def test_list_to_latex_matrix(self): r""" Checking utility: list_to_latex_matrix """ identity_list = [[1, 0], [0, 1]] identity_rep = '\\left(\\begin{array}{*{2}{r}}1 & 0\\\\0 & 1\\end{array}\\right)' self.assertEqual(list_to_latex_matrix(identity_list), identity_rep) # malformed matrices should work malformed = [[1, 0], [0]] malform_rep = '\\left(\\begin{array}{*{2}{r}}1 & 0\\\\0\\end{array}\\right)' self.assertEqual(list_to_latex_matrix(malformed), malform_rep)
def test_list_to_latex_matrix(self): r""" Checking utility: list_to_latex_matrix """ identity_list = [[1,0], [0,1]] identity_rep = '\\left(\\begin{array}{*{2}{r}}1 & 0\\\\0 & 1\\end{array}\\right)' self.assertEqual(list_to_latex_matrix(identity_list), identity_rep) # malformed matrices should work malformed = [[1,0], [0]] malform_rep = '\\left(\\begin{array}{*{2}{r}}1 & 0\\\\0\\end{array}\\right)' self.assertEqual(list_to_latex_matrix(malformed), malform_rep)
def galois_module_knowl_guts(n, t, index): mymod = db.gps_gmodules.lucky({'n': int(n), 't': int(t), 'index': int(index)}, ['name','dim','gens']) if mymod is None: return 'Database call failed' name = mymod['name'] out = "$\\Z[G]$ module %s with $G=$ " % str(name) out += group_display_knowl(n, t) out += " = %sT%s " %(n, t) out += "<blockquote>" out += "Dimension: %s" % str(mymod['dim']) out += r"<br>Action: $$\begin{aligned}" for g in mymod['gens']: matg = list_to_latex_matrix(g[1]) out += "%s &\\mapsto %s \\\\" %(str(g[0]), matg) out = out[:-2] out += r"\end{aligned}$$" out += "</blockquote>" return out
def render_group_webpage(args): data = {} if 'label' in args: label = clean_input(args['label']) label = label.replace('t', 'T') data = db.gps_transitive.lookup(label) if data is None: if re.match(r'^\d+T\d+$', label): flash_error("Group %s was not found in the database.", label) else: flash_error("%s is not a valid label for a Galois group.", label) return redirect(url_for(".index")) title = 'Galois group: ' + label wgg = WebGaloisGroup.from_nt(data['n'], data['t']) data['wgg'] = wgg n = data['n'] t = data['t'] data['yesno'] = yesno order = data['order'] data['orderfac'] = latex(ZZ(order).factor()) orderfac = latex(ZZ(order).factor()) data['ordermsg'] = "$%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 wgg.num_conjclasses() < 50: data['cclasses'] = wgg.conjclasses() if ZZ(order) < ZZ(10000000) and wgg.num_conjclasses() < 21: data['chartable'] = chartable(n, t) data['gens'] = wgg.generator_string() if n == 1 and t == 1: data['gens'] = 'None needed' data['num_cc'] = comma(wgg.num_conjclasses()) data['parity'] = "$%s$" % data['parity'] data['subinfo'] = subfield_display(n, data['subfields']) data['resolve'] = resolve_display(data['quotients']) if data['gapid'] == 0: data['gapid'] = "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 = data['arith_equiv'] 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.' elif ae > -1: 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.' else: data[ 'arith_equiv'] = r'Data on whether or not a number field with this Galois group has <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields has not been computed.' 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({'galois_label': "%dT%d" % (n, 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), ('Degree', prop_int_pretty(data['n'])), ('Order', prop_int_pretty(order)), ('Cyclic', yesno(data['cyc'])), ('Abelian', yesno(data['ab'])), ('Solvable', yesno(data['solv'])), ('Primitive', yesno(data['prim'])), ('$p$-group', yesno(pgroup)), ] pretty = group_display_short(n, t, emptyifnotpretty=True) if len(pretty) > 0: prop2.extend([('Group:', pretty)]) data['pretty_name'] = pretty data['name'] = re.sub(r'_(\d+)', r'_{\1}', data['name']) data['name'] = re.sub(r'\^(\d+)', r'^{\1}', data['name']) data['nilpotency'] = '$%s$' % data['nilpotency'] if data['nilpotency'] == '$-1$': data['nilpotency'] += ' (not nilpotent)' bread = get_bread([(label, ' ')]) return render_template("gg-show-group.html", credit=GG_credit, title=title, bread=bread, info=data, properties=prop2, friends=friends, KNOWL_ID="gg.%s" % label, 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 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 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 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)