info['fields'] = res
    info['number'] = nres
    info['start'] = start
    if nres == 1:
        info['report'] = 'unique match'
    else:
        if nres > count or start != 0:
            info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
        else:
            info['report'] = 'displaying all %s matches' % nres

    info['wnf'] = WebNumberField.from_data
    return render_template("number_field_search.html", info=info, title=t, bread=bread)
Ejemplo n.º 41
0
def render_hecke_algebras_webpage_l_adic(**args):
    data = None
    if 'orbit_label' in args and 'prime' in args:
        lab = clean_input(args.get('orbit_label'))
        if lab != args.get('orbit_label'):
            base_lab=".".join([split(lab)[i] for i in [0,1,2]])
            return redirect(url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        try:
            ell = int(args.get('prime'))
        except ValueError:
            base_lab=".".join([split(lab)[i] for i in [0,1,2]])
            return redirect(url_for('.render_hecke_algebras_webpage', label=base_lab), 301)
        data = hecke_l_adic_db().find_one({'orbit_label': lab , 'ell': ell})
    if data is None:
        t = "Hecke Agebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for the &#x2113;-adic information for an Hecke Algebra orbit in the database." % (lab)),"error")
        return render_template("hecke_algebras-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
    info = {}
    info.update(data)
    res = hecke_l_adic_db().find({'level': data['level'],'weight': data['weight'],'orbit_label': data['orbit_label'], 'ell': data['ell']})

    info['num_l_adic_orbits']=res.count()
    res_clean = []
    for f in res:
        f_clean = {}
        f_clean['index']=int(f['index'])
        f_clean['orbit_label']=str(f['orbit_label'])
        f_clean['ell']=int(f['ell'])
        if f['idempotent'] != "":
            f['dim']=len(sage_eval(f['idempotent']))
            l_max= sage_eval(f['idempotent'])[0][0].ndigits()
            if f['dim']>4 or l_max>5:
                f_clean['idempotent_display']=[]
            elif f['dim']==1:
                f_clean['idempotent_display']=sage_eval(f['idempotent'])[0][0]
            else:
                f_clean['idempotent_display']=latex(matrix(sage_eval(f['idempotent'])))
        else:
            f_clean['idempotent_display']=latex(matrix([[1]]))
        f_clean['download_id'] = [(i, url_for(".render_hecke_algebras_webpage_ell_download", orbit_label=f_clean['orbit_label'], index=f_clean['index'], prime=f_clean['ell'], lang=i, obj='idempotents')) for i in ['magma','sage']]  # for 'gp' the code does not work, since p-adics are not implemented


        try:
            f_clean['deg']=int(f['field'][1])
            f_clean['field_poly']=str(f['field'][2])
            f_clean['dim']=int(f['structure'][0])
            f_clean['num_gen']=int(f['structure'][1])
            f_clean['gens']=[[int(sage_eval(f['structure'][2]).index(i)+1), str(i)] for i in sage_eval(f['structure'][2])]
            f_clean['rel']=sage_eval(f['structure'][3])
            f_clean['grading']=[int(i) for i in f['properties'][0]]
            f_clean['gorenstein_def']=int(f['properties'][1])
            if f_clean['gorenstein_def']==0:
                f_clean['gorenstein']="yes"
            else:
                f_clean['gorenstein']="no"
            f_clean['operators_mod_l']=[[int(i) for i in j] for j in f['operators']]
            f_clean['num_hecke_op']=len(f_clean['operators_mod_l'])
            f_clean['download_op'] = [(i, url_for(".render_hecke_algebras_webpage_ell_download", orbit_label=f_clean['orbit_label'], index=f_clean['index'], prime=f_clean['ell'], lang=i, obj='operators')) for i in ['magma','sage']]  # for 'gp' the code does not work
            f_clean['size_op']=sqrt(len(f_clean['operators_mod_l'][0]))
            if f_clean['size_op']>4:
                f_clean['operators_mod_l_display']=[]
            elif f_clean['size_op']==1:
                f_clean['operators_mod_l_display']=[[i+1, f_clean['operators_mod_l'][i][0]] for i in range(0,10)]
            else:
                f_clean['operators_mod_l_display']=[[i+1,latex(matrix(f_clean['size_op'],f_clean['size_op'], f_clean['operators_mod_l'][i]))] for i in range(0,5)]
            res_clean.append(f_clean)
        except KeyError:
            pass    

    info['l_adic_orbits']=res_clean

    info['level']=int(data['level'])
    info['weight']= int(data['weight'])
    info['base_lab']=".".join([split(data['orbit_label'])[i] for i in [0,1,2]])
    info['orbit_label']= str(data['orbit_label'])
    info['ell']=int(data['ell'])

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")), ('%s' % info['base_lab'], url_for('.render_hecke_algebras_webpage', label=info['base_lab'])), ('%s' % info['ell'], ' ')]
    credit = hecke_algebras_credit
    info['properties'] = [
        ('Level', '%s' %info['level']),
        ('Weight', '%s' %info['weight']),
        ('Characteristic', '%s' %info['ell']),
        ('Orbit label', '%s' %info['orbit_label'])]    
    info['friends'] = [('Modular form ' + info['base_lab'], url_for("emf.render_elliptic_modular_forms", level=info['level'], weight=info['weight'], character=1))]

    t = "%s-adic and mod %s data for the Hecke Algebra orbit %s" % (info['ell'], info['ell'], info['orbit_label'])
    return render_template("hecke_algebras_l_adic-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list(), friends=info['friends'])
Ejemplo n.º 42
0
def render_family(args):
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        dataz = list(db.hgcwa_passports.search({'label':label}))
        if len(dataz) == 0:
            flash_error( "No family with label %s was found in the database.", label)
            return redirect(url_for(".index"))
        data=dataz[0]
        g = data['genus']
        GG = ast.literal_eval(data['group'])
        gn = GG[0]
        gt = GG[1]

        gp_string = str(gn) + '.' + str(gt)
        pretty_group = sg_pretty(gp_string)

        if gp_string == pretty_group:
            spname = False
        else:
            spname = True
        title = 'Family of Genus ' + str(g) + ' Curves with Automorphism Group $' + pretty_group +'$'
        smallgroup="[" + str(gn) + "," +str(gt) + "]"

        prop2 = [
            ('Genus', '\(%d\)' % g),
            ('Group', '\(%s\)' %  pretty_group),
            ('Signature', '\(%s\)' % sign_display(ast.literal_eval(data['signature'])))
        ]
        info.update({'genus': data['genus'],
                    'sign': sign_display(ast.literal_eval(data['signature'])),
                     'group': pretty_group,
                    'g0':data['g0'],
                    'dim':data['dim'],
                    'r':data['r'],
                    'gpid': smallgroup
                   })

        if spname:
            info.update({'specialname': True})

        Lcc=[]
        Lall=[]
        i=1
        for dat in dataz:
            if ast.literal_eval(dat['con']) not in Lcc:
                urlstrng=dat['passport_label']
                Lcc.append(ast.literal_eval(dat['con']))
                Lall.append([cc_display(ast.literal_eval(dat['con'])),dat['passport_label'],
                             urlstrng])
                i=i+1

        info.update({'passport': Lall})


        g2List = ['[2,1]','[4,2]','[8,3]','[10,2]','[12,4]','[24,8]','[48,29]']
        if g  == 2 and data['group'] in g2List:
            g2url = "/Genus2Curve/Q/?geom_aut_grp_id=" + data['group']
            friends = [("Genus 2 curves over $\Q$", g2url ) ]
        else:
            friends = [ ]


        br_g, br_gp, br_sign = split_family_label(label)

        bread_sign = label_to_breadcrumbs(br_sign)
        bread_gp = label_to_breadcrumbs(br_gp)

        bread = get_bread([(br_g, './?genus='+br_g),('$'+pretty_group+'$','./?genus='+br_g + '&group='+bread_gp), (bread_sign,' ')])
        learnmore =[('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Labeling convention', url_for(".labels_page"))]

        downloads = [('Download Magma code', url_for(".hgcwa_code_download",  label=label, download_type='magma')),
                     ('Download Gap code', url_for(".hgcwa_code_download", label=label, download_type='gap'))]

        return render_template("hgcwa-show-family.html",
                               title=title, bread=bread, info=info,
                               properties2=prop2, friends=friends,
                               learnmore=learnmore, downloads=downloads, credit=credit)
Ejemplo n.º 43
0
def render_passport(args):
    info = {}
    if 'passport_label' in args:
        label = clean_input(args['passport_label'])
        dataz = list(db.hgcwa_passports.search({'passport_label': label}))
        if len(dataz) == 0:
            bread = get_bread([("Search Error", url_for('.index'))])
            flash_error( "No refined passport with label %s was found in the database.", label)
            return redirect(url_for(".index"))
        data=dataz[0]
        g = data['genus']
        GG = ast.literal_eval(data['group'])
        gn = GG[0]
        gt = GG[1]

        gp_string=str(gn) + '.' + str(gt)
        pretty_group=sg_pretty(gp_string)

        if gp_string == pretty_group:
            spname=False
        else:
            spname=True

        numb = len(dataz)

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

        title = 'One Refined Passport of Genus ' + str(g) + ' with Automorphism Group $' + pretty_group +'$'
        smallgroup="[" + str(gn) + "," +str(gt) +"]"

        prop2 = [
            ('Genus', '\(%d\)' % g),
            ('Small Group', '\(%s\)' %  pretty_group),
            ('Signature', '\(%s\)' % sign_display(ast.literal_eval(data['signature']))),
            ('Generating Vectors','\(%d\)' % numb)
        ]
        info.update({'genus': data['genus'],
                    'cc': cc_display(data['con']),
                    'sign': sign_display(ast.literal_eval(data['signature'])),
                     'group': pretty_group,
                     'gpid': smallgroup,
                     'numb':numb,
                     'disp_numb':min(numb,numgenvecs)
                   })

        if spname:
            info.update({'specialname': True})

        Ldata=[]
        HypColumn = False
        Lfriends=[]
        for i in range (0, min(numgenvecs,numb)):
            dat= dataz[i]
            x1=dat['total_label']
            if 'full_auto' in dat:
                x2='No'
                if dat['full_label'] not in Lfriends:
                    Lfriends.append(dat['full_label'])
            else:
                x2='Yes'

            if 'hyperelliptic' in dat:
                x3=tfTOyn(dat['hyperelliptic'])
                HypColumn= True
            else:
                x3=' '

            x4=[]
            for perm in dat['gen_vectors']:
                cycperm=Permutation(perm).cycle_string()

                x4.append(sep.join(split_perm(cycperm)))

            Ldata.append([x1,x2,x3,x4])



        info.update({'genvects': Ldata, 'HypColumn' : HypColumn})

        info.update({'passport_cc': cc_display(ast.literal_eval(data['con']))})

        if 'eqn' in data:
            info.update({'eqns': data['eqn']})

        if 'ndim' in data:
            info.update({'Ndim': data['ndim']})

        other_data = False

        if 'hyperelliptic' in data:
            info.update({'ishyp':  tfTOyn(data['hyperelliptic'])})
            other_data = True

        if 'hyp_involution' in data:
            inv=Permutation(data['hyp_involution']).cycle_string()
            info.update({'hypinv': sep.join(split_perm(inv))})


        if 'cyclic_trigonal' in data:
            info.update({'iscyctrig':  tfTOyn(data['cyclic_trigonal'])})
            other_data = True

        if 'jacobian_decomp' in data:
            jcLatex, corrChar = decjac_format(data['jacobian_decomp'])
            info.update({'corrChar': corrChar, 'jacobian_decomp': jcLatex})


        if 'cinv' in data:
            cinv=Permutation(data['cinv']).cycle_string()
            info.update({'cinv': sep.join(split_perm(cinv))})

        info.update({'other_data': other_data})


        if 'full_auto' in data:
            full_G=ast.literal_eval(data['full_auto'])
            full_gn = full_G[0]
            full_gt = full_G[1]

            full_gp_string=str(full_gn) + '.' + str(full_gt)
            full_pretty_group=sg_pretty(full_gp_string)
            info.update({'fullauto': full_pretty_group,
                         'signH':sign_display(ast.literal_eval(data['signH'])),
                         'higgenlabel' : data['full_label'] })


        urlstrng,br_g, br_gp, br_sign, refined_p = split_passport_label(label)


        if Lfriends:
           for Lf in Lfriends:
              friends = [("Full automorphism " + Lf, Lf),("Family containing this refined passport ",  urlstrng) ]

        else:
            friends = [("Family containing this refined passport",  urlstrng) ]


        bread_sign = label_to_breadcrumbs(br_sign)
        bread_gp = label_to_breadcrumbs(br_gp)

        bread = get_bread([(br_g, './?genus='+br_g),('$'+pretty_group+'$','./?genus='+br_g + '&group='+bread_gp), (bread_sign, urlstrng),(data['cc'][0],' ')])

        learnmore =[('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Labeling convention', url_for(".labels_page"))]

        downloads = [('Download Magma code', url_for(".hgcwa_code_download",  label=label, download_type='magma')),
                     ('Download Gap code', url_for(".hgcwa_code_download", label=label, download_type='gap'))]

        return render_template("hgcwa-show-passport.html",
                               title=title, bread=bread, info=info,
                               properties2=prop2, friends=friends,
                               learnmore=learnmore, downloads=downloads, credit=credit)
Ejemplo n.º 44
0
def render_lattice_webpage(**args):
    data = None
    if 'label' in args:
        lab = clean_input(args.get('label'))
        if lab != args.get('label'):
            return redirect(url_for('.render_lattice_webpage', label=lab), 301)
        data = lattice_db().find_one({'$or':[{'label': lab }, {'name': lab }]})
    if data is None:
        t = "Integral Lattices Search Error"
        bread = [('Lattice', url_for(".lattice_render_webpage"))]
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label or name for an integral lattice in the database." % (lab)),"error")
        return render_template("lattice-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
    info = {}
    info.update(data)

    info['friends'] = []

    bread = [('Lattice', url_for(".lattice_render_webpage")), ('%s' % data['label'], ' ')]
    credit = lattice_credit
    f = lattice_db().find_one({'dim': data['dim'],'det': data['det'],'level': data['level'],'gram': data['gram'],'minimum': data['minimum'],'class_number': data['class_number'],'aut': data[ 'aut'],'name': data['name']})
    info['dim']= int(f['dim'])
    info['det']= int(f['det'])
    info['level']=int(f['level'])
    info['gram']=vect_to_matrix(f['gram'])
    info['density']=str(f['density'])
    info['hermite']=str(f['hermite'])
    info['minimum']=int(f['minimum'])
    info['kissing']=int(f['kissing'])
    info['aut']=int(f['aut'])

    if f['shortest']=="":
        info['shortest']==f['shortest']
    else:
        if f['dim']==1:
            info['shortest']=str(f['shortest']).strip('[').strip(']')
        else:
            if info['dim']*info['kissing']<100:
                info['shortest']=[str([tuple(v)]).strip('[').strip(']').replace('),', '), ') for v in f['shortest']]
            else:
                max_vect_num=min(int(round(100/(info['dim']))), int(round(info['kissing']/2))-1);
                info['shortest']=[str([tuple(f['shortest'][i])]).strip('[').strip(']').replace('),', '), ') for i in range(max_vect_num+1)]
                info['all_shortest']="no"
        info['download_shortest'] = [
            (i, url_for(".render_lattice_webpage_download", label=info['label'], lang=i, obj='shortest_vectors')) for i in ['gp', 'magma','sage']]

    if f['name']==['Leech']:
        info['shortest']=[str([1,-2,-2,-2,2,-1,-1,3,3,0,0,2,2,-1,-1,-2,2,-2,-1,-1,0,0,-1,2]), 
str([1,-2,-2,-2,2,-1,0,2,3,0,0,2,2,-1,-1,-2,2,-1,-1,-2,1,-1,-1,3]), str([1,-2,-2,-1,1,-1,-1,2,2,0,0,2,2,0,0,-2,2,-1,-1,-1,0,-1,-1,2])]
        info['all_shortest']="no"
        info['download_shortest'] = [
            (i, url_for(".render_lattice_webpage_download", label=info['label'], lang=i, obj='shortest_vectors')) for i in ['gp', 'magma','sage']]

    ncoeff=20
    if f['theta_series'] != "":
        coeff=[f['theta_series'][i] for i in range(ncoeff+1)]
        info['theta_series']=my_latex(print_q_expansion(coeff))
        info['theta_display'] = url_for(".theta_display", label=f['label'], number="")

    info['class_number']=int(f['class_number'])

    if f['dim']==1:
        info['genus_reps']=str(f['genus_reps']).strip('[').strip(']')
    else:
        if info['dim']*info['class_number']<50:
            info['genus_reps']=[vect_to_matrix(n) for n in f['genus_reps']]
        else:
            max_matrix_num=min(int(round(25/(info['dim']))), info['class_number']);
            info['all_genus_rep']="no"
            info['genus_reps']=[vect_to_matrix(f['genus_reps'][i]) for i in range(max_matrix_num+1)]
    info['download_genus_reps'] = [
        (i, url_for(".render_lattice_webpage_download", label=info['label'], lang=i, obj='genus_reps')) for i in ['gp', 'magma','sage']]

    if f['name'] != "":
        if f['name']==str(f['name']):
            info['name']= str(f['name'])
        else:
            info['name']=str(", ".join(str(i) for i in f['name']))
    else:
        info['name'] == ""
    info['comments']=str(f['comments'])
    if 'Leech' in info['comments']: # no need to duplicate as it is in the name
        info['comments'] = ''
    if info['name'] == "":
        t = "Integral Lattice %s" % info['label']
    else:
        t = "Integral Lattice "+info['label']+" ("+info['name']+")"
#This part code was for the dinamic knowl with comments, since the test is displayed this is redundant
#    if info['name'] != "" or info['comments'] !="":
#        info['knowl_args']= "name=%s&report=%s" %(info['name'], info['comments'].replace(' ', '-space-'))
    info['properties'] = [
        ('Dimension', '%s' %info['dim']),
        ('Determinant', '%s' %info['det']),
        ('Level', '%s' %info['level'])]
    if info['class_number'] == 0:
        info['properties']=[('Class number', 'not available')]+info['properties']
    else:
        info['properties']=[('Class number', '%s' %info['class_number'])]+info['properties']
    info['properties']=[('Label', '%s' % info['label'])]+info['properties']

    if info['name'] != "" :
        info['properties']=[('Name','%s' % info['name'] )]+info['properties']
#    friends = [('L-series (not available)', ' ' ),('Half integral weight modular forms (not available)', ' ')]
    return render_template("lattice-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list())
Ejemplo n.º 45
0
def render_group_webpage(args):
    data = None
    info = {}
    if "label" in args:
        label = clean_input(args["label"])
        label = label.replace("t", "T")
        C = base.getDBConnection()
        data = C.transitivegroups.groups.find_one({"label": label})
        if data is None:
            bread = get_bread([("Search error", url_for(".search"))])
            info["err"] = "Group " + label + " was not found in the database."
            info["label"] = label
            return search_input_error(info, bread)
        title = "Galois Group: " + label
        wgg = WebGaloisGroup.from_data(data)
        n = data["n"]
        t = data["t"]
        data["yesno"] = yesno
        order = data["order"]
        data["orderfac"] = latex(ZZ(order).factor())
        orderfac = latex(ZZ(order).factor())
        data["ordermsg"] = "$%s=%s$" % (order, latex(orderfac))
        if order == 1:
            data["ordermsg"] = "$1$"
        if ZZ(order).is_prime():
            data["ordermsg"] = "$%s$ (is prime)" % order
        pgroup = len(ZZ(order).prime_factors()) < 2
        if n == 1:
            G = gap.SmallGroup(n, t)
        else:
            G = gap.TransitiveGroup(n, t)
        if ZZ(order) < ZZ("10000000000"):
            ctable = chartable(n, t)
        else:
            ctable = "Group too large"
        data["gens"] = generators(n, t)
        if n == 1 and t == 1:
            data["gens"] = "None needed"
        data["chartable"] = ctable
        data["parity"] = "$%s$" % data["parity"]
        data["cclasses"] = conjclasses(G, n)
        data["subinfo"] = subfield_display(C, n, data["subs"])
        data["resolve"] = resolve_display(C, data["resolve"])
        data["otherreps"] = wgg.otherrep_list()
        if len(data["otherreps"]) == 0:
            data["otherreps"] = "There is no other low degree representation."
        query = {"galois": bson.SON([("n", n), ("t", t)])}
        C = base.getDBConnection()
        intreps = C.transitivegroups.Gmodules.find({"n": n, "t": t}).sort("index", pymongo.ASCENDING)
        # turn cursor into a list
        intreps = [z for z in intreps]
        if len(intreps) > 0:
            data["int_rep_classes"] = [str(z[0]) for z in intreps[0]["gens"]]
            for onerep in intreps:
                onerep["gens"] = [list_to_latex_matrix(z[1]) for z in onerep["gens"]]
            data["int_reps"] = intreps
            data["int_reps_complete"] = int_reps_are_complete(intreps)
            dcq = data["moddecompuniq"]
            if dcq[0] == 0:
                data["decompunique"] = 0
            else:
                data["decompunique"] = dcq[0]
                data["isoms"] = [[mult2mult(z[0]), mult2mult(z[1])] for z in dcq[1]]
                data["isoms"] = [[modules2string(n, t, z[0]), modules2string(n, t, z[1])] for z in data["isoms"]]
                print dcq[1]
                print data["isoms"]

        friends = []
        one = C.numberfields.fields.find_one(query)
        if one:
            friends.append(
                (
                    "Number fields with this Galois group",
                    url_for("number_fields.number_field_render_webpage") + "?galois_group=%dT%d" % (n, t),
                )
            )
        prop2 = [
            ("Order:", "\(%s\)" % order),
            ("n:", "\(%s\)" % data["n"]),
            ("Cyclic:", yesno(data["cyc"])),
            ("Abelian:", yesno(data["ab"])),
            ("Solvable:", yesno(data["solv"])),
            ("Primitive:", yesno(data["prim"])),
            ("$p$-group:", yesno(pgroup)),
        ]
        pretty = group_display_pretty(n, t, C)
        if len(pretty) > 0:
            prop2.extend([("Group:", pretty)])
            info["pretty_name"] = pretty
        data["name"] = re.sub(r"_(\d+)", r"_{\1}", data["name"])
        data["name"] = re.sub(r"\^(\d+)", r"^{\1}", data["name"])
        info.update(data)

        bread = get_bread([(label, " ")])
        return render_template(
            "gg-show-group.html",
            credit=GG_credit,
            title=title,
            bread=bread,
            info=info,
            properties2=prop2,
            friends=friends,
        )
Ejemplo n.º 46
0
def number_field_search(**args):
    info = to_dict(args)

    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")), ('Quadratic imaginary class groups', url_for(".render_class_group_data"))]
    t = 'Global Number Field search results'
    bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search results', ' ')]

    # for k in info.keys():
    #  nf_logger.debug(str(k) + ' ---> ' + str(info[k]))
    # nf_logger.debug('******************* '+ str(info['search']))

    if 'natural' in info:
        query = {'label_orig': info['natural']}
        try:
            parse_nf_string(info,query,'natural',name="Label",qfield='label')
            return redirect(url_for(".by_label", label= clean_input(query['label_orig'])))
        except ValueError:
            query['err'] = info['err']
            return search_input_error(query, bread)

    query = {}
    try:
        parse_galgrp(info,query, qfield='galois')
        parse_ints(info,query,'degree')
        parse_bracketed_posints(info,query,'signature',split=False,exactlength=2)
        parse_signed_ints(info,query,'discriminant',qfield=('disc_sign','disc_abs_key'),parse_one=make_disc_key)
        parse_ints(info,query,'class_number')
        parse_bracketed_posints(info,query,'class_group',split=False,check_divisibility='increasing')
        parse_primes(info,query,'ur_primes',name='Unramified primes',qfield='ramps',mode='complement',to_string=True)
        # modes are now contained (in), exactly, include
        if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'include':
            mode = 'append'
            parse_primes(info,query,'ram_primes','ramified primes','ramps',mode,to_string=True)
        elif 'ram_quantifier' in info and str(info['ram_quantifier']) == 'contained':
            parse_primes(info,query,'ram_primes','ramified primes','ramps_all','subsets',to_string=False)
            pass # build list
        else:
            mode = 'liststring'
            parse_primes(info,query,'ram_primes','ramified primes','ramps_all',mode)
    except ValueError:
        return search_input_error(info, bread)
    count = parse_count(info)
    start = parse_start(info)

    if info.get('paging'):
        try:
            paging = int(info['paging'])
            if paging == 0:
                start = 0
        except:
            pass

    C = base.getDBConnection()
    # nf_logger.debug(query)
    info['query'] = dict(query)
    if 'lucky' in args:
        one = C.numberfields.fields.find_one(query)
        if one:
            label = one['label']
            return redirect(url_for(".by_label", label=clean_input(label)))

    fields = C.numberfields.fields

    res = fields.find(query)
    res = res.sort([('degree', ASC), ('disc_abs_key', ASC),('disc_sign', ASC)])

    if 'download' in info and info['download'] != '0':
        return download_search(info, res)

    nres = res.count()
    res = res.skip(start).limit(count)

    if(start >= nres):
        start -= (1 + (start - nres) / count) * count
    if(start < 0):
        start = 0

    info['fields'] = res
    info['number'] = nres
    info['start'] = start
    if nres == 1:
        info['report'] = 'unique match'
    else:
        if nres > count or start != 0:
            info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
        else:
            info['report'] = 'displaying all %s matches' % nres

    info['wnf'] = WebNumberField.from_data
    return render_template("number_field_search.html", info=info, title=t, bread=bread)
Ejemplo n.º 47
0
def render_group_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        label = label.replace('t', 'T')
        C = base.getDBConnection()
        data = C.transitivegroups.groups.find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info['err'] = "Group " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        data['label_raw'] = label.lower()
        title = 'Galois Group: ' + label
        wgg = WebGaloisGroup.from_data(data)
        n = data['n']
        t = data['t']
        data['yesno'] = yesno
        order = data['order']
        data['orderfac'] = latex(ZZ(order).factor())
        orderfac = latex(ZZ(order).factor())
        data['ordermsg'] = "$%s=%s$" % (order, latex(orderfac))
        if order == 1:
            data['ordermsg'] = "$1$"
        if ZZ(order).is_prime():
            data['ordermsg'] = "$%s$ (is prime)" % order
        pgroup = len(ZZ(order).prime_factors()) < 2
        if n == 1:
            G = gap.SmallGroup(n, t)
        else:
            G = gap.TransitiveGroup(n, t)
        if ZZ(order) < ZZ('10000000000'):
            ctable = chartable(n, t)
        else:
            ctable = 'Group too large'
        data['gens'] = generators(n, t)
        if n == 1 and t == 1:
            data['gens'] = 'None needed'
        data['chartable'] = ctable
        data['parity'] = "$%s$" % data['parity']
        data['cclasses'] = conjclasses(G, n)
        data['subinfo'] = subfield_display(C, n, data['subs'])
        data['resolve'] = resolve_display(C, data['resolve'])
        data['otherreps'] = wgg.otherrep_list()
        if len(data['otherreps']) == 0:
            data['otherreps'] = "There is no other low degree representation."
        query = {'galois': bson.SON([('n', n), ('t', t)])}
        C = base.getDBConnection()
        intreps = C.transitivegroups.Gmodules.find({
            'n': n,
            't': t
        }).sort('index', pymongo.ASCENDING)
        # turn cursor into a list
        intreps = [z for z in intreps]
        if len(intreps) > 0:
            data['int_rep_classes'] = [str(z[0]) for z in intreps[0]['gens']]
            for onerep in intreps:
                onerep['gens'] = [
                    list_to_latex_matrix(z[1]) for z in onerep['gens']
                ]
            data['int_reps'] = intreps
            data['int_reps_complete'] = int_reps_are_complete(intreps)
            dcq = data['moddecompuniq']
            if dcq[0] == 0:
                data['decompunique'] = 0
            else:
                data['decompunique'] = dcq[0]
                data['isoms'] = [[mult2mult(z[0]),
                                  mult2mult(z[1])] for z in dcq[1]]
                data['isoms'] = [[
                    modules2string(n, t, z[0]),
                    modules2string(n, t, z[1])
                ] for z in data['isoms']]
                print dcq[1]
                print data['isoms']

        friends = []
        one = C.numberfields.fields.find_one(query)
        if one:
            friends.append(
                ('Number fields with this Galois group',
                 url_for('number_fields.number_field_render_webpage') +
                 "?galois_group=%dT%d" % (n, t)))
        prop2 = [
            ('Order:', '\(%s\)' % order),
            ('n:', '\(%s\)' % data['n']),
            ('Cyclic:', yesno(data['cyc'])),
            ('Abelian:', yesno(data['ab'])),
            ('Solvable:', yesno(data['solv'])),
            ('Primitive:', yesno(data['prim'])),
            ('$p$-group:', yesno(pgroup)),
        ]
        pretty = group_display_pretty(n, t, C)
        if len(pretty) > 0:
            prop2.extend([('Group:', pretty)])
            info['pretty_name'] = pretty
        data['name'] = re.sub(r'_(\d+)', r'_{\1}', data['name'])
        data['name'] = re.sub(r'\^(\d+)', r'^{\1}', data['name'])
        info.update(data)

        bread = get_bread([(label, ' ')])
        return render_template("gg-show-group.html",
                               credit=GG_credit,
                               title=title,
                               bread=bread,
                               info=info,
                               properties2=prop2,
                               friends=friends)
Ejemplo n.º 48
0
def by_label(label):
    clean_label = clean_input(label)
    if label != clean_label:
        return redirect(url_for('.by_label',label=clean_label), 301)
    return render_field_webpage({'label': label})
Ejemplo n.º 49
0
def render_passport(args):
    info = {}
    if 'passport_label' in args:
        label = clean_input(args['passport_label'])

        C = base.getDBConnection()

        dataz = C.curve_automorphisms.passports.find({'passport_label': label})
        if dataz.count() is 0:
            bread = get_bread([("Search error", url_for('.search'))])
            flash_error(
                "No refined passport with label %s was found in the database.",
                label)
            return redirect(url_for(".index"))
        data = dataz[0]
        g = data['genus']
        GG = ast.literal_eval(data['group'])
        gn = GG[0]
        gt = GG[1]

        gp_string = str(gn) + '.' + str(gt)
        pretty_group = sg_pretty(gp_string)

        if gp_string == pretty_group:
            spname = False
        else:
            spname = True

        numb = dataz.count()

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

        title = 'One refined passport of genus ' + str(
            g) + ' with automorphism group $' + pretty_group + '$'
        smallgroup = "[" + str(gn) + "," + str(gt) + "]"

        prop2 = [
            ('Genus', '\(%d\)' % g), ('Small Group', '\(%s\)' % pretty_group),
            ('Signature',
             '\(%s\)' % sign_display(ast.literal_eval(data['signature']))),
            ('Generating Vectors', '\(%d\)' % numb)
        ]
        info.update({
            'genus': data['genus'],
            'cc': cc_display(data['con']),
            'sign': sign_display(ast.literal_eval(data['signature'])),
            'group': pretty_group,
            'gpid': smallgroup,
            'numb': numb,
            'disp_numb': min(numb, numgenvecs)
        })

        if spname:
            info.update({'specialname': True})

        Ldata = []
        HypColumn = False
        Lfriends = []
        for i in range(0, min(numgenvecs, numb)):
            dat = dataz[i]
            x1 = dat['total_label']
            if 'full_auto' in dat:
                x2 = 'No'
                if dat['full_label'] not in Lfriends:
                    Lfriends.append(dat['full_label'])
            else:
                x2 = 'Yes'

            if 'hyperelliptic' in dat:
                x3 = tfTOyn(dat['hyperelliptic'])
                HypColumn = True
            else:
                x3 = ' '

            x4 = []
            for perm in dat['gen_vectors']:
                cycperm = Permutation(perm).cycle_string()

                x4.append(sep.join(split_perm(cycperm)))

            Ldata.append([x1, x2, x3, x4])

        info.update({'genvects': Ldata, 'HypColumn': HypColumn})

        info.update({'passport_cc': cc_display(ast.literal_eval(data['con']))})

        if 'eqn' in data:
            info.update({'eqns': data['eqn']})

        if 'ndim' in data:
            info.update({'Ndim': data['ndim']})

        other_data = False

        if 'hyperelliptic' in data:
            info.update({'ishyp': tfTOyn(data['hyperelliptic'])})
            other_data = True

        if 'hyp_involution' in data:
            inv = Permutation(data['hyp_involution']).cycle_string()
            info.update({'hypinv': sep.join(split_perm(inv))})

        if 'cyclic_trigonal' in data:
            info.update({'iscyctrig': tfTOyn(data['cyclic_trigonal'])})
            other_data = True

        if 'jacobian_decomp' in data:
            jcLatex, corrChar = decjac_format(data['jacobian_decomp'])
            info.update({'corrChar': corrChar, 'jacobian_decomp': jcLatex})

        if 'cinv' in data:
            cinv = Permutation(data['cinv']).cycle_string()
            info.update({'cinv': sep.join(split_perm(cinv))})

        info.update({'other_data': other_data})

        if 'full_auto' in data:
            full_G = ast.literal_eval(data['full_auto'])
            full_gn = full_G[0]
            full_gt = full_G[1]

            full_gp_string = str(full_gn) + '.' + str(full_gt)
            full_pretty_group = sg_pretty(full_gp_string)
            info.update({
                'fullauto': full_pretty_group,
                'signH': sign_display(ast.literal_eval(data['signH'])),
                'higgenlabel': data['full_label']
            })

        urlstrng, br_g, br_gp, br_sign, refined_p = split_passport_label(label)

        if Lfriends:
            for Lf in Lfriends:
                friends = [("Full automorphism " + Lf, Lf),
                           ("Family containing this refined passport ",
                            urlstrng)]

        else:
            friends = [("Family containing this refined passport", urlstrng)]

        bread_sign = label_to_breadcrumbs(br_sign)
        bread_gp = label_to_breadcrumbs(br_gp)

        bread = get_bread([(br_g, './?genus=' + br_g),
                           ('$' + pretty_group + '$',
                            './?genus=' + br_g + '&group=' + bread_gp),
                           (bread_sign, urlstrng), (data['cc'][0], ' ')])

        learnmore = [('Completeness of the data',
                      url_for(".completeness_page")),
                     ('Source of the data', url_for(".how_computed_page")),
                     ('Labeling convention', url_for(".labels_page"))]

        downloads = [('Download Magma code',
                      url_for(".hgcwa_code_download",
                              label=label,
                              download_type='magma')),
                     ('Download Gap code',
                      url_for(".hgcwa_code_download",
                              label=label,
                              download_type='gap'))]

        return render_template("hgcwa-show-passport.html",
                               title=title,
                               bread=bread,
                               info=info,
                               properties2=prop2,
                               friends=friends,
                               learnmore=learnmore,
                               downloads=downloads,
                               credit=credit)
Ejemplo n.º 50
0
def render_field_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        data = db.lf_fields.lookup(label)
        if data is None:
            bread = get_bread([("Search Error", ' ')])
            info['err'] = "Field " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Local Number Field ' + prettyname(data)
        polynomial = coeff_to_poly(data['coeffs'])
        p = data['p']
        Qp = r'\Q_{%d}' % p
        e = data['e']
        f = data['f']
        cc = data['c']
        gt = data['gal']
        gn = data['n']
        the_gal = WebGaloisGroup.from_nt(gn,gt)
        isgal = ' Galois' if the_gal.order() == gn else ' not Galois'
        abelian = ' and abelian' if the_gal.is_abelian() else ''
        galphrase = 'This field is'+isgal+abelian+' over $\Q_{%d}$.'%p
        autstring = r'\Gal' if the_gal.order() == gn else r'\Aut'
        prop2 = [
            ('Label', label),
            ('Base', '\(%s\)' % Qp),
            ('Degree', '\(%s\)' % data['n']),
            ('e', '\(%s\)' % e),
            ('f', '\(%s\)' % f),
            ('c', '\(%s\)' % cc),
            ('Galois group', group_display_short(gn, gt)),
        ]
        # Look up the unram poly so we can link to it
        unramlabel = db.lf_fields.lucky({'p': p, 'n': f, 'c': 0}, projection=0)
        if unramlabel is None:
            logger.fatal("Cannot find unramified field!")
            unramfriend = ''
        else:
            unramfriend = "/LocalNumberField/%s" % unramlabel
            unramdata = db.lf_fields.lookup(unramlabel)

        Px = PolynomialRing(QQ, 'x')
        Pxt=PolynomialRing(Px,'t')
        Pt = PolynomialRing(QQ, 't')
        Ptx = PolynomialRing(Pt, 'x')
        if data['f'] == 1:
            unramp = r'$%s$' % Qp
            # Eliminate t from the eisenstein polynomial
            eisenp = Pxt(str(data['eisen']).replace('y','x'))
            eisenp = Pt(str(data['unram'])).resultant(eisenp)
            eisenp = web_latex(eisenp)

        else:
            unramp = data['unram'].replace('t','x')
            unramp = web_latex(Px(str(unramp)))
            unramp = prettyname(unramdata)+' $\\cong '+Qp+'(t)$ where $t$ is a root of '+unramp
            eisenp = Ptx(str(data['eisen']).replace('y','x'))
            eisenp = '$'+web_latex(eisenp, False)+'\\in'+Qp+'(t)[x]$'


        rflabel = db.lf_fields.lucky({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']}, projection=0)
        if rflabel is None:
            logger.fatal("Cannot find discriminant root field!")
            rffriend = ''
        else:
            rffriend = "/LocalNumberField/%s" % rflabel
        gsm = data['gsm']
        if gsm == [0]:
            gsm = 'Not computed'
        elif gsm == [-1]:
            gsm = 'Does not exist'
        else:
            gsm = web_latex(coeff_to_poly(gsm))


        info.update({
                    'polynomial': web_latex(polynomial),
                    'n': data['n'],
                    'p': p,
                    'c': data['c'],
                    'e': data['e'],
                    'f': data['f'],
                    't': data['t'],
                    'u': data['u'],
                    'rf': lf_display_knowl( rflabel, name=printquad(data['rf'], p)),
                    'base': lf_display_knowl(str(p)+'.1.0.1', name='$%s$'%Qp),
                    'hw': data['hw'],
                    'slopes': show_slopes(data['slopes']),
                    'gal': group_display_knowl(gn, gt),
                    'gt': gt,
                    'inertia': group_display_inertia(data['inertia']),
                    'unram': unramp,
                    'eisen': eisenp,
                    'gms': data['gms'],
                    'gsm': gsm,
                    'galphrase': galphrase,
                    'autstring': autstring,
                    'subfields': format_subfields(data['subfields'],p),
                    'aut': data['aut'],
                    })
        friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
        if unramfriend != '':
            friends.append(('Unramified subfield', unramfriend))
        if rffriend != '':
            friends.append(('Discriminant root field', rffriend))

        bread = get_bread([(label, ' ')])
        learnmore = [('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Local field labels', url_for(".labels_page"))]
        return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
Ejemplo n.º 51
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' % 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))
    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 = [('Label', label),
                   ('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, code=nf.code, friends=info.pop('friends'), learnmore=info.pop('learnmore'), info=info)
Ejemplo n.º 52
0
def render_hgm_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        data = motivedb().find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info['err'] = "Motive " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Hypergeometric Motive:' + label
        A = data['A']
        B = data['B']
        myfam = familydb().find_one({'A': A, 'B': B})
        if myfam is None:
            det = 'data not computed'
        else:
            det = myfam['det']
            det = [det[0],str(det[1])]
            d1 = det[1]
            d1 = re.sub(r'\s','', d1)
            d1 = re.sub(r'(.)\(', r'\1*(', d1)
            R = PolynomialRing(ZZ, 't')
            if det[1]=='':
                d2 = R(1)
            else:
                d2 = R(d1)
            det = d2(QQ(data['t']))*det[0]
        t = latex(QQ(data['t']))
        typee = 'Orthogonal'
        if (data['weight'] % 2) == 1 and (data['degree'] % 2) == 0:
            typee = 'Symplectic'
        primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
        locinfo = data['locinfo']
        for j in range(len(locinfo)):
            locinfo[j] = [primes[j]] + locinfo[j]
            #locinfo[j][2] = poly_with_factored_coeffs(locinfo[j][2], primes[j])
            locinfo[j][2] = list_to_factored_poly_otherorder(locinfo[j][2], vari='x')
        hodge = string2list(data['hodge'])
        famhodge = string2list(data['famhodge'])
        prop2 = [
            ('Degree', '\(%s\)' % data['degree']),
            ('Weight',  '\(%s\)' % data['weight']),
            ('Hodge vector',  '\(%s\)' % hodge),
            ('Conductor', '\(%s\)' % data['cond']),
        ]
        # Now add factorization of conductor
        Cond = ZZ(data['cond'])
        if not (Cond.abs().is_prime() or Cond == 1):
            data['cond'] = "%s=%s" % (str(Cond), factorint(data['cond']))

        info.update({
                    'A': A,
                    'B': B,
                    't': t,
                    'degree': data['degree'],
                    'weight': data['weight'],
                    'sign': data['sign'],
                    'sig': data['sig'],
                    'hodge': hodge,
                    'famhodge': famhodge,
                    'cond': data['cond'],
                    'req': data['req'],
                    'lcms': data['lcms'],
                    'type': typee,
                    'det': det,
                    'locinfo': locinfo
                    })
        AB_data, t_data = data["label"].split("_t")
        friends = [("Motive family "+AB_data.replace("_"," "), url_for(".by_family_label", label = AB_data))]
        friends.append(('L-function', url_for("l_functions.l_function_hgm_page", label=AB_data, t='t'+t_data)))
#        if rffriend != '':
#            friends.append(('Discriminant root field', rffriend))


        bread = get_bread([(label, ' ')])
        return render_template("hgm-show-motive.html", credit=HGM_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore_list())
Ejemplo n.º 53
0
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:
        gpK = nf.gpK()
        rootof1coeff = gpK.nfrootsof1()
        rootofunityorder = int(rootof1coeff[1])
        rootof1coeff = rootof1coeff[2]
        rootofunity = web_latex(
            Ra(
                str(pari("lift(%s)" % gpK.nfbasistoalg(rootof1coeff))).replace(
                    'x', 'a')))
        rootofunity += ' (order $%d$)' % rootofunityorder
    else:
        rootofunity = web_latex(Ra('-1')) + ' (order $2$)'

    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': rootofunity,
        'fund_units': nf.units(),
        'grh_label': grh_label,
        'loc_alg': loc_alg
    })

    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 character group',
                                url_for("characters.dirichlet_group_table",
                                        modulus=int(conductor),
                                        char_number_list=','.join(
                                            [str(a) for a in dirichlet_chars]),
                                        poly=info['polynomial'])))
    resinfo = []
    galois_closure = nf.galois_closure()
    if galois_closure[0] > 0:
        if len(galois_closure[1]) > 0:
            resinfo.append(('gc', galois_closure[1]))
            if len(galois_closure[2]) > 0:
                info['friends'].append(('Galois closure',
                                        url_for(".by_label",
                                                label=galois_closure[2][0])))
        else:
            resinfo.append(('gc', [dnc]))

    sextic_twins = nf.sextic_twin()
    if sextic_twins[0] > 0:
        if len(sextic_twins[1]) > 0:
            resinfo.append(('sex', r' $\times$ '.join(sextic_twins[1])))
        else:
            resinfo.append(('sex', dnc))

    siblings = nf.siblings()
    # [degsib list, label list]
    # first is list of [deg, num expected, list of knowls]
    if len(siblings[0]) > 0:
        for sibdeg in siblings[0]:
            if len(sibdeg[2]) == 0:
                sibdeg[2] = dnc
            else:
                sibdeg[2] = ', '.join(sibdeg[2])
                if len(sibdeg[2]) < sibdeg[1]:
                    sibdeg[2] += ', some ' + dnc

        resinfo.append(('sib', siblings[0]))
        for lab in siblings[1]:
            if lab != '':
                labparts = lab.split('.')
                info['friends'].append(("Degree %s sibling" % labparts[0],
                                        url_for(".by_label", label=lab)))

    arith_equiv = nf.arith_equiv()
    if arith_equiv[0] > 0:
        if len(arith_equiv[1]) > 0:
            resinfo.append(
                ('ae', ', '.join(arith_equiv[1]), len(arith_equiv[1])))
            for aelab in arith_equiv[2]:
                info['friends'].append(('Arithmetically equivalent sibling',
                                        url_for(".by_label", label=aelab)))
        else:
            resinfo.append(('ae', dnc, len(arith_equiv[1])))

    info['resinfo'] = resinfo
    learnmore = learnmore_list()
    #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 = [('Label', label), ('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))]
    downloads = []
    for lang in [["Magma", "magma"], ["SageMath", "sage"], ["Pari/GP", "gp"]]:
        downloads.append(('Download {} code'.format(lang[0]),
                          url_for(".nf_code_download",
                                  nf=label,
                                  download_type=lang[1])))
    from lmfdb.artin_representations.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
    return render_template("number_field.html",
                           properties2=properties2,
                           credit=NF_credit,
                           title=title,
                           bread=bread,
                           code=nf.code,
                           friends=info.pop('friends'),
                           downloads=downloads,
                           learnmore=learnmore,
                           info=info)
Ejemplo n.º 54
0
def render_hgm_family_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        data = familydb().find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", url_for('.search'))])
            info['err'] = "Family of hypergeometric motives " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Hypergeometric Motive Family:' + label
        A = string2list(data['A'])
        B = string2list(data['B'])
        hodge = data['famhodge']
        mydet = data['det']
        detexp = QQ(data['weight']*data['degree'])
        detexp = -detexp/2
        mydet = r'\Q(%s)\otimes\Q(\sqrt{'%str(detexp)
        if int(data['det'][0]) != 1:
            mydet += str(data['det'][0])
        if len(data['det'][1])>0:
            mydet += data['det'][1]
        if int(data['det'][0]) == 1 and len(data['det'][1])==0:
            mydet += '1'
        mydet += '})'
        bezoutmat = matrix(data['bezout'])
        bezoutdet = bezoutmat.det()
        bezoutmat = latex(bezoutmat)
        snf = string2list(data['snf'])
        snf = list2Cnstring(snf)
        typee = 'Orthogonal'
        if (data['weight'] % 2) == 1 and (data['degree'] % 2) == 0:
            typee = 'Symplectic'
        ppart = [[2, [string2list(u) for u in [data['A2'],data['B2'],data['C2']]]],
            [3, [string2list(u) for u in [data['A3'],data['B3'],data['C3']]]],
            [5, [string2list(u) for u in [data['A5'],data['B5'],data['C5']]]],
            [7, [string2list(u) for u in [data['A7'],data['B7'],data['C7']]]]]
        prop2 = [
            ('Degree', '\(%s\)' % data['degree']),
            ('Weight',  '\(%s\)' % data['weight'])
        ]
        mono = [[m[0], dogapthing(m[1]), 
          getgroup(m[1],m[0]),
          latex(ZZ(m[1][0]).factor())] for m in data['mono']]
        mono = [[m[0], m[1], m[2][0], splitint(m[1][0]/m[2][1],m[0]), m[3]] for m in mono]
        info.update({
                    'A': A,
                    'B': B,
                    'degree': data['degree'],
                    'weight': data['weight'],
                    'hodge': hodge,
                    'det': mydet,
                    'snf': snf,
                    'bezoutmat': bezoutmat,
                    'bezoutdet': bezoutdet,
                    'mono': mono,
                    'imprim': data['imprim'],
                    'ppart': ppart,
                    'type': typee,
                    'junk': small_group_display_knowl(18,2,db()),
                    'showlist': showlist
                    })
        friends = [('Motives in the family', url_for('hypergm.index')+"?A=%s&B=%s" % (str(A), str(B)))]
#        if unramfriend != '':
#            friends.append(('Unramified subfield', unramfriend))
#        if rffriend != '':
#            friends.append(('Discriminant root field', rffriend))

        info.update({"plotcircle":  url_for(".hgm_family_circle_image", AB  =  "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
        info.update({"plotlinear": url_for(".hgm_family_linear_image", AB  = "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
        info.update({"plotconstant": url_for(".hgm_family_constant_image", AB  = "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
        bread = get_bread([(label, ' ')])
        return render_template("hgm-show-family.html", credit=HGM_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore_list())
Ejemplo n.º 55
0
def render_field_webpage(args):
    data = None
    info = {}
    if 'label' in args:
        label = clean_input(args['label'])
        data = lfdb().find_one({'label': label})
        if data is None:
            bread = get_bread([("Search error", ' ')])
            info['err'] = "Field " + label + " was not found in the database."
            info['label'] = label
            return search_input_error(info, bread)
        title = 'Local Number Field ' + label
        polynomial = coeff_to_poly(string2list(data['coeffs']))
        p = data['p']
        e = data['e']
        f = data['f']
        cc = data['c']
        GG = data['gal']
        gn = GG[0]
        gt = GG[1]
        the_gal = WebGaloisGroup.from_nt(gn,gt)
        isgal = ' Galois' if the_gal.order() == gn else ' not Galois'
        abelian = ' and abelian' if the_gal.is_abelian() else ''
        galphrase = 'This field is'+isgal+abelian+' over $\Q_{%d}$.'%p
        autstring = r'\Gal' if the_gal.order() == gn else r'\Aut'
        prop2 = [
            ('Label', label),
            ('Base', '\(\Q_{%s}\)' % p),
            ('Degree', '\(%s\)' % data['n']),
            ('e', '\(%s\)' % e),
            ('f', '\(%s\)' % f),
            ('c', '\(%s\)' % cc),
            ('Galois group', group_display_short(gn, gt, db())),
        ]
        Pt = PolynomialRing(QQ, 't')
        Pyt = PolynomialRing(Pt, 'y')
        eisenp = Pyt(str(data['eisen']))
        unramp = Pyt(str(data['unram']))
        # Look up the unram poly so we can link to it
        unramdata = lfdb().find_one({'p': p, 'n': f, 'c': 0})
        if unramdata is not None:
            unramfriend = "/LocalNumberField/%s" % unramdata['label']
        else:
            logger.fatal("Cannot find unramified field!")
            unramfriend = ''
        rfdata = lfdb().find_one({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']})
        if rfdata is None:
            logger.fatal("Cannot find discriminant root field!")
            rffriend = ''
        else:
            rffriend = "/LocalNumberField/%s" % rfdata['label']
        gsm = data['gsm']
        if gsm == '0':
            gsm = 'Not computed'
        elif gsm == '-1':
            gsm = 'Does not exist'
        else:
            gsm = web_latex(coeff_to_poly(string2list(gsm)))


        info.update({
                    'polynomial': web_latex(polynomial),
                    'n': data['n'],
                    'p': p,
                    'c': data['c'],
                    'e': data['e'],
                    'f': data['f'],
                    't': data['t'],
                    'u': data['u'],
                    'rf': printquad(data['rf'], p),
                    'hw': data['hw'],
                    'slopes': show_slopes(data['slopes']),
                    'gal': group_display_knowl(gn, gt, db()),
                    'gt': gt,
                    'inertia': group_display_inertia(data['inertia'], db()),
                    'unram': web_latex(unramp),
                    'eisen': web_latex(eisenp),
                    'gms': data['gms'],
                    'gsm': gsm,
                    'galphrase': galphrase,
                    'autstring': autstring,
                    'subfields': format_subfields(data['subfields'],p),
                    'aut': data['aut'],
                    })
        friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
        if unramfriend != '':
            friends.append(('Unramified subfield', unramfriend))
        if rffriend != '':
            friends.append(('Discriminant root field', rffriend))

        bread = get_bread([(label, ' ')])
        learnmore = [('Completeness of the data', url_for(".completeness_page")),
                ('Source of the data', url_for(".how_computed_page")),
                ('Local field labels', url_for(".labels_page"))]
        return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
Ejemplo n.º 56
0
def render_hecke_algebras_webpage(**args):
    data = None
    if 'label' in args:
        lab = clean_input(args.get('label'))
        if lab != args.get('label'):
            return redirect(url_for('.render_hecke_algebras_webpage', label=lab), 301)
        data = hecke_db().find_one({'label': lab })
    if data is None:
        t = "Hecke Algebras Search Error"
        bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage"))]
        flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for a Hecke Algebras in the database." % (lab)),"error")
        return render_template("hecke_algebras-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
    info = {}
    info.update(data)

    bread = [('HeckeAlgebra', url_for(".hecke_algebras_render_webpage")), ('%s' % data['label'], ' ')]
    credit = hecke_algebras_credit
    f = hecke_db().find_one({'level': data['level'],'weight': data['weight'],'num_orbits': data['num_orbits']})
    info['level']=int(f['level'])
    info['weight']= int(f['weight'])
    info['num_orbits']= int(f['num_orbits'])
    dim_count = "not available"

    orb = hecke_orbits_db().find({'parent_label': f['label']}).sort([('orbit', ASC)])
    if orb.count()!=0:
        #consistency check
        if orb.count()!= int(f['num_orbits']):
            return search_input_error(info)

        dim_count=0
        res_clean = []
        for v in orb:
            v_clean = {}
            v_clean['orbit_label'] = v['orbit_label']
            v_clean['hecke_op'] = v['hecke_op']
            v_clean['gen'] = v['gen']
            v_clean['dim'] = int(matrix(sage_eval(v_clean['hecke_op'])[0]).dimensions()[0])
            dim_count = dim_count + v_clean['dim']
            if v_clean['dim']>4:
                v_clean['hecke_op_display'] = []
            elif v_clean['dim']==1:
                v_clean['hecke_op_display'] = [[i+1, (sage_eval(v_clean['hecke_op'])[i])[0][0]] for i in range(0,10)]
            else:
                v_clean['hecke_op_display'] = [[i+1, latex(matrix(sage_eval(v_clean['hecke_op'])[i]))] for i in range(0,5)]
            v_clean['num_hecke_op'] = v['num_hecke_op']
            v_clean['download_op'] = [(i, url_for(".render_hecke_algebras_webpage_download", orbit_label=v_clean['orbit_label'], lang=i, obj='operators')) for i in ['gp', 'magma','sage']]
            if 'Zbasis' in v.keys():
                v_clean['Zbasis'] = [[int(i) for i in j] for j in v['Zbasis']]
                if v_clean['dim']>4:
                    v_clean['gen_display'] = []
                elif v_clean['dim']==1:
                    v_clean['gen_display'] = [v_clean['Zbasis'][0][0]]
                else:
                    v_clean['gen_display'] = [latex(matrix(v_clean['dim'],v_clean['dim'], v_clean['Zbasis'][i])) for i in range(0,v_clean['dim'])]
                v_clean['discriminant'] = int(v['discriminant'])
                v_clean['disc_fac'] = [[int(i) for i in j] for j in v['disc_fac']]
                v_clean['Qbasis'] = [int(i) for i in v['Qbasis']]
                v_clean['Qalg_gen'] = [int(i) for i in v['Qalg_gen']]
                if 'inner_twists' in v.keys():
                    v_clean['inner_twists'] = [str(i) for i in v['inner_twists']]
                else:
                    v_clean['inner_twists'] = "not available"
                v_clean['download_gen'] = [(i, url_for(".render_hecke_algebras_webpage_download", orbit_label=v_clean['orbit_label'], lang=i, obj='gen')) for i in ['gp', 'magma','sage']]
            res_clean.append(v_clean)

        info['orbits'] = res_clean

    info['dim_alg'] = dim_count
    info['l_adic'] = l_range
    info['properties'] = [
        ('Label', '%s' %info['label']),
        ('Level', '%s' %info['level']),
        ('Weight', '%s' %info['weight'])]
    if info['num_orbits']!=0:      
        info['friends'] = [('Newforms space ' + info['label'], url_for("emf.render_elliptic_modular_forms", level=info['level'], weight=info['weight'], character=1))]
    else:
        info['friends'] = []    
    t = "Hecke Algebra %s" % info['label']
    return render_template("hecke_algebras-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list(), friends=info['friends'])