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+$').match(label): return label else: raise ValueError( "Error parsing input %s. It is not in a valid form for an Artin representation label, such as 9.2e12_587e3.10t32.1c1" % label)
def parse_artin_label(label): label = clean_input(label) if LABEL_RE.match(label): return label else: raise ValueError( "Error parsing input %s. It is not in a valid form for an Artin representation label, such as 9.2e12_587e3.10t32.1c1" % label)
def hgm_jump(info): label = clean_input(info['jump_to']) if HGM_LABEL_RE.match(label): return render_hgm_webpage(normalize_motive(label)) if HGM_FAMILY_LABEL_RE.match(label): return render_hgm_family_webpage(normalize_family(label)) flash_error('%s is not a valid label for a hypergeometric motive or family of hypergeometric motives', label) return redirect(url_for(".index"))
def parse_artin_label(label): label = clean_input(label) if re.compile(r"^\d+\.\d+e\d+(_\d+e\d+)*\.\d+t\d\.\d+c\d+$").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 )
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)
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)
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)
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 ℓ-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'])
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)
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)
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)
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'])
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)
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)
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)
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)
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)
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)
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 ℓ-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'])
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'])
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)
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">$\chi_{%s}(%s,·)$</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)
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">$\chi_{%s}(%s,·)$</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, )
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)
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)
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)
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 ℓ-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'])
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())
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)
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})
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())
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)
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)
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'])
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)
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,·)$</a>' % (url_for('characters.render_Dirichletwebpage',modulus=data['conductor'], number=j), data['conductor'], j) for j in dirichlet_chars] data['dirichlet_group'] = r'$\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)
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)
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)
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 ℓ-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'])
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)
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)
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())
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, )
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)
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)
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})
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)
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$'%Qp), 'hw': data['hw'], 'slopes': show_slopes(data['slopes']), 'gal': group_display_knowl(gn, gt), 'gt': gt, 'inertia': group_display_inertia(data['inertia']), 'unram': unramp, 'eisen': eisenp, 'gms': data['gms'], 'gsm': gsm, 'galphrase': galphrase, 'autstring': autstring, 'subfields': format_subfields(data['subfields'],p), 'aut': data['aut'], }) friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))] if unramfriend != '': friends.append(('Unramified subfield', unramfriend)) if rffriend != '': friends.append(('Discriminant root field', rffriend)) bread = get_bread([(label, ' ')]) learnmore = [('Completeness of the data', url_for(".completeness_page")), ('Source of the data', url_for(".how_computed_page")), ('Local field labels', url_for(".labels_page"))] return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
def render_field_webpage(args): data = None C = base.getDBConnection() info = {} bread = [('Global Number Fields', url_for(".number_field_render_webpage"))] # This function should not be called unless label is set. label = clean_input(args['label']) nf = WebNumberField(label) data = {} if nf.is_null(): bread.append(('Search results', ' ')) info['err'] = 'There is no field with label %s in the database' % label info['label'] = args['label_orig'] if 'label_orig' in args else args['label'] return search_input_error(info, bread) info['wnf'] = nf data['degree'] = nf.degree() data['class_number'] = nf.class_number() t = nf.galois_t() n = nf.degree() data['is_galois'] = nf.is_galois() data['is_abelian'] = nf.is_abelian() if nf.is_abelian(): conductor = nf.conductor() data['conductor'] = conductor dirichlet_chars = nf.dirichlet_group() if len(dirichlet_chars)>0: data['dirichlet_group'] = ['<a href = "%s">$\chi_{%s}(%s,·)$</a>' % (url_for('characters.render_Dirichletwebpage',modulus=data['conductor'], number=j), data['conductor'], j) for j in dirichlet_chars] data['dirichlet_group'] = r'$\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)
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())
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">$\chi_{%s}(%s,·)$</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)
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())
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'])