For 4 of the 6 knots we determine QA slopes. We have computed their tangle exteriors and the Khovanov homologies of their tangle fillings. For 4 of the 6 knots we found a whole interval of KH thin branching sets. We conjecture that they are all QA. Here we confirm that for the first of these.

For that we load our list of low-crossing QA links.

In [1]:
import snappy
In [2]:
QA=['K8n1', 'K8n2', 'K9n1', 'K9n2', 'K9n3', 'K9n5', 'K9n6', 'K9n7', 'K9n8', 'L7n2', 'L8n1', 'L8n2', 'L8n4', 'L8n5', 'L9n1', 'L9n2', 'L9n3', 'L9n5', 'L9n6', 'L9n7', 'L9n8', 'K10n1', 'K10n2', 'K10n4', 'K10n5', 'K10n6', 'K10n8', 'K10n9', 'K11n1', 'K11n2', 'K11n3', 'K11n4', 'K11n5', 'K11n7', 'K11n8', 'K12n1', 'K12n2', 'K12n3', 'K12n4', 'K12n5', 'K12n6', 'K12n8', 'K12n9', 'L10n1', 'L10n2', 'L10n3', 'L10n4', 'L10n5', 'L10n6', 'L10n7', 'L10n8', 'L10n9', 'L11n1', 'L11n2', 'L11n3', 'L11n4', 'L11n5', 'L11n6', 'L11n7', 'L11n8', 'L11n9', 'L12n1', 'L12n2', 'L12n3', 'L12n5', 'L12n6', 'L12n7', 'L12n8', 'L12n9', 'L9n10', 'L9n11', 'L9n13', 'L9n16', 'L9n17', 'L9n20', 'L9n21', 'L9n24', 'L9n25', 'L9n28', 'K10n11', 'K10n12', 'K10n15', 'K10n16', 'K10n17', 'K10n18', 'K10n19', 'K10n20', 'K10n23', 'K10n24', 'K10n25', 'K10n26', 'K10n28', 'K10n29', 'K10n30', 'K10n31', 'K10n32', 'K10n33', 'K10n34', 'K10n35', 'K10n37', 'K10n38', 'K10n39', 'K10n40', 'K10n41', 'K10n42', 'K11n10', 'K11n11', 'K11n13', 'K11n14', 'K11n15', 'K11n16', 'K11n17', 'K11n18', 'K11n21', 'K11n22', 'K11n23', 'K11n25', 'K11n26', 'K11n28', 'K11n29', 'K11n30', 'K11n32', 'K11n33', 'K11n35', 'K11n36', 'K11n37', 'K11n40', 'K11n41', 'K11n43', 'K11n44', 'K11n46', 'K11n47', 'K11n48', 'K11n50', 'K11n51', 'K11n52', 'K11n53', 'K11n54', 'K11n55', 'K11n56', 'K11n58', 'K11n59', 'K11n60', 'K11n62', 'K11n63', 'K11n64', 'K11n65', 'K11n66', 'K11n68', 'K11n69', 'K11n71', 'K11n72', 'K11n75', 'K11n76', 'K11n77', 'K11n78', 'K11n82', 'K11n83', 'K11n84', 'K11n85', 'K11n86', 'K11n87', 'K11n89', 'K11n90', 'K11n91', 'K11n93', 'K11n94', 'K11n95', 'K11n98', 'K11n99', 'K12n11', 'K12n12', 'K12n13', 'K12n14', 'K12n15', 'K12n17', 'K12n18', 'K12n21', 'K12n22', 'K12n24', 'K12n26', 'K12n27', 'K12n29', 'K12n30', 'K12n32', 'K12n33', 'K12n35', 'K12n36', 'K12n37', 'K12n38', 'K12n39', 'K12n40', 'K12n42', 'K12n43', 'K12n44', 'K12n46', 'K12n47', 'K12n48', 'K12n49', 'K12n50', 'K12n52', 'K12n53', 'K12n55', 'K12n58', 'K12n60', 'K12n61', 'K12n62', 'K12n63', 'K12n64', 'K12n66', 'K12n69', 'K12n70', 'K12n71', 'K12n72', 'K12n73', 'K12n74', 'K12n75', 'K12n76', 'K12n77', 'K12n78', 'K12n79', 'K12n80', 'K12n81', 'K12n83', 'K12n84', 'K12n85', 'K12n86', 'K12n88', 'K12n90', 'K12n92', 'K12n94', 'K12n95', 'K12n97', 'K12n98', 'K12n99', 'L10n10', 'L10n11', 'L10n12', 'L10n15', 'L10n16', 'L10n17', 'L10n19', 'L10n20', 'L10n21', 'L10n22', 'L10n26', 'L10n27', 'L10n29', 'L10n30', 'L10n31', 'L10n33', 'L10n34', 'L10n35', 'L10n37', 'L10n38', 'L10n40', 'L10n41', 'L10n43', 'L10n44', 'L10n46', 'L10n47', 'L10n48', 'L10n49', 'L10n50', 'L10n51', 'L10n52', 'L10n53', 'L10n55', 'L10n58', 'L10n60', 'L10n61', 'L10n63', 'L10n64', 'L10n65', 'L10n66', 'L10n67', 'L10n68', 'L10n69', 'L10n70', 'L10n71', 'L10n73', 'L10n74', 'L10n75', 'L10n76', 'L10n78', 'L10n79', 'L10n80', 'L10n81', 'L10n83', 'L10n85', 'L10n86', 'L10n89', 'L10n90', 'L10n92', 'L10n95', 'L10n96', 'L10n99', 'L11n10', 'L11n11', 'L11n12', 'L11n13', 'L11n14', 'L11n15', 'L11n16', 'L11n17', 'L11n18', 'L11n19', 'L11n20', 'L11n21', 'L11n22', 'L11n23', 'L11n25', 'L11n26', 'L11n29', 'L11n30', 'L11n31', 'L11n32', 'L11n34', 'L11n35', 'L11n36', 'L11n37', 'L11n38', 'L11n40', 'L11n41', 'L11n42', 'L11n43', 'L11n45', 'L11n46', 'L11n47', 'L11n48', 'L11n49', 'L11n50', 'L11n55', 'L11n56', 'L11n58', 'L11n60', 'L11n62', 'L11n63', 'L11n66', 'L11n67', 'L11n69', 'L11n70', 'L11n72', 'L11n73', 'L11n76', 'L11n77', 'L11n78', 'L11n79', 'L11n80', 'L11n81', 'L11n82', 'L11n83', 'L11n84', 'L11n85', 'L11n86', 'L11n88', 'L11n90', 'L11n92', 'L11n97', 'L12n10', 'L12n11', 'L12n12', 'L12n13', 'L12n14', 'L12n15', 'L12n16', 'L12n17', 'L12n18', 'L12n20', 'L12n21', 'L12n23', 'L12n24', 'L12n25', 'L12n26', 'L12n27', 'L12n28', 'L12n29', 'L12n30', 'L12n31', 'L12n32', 'L12n33', 'L12n34', 'L12n35', 'L12n36', 'L12n37', 'L12n38', 'L12n39', 'L12n40', 'L12n41', 'L12n42', 'L12n43', 'L12n44', 'L12n45', 'L12n46', 'L12n47', 'L12n48', 'L12n49', 'L12n50', 'L12n51', 'L12n52', 'L12n53', 'L12n54', 'L12n55', 'L12n56', 'L12n57', 'L12n58', 'L12n60', 'L12n61', 'L12n62', 'L12n63', 'L12n64', 'L12n65', 'L12n66', 'L12n67', 'L12n69', 'L12n70', 'L12n71', 'L12n72', 'L12n73', 'L12n74', 'L12n75', 'L12n77', 'L12n78', 'L12n79', 'L12n80', 'L12n81', 'L12n82', 'L12n83', 'L12n85', 'L12n86', 'L12n87', 'L12n88', 'L12n89', 'L12n90', 'L12n91', 'L12n92', 'L12n93', 'L12n94', 'L12n95', 'L12n96', 'L12n98', 'L12n99', 'K11n100', 'K11n101', 'K11n103', 'K11n105', 'K11n106', 'K11n108', 'K11n109', 'K11n110', 'K11n112', 'K11n113', 'K11n114', 'K11n115', 'K11n117', 'K11n118', 'K11n119', 'K11n120', 'K11n121', 'K11n122', 'K11n123', 'K11n124', 'K11n125', 'K11n127', 'K11n128', 'K11n129', 'K11n130', 'K11n131', 'K11n132', 'K11n134', 'K11n136', 'K11n137', 'K11n139', 'K11n140', 'K11n141', 'K11n142', 'K11n144', 'K11n146', 'K11n147', 'K11n148', 'K11n149', 'K11n150', 'K11n153', 'K11n154', 'K11n155', 'K11n156', 'K11n157', 'K11n158', 'K11n159', 'K11n160', 'K11n161', 'K11n162', 'K11n163', 'K11n164', 'K11n165', 'K11n166', 'K11n167', 'K11n168', 'K11n169', 'K11n170', 'K11n171', 'K11n172', 'K11n173', 'K11n174', 'K11n175', 'K11n176', 'K11n177', 'K11n178', 'K11n179', 'K11n180', 'K11n181', 'K11n182', 'K11n184', 'K11n185', 'K12n100', 'K12n101', 'K12n103', 'K12n104', 'K12n106', 'K12n107', 'K12n108', 'K12n109', 'K12n111', 'K12n112', 'K12n113', 'K12n114', 'K12n116', 'K12n117', 'K12n122', 'K12n123', 'K12n125', 'K12n126', 'K12n127', 'K12n128', 'K12n130', 'K12n131', 'K12n133', 'K12n135', 'K12n137', 'K12n139', 'K12n140', 'K12n142', 'K12n144', 'K12n145', 'K12n146', 'K12n147', 'K12n150', 'K12n151', 'K12n152', 'K12n154', 'K12n155', 'K12n157', 'K12n158', 'K12n159', 'K12n160', 'K12n161', 'K12n162', 'K12n163', 'K12n164', 'K12n165', 'K12n166', 'K12n167', 'K12n168', 'K12n169', 'K12n170', 'K12n171', 'K12n173', 'K12n174', 'K12n176', 'K12n177', 'K12n178', 'K12n180', 'K12n181', 'K12n182', 'K12n183', 'K12n185', 'K12n186', 'K12n188', 'K12n189', 'K12n190', 'K12n191', 'K12n193', 'K12n194', 'K12n196', 'K12n197', 'K12n201', 'K12n202', 'K12n204', 'K12n205', 'K12n206', 'K12n208', 'K12n209', 'K12n211', 'K12n212', 'K12n213', 'K12n215', 'K12n216', 'K12n219', 'K12n222', 'K12n223', 'K12n224', 'K12n225', 'K12n226', 'K12n227', 'K12n233', 'K12n234', 'K12n235', 'K12n236', 'K12n237', 'K12n238', 'K12n239', 'K12n240', 'K12n241', 'K12n245', 'K12n246', 'K12n247', 'K12n248', 'K12n249', 'K12n250', 'K12n252', 'K12n253', 'K12n254', 'K12n255', 'K12n259', 'K12n261', 'K12n262', 'K12n263', 'K12n266', 'K12n269', 'K12n270', 'K12n271', 'K12n272', 'K12n274', 'K12n275', 'K12n277', 'K12n278', 'K12n280', 'K12n281', 'K12n283', 'K12n284', 'K12n285', 'K12n286', 'K12n287', 'K12n288', 'K12n289', 'K12n290', 'K12n291', 'K12n294', 'K12n295', 'K12n296', 'K12n297', 'K12n298', 'K12n299', 'K12n300', 'K12n301', 'K12n302', 'K12n303', 'K12n304', 'K12n305', 'K12n306', 'K12n307', 'K12n308', 'K12n311', 'K12n312', 'K12n315', 'K12n316', 'K12n317', 'K12n319', 'K12n320', 'K12n321', 'K12n323', 'K12n324', 'K12n325', 'K12n326', 'K12n327', 'K12n328', 'K12n330', 'K12n333', 'K12n334', 'K12n335', 'K12n337', 'K12n338', 'K12n339', 'K12n340', 'K12n341', 'K12n342', 'K12n343', 'K12n344', 'K12n345', 'K12n347', 'K12n348', 'K12n350', 'K12n353', 'K12n356', 'K12n357', 'K12n358', 'K12n359', 'K12n360', 'K12n361', 'K12n363', 'K12n364', 'K12n365', 'K12n367', 'K12n369', 'K12n372', 'K12n373', 'K12n375', 'K12n376', 'K12n378', 'K12n379', 'K12n380', 'K12n381', 'K12n383', 'K12n384', 'K12n385', 'K12n388', 'K12n389', 'K12n390', 'K12n391', 'K12n392', 'K12n393', 'K12n395', 'K12n396', 'K12n399', 'K12n400', 'K12n401', 'K12n405', 'K12n406', 'K12n407', 'K12n408', 'K12n409', 'K12n410', 'K12n412', 'K12n413', 'K12n415', 'K12n416', 'K12n420', 'K12n421', 'K12n422', 'K12n424', 'K12n427', 'K12n428', 'K12n429', 'K12n431', 'K12n434', 'K12n435', 'K12n440', 'K12n441', 'K12n443', 'K12n444', 'K12n445', 'K12n447', 'K12n448', 'K12n450', 'K12n451', 'K12n452', 'K12n453', 'K12n454', 'K12n455', 'K12n458', 'K12n459', 'K12n460', 'K12n461', 'K12n462', 'K12n463', 'K12n465', 'K12n466', 'K12n467', 'K12n468', 'K12n469', 'K12n470', 'K12n471', 'K12n472', 'K12n474', 'K12n476', 'K12n477', 'K12n478', 'K12n479', 'K12n480', 'K12n481', 'K12n482', 'K12n484', 'K12n485', 'K12n486', 'K12n489', 'K12n490', 'K12n491', 'K12n492', 'K12n493', 'K12n496', 'K12n497', 'K12n498', 'K12n500', 'K12n501', 'K12n504', 'K12n505', 'K12n506', 'K12n507', 'K12n508', 'K12n509', 'K12n510', 'K12n511', 'K12n512', 'K12n513', 'K12n514', 'K12n515', 'K12n516', 'K12n517', 'K12n520', 'K12n521', 'K12n522', 'K12n524', 'K12n525', 'K12n527', 'K12n529', 'K12n530', 'K12n531', 'K12n532', 'K12n533', 'K12n534', 'K12n536', 'K12n537', 'K12n538', 'K12n539', 'K12n540', 'K12n541', 'K12n542', 'K12n543', 'K12n544', 'K12n545', 'K12n546', 'K12n547', 'K12n548', 'K12n551', 'K12n553', 'K12n555', 'K12n556', 'K12n557', 'K12n559', 'K12n560', 'K12n561', 'K12n562', 'K12n563', 'K12n564', 'K12n565', 'K12n566', 'K12n567', 'K12n568', 'K12n569', 'K12n570', 'K12n571', 'K12n572', 'K12n573', 'K12n576', 'K12n578', 'K12n580', 'K12n581', 'K12n582', 'K12n583', 'K12n584', 'K12n585', 'K12n586', 'K12n587', 'K12n588', 'K12n589', 'K12n590', 'K12n592', 'K12n593', 'K12n595', 'K12n596', 'K12n597', 'K12n598', 'K12n599', 'K12n600', 'K12n602', 'K12n604', 'K12n606', 'K12n607', 'K12n608', 'K12n609', 'K12n610', 'K12n611', 'K12n612', 'K12n613', 'K12n614', 'K12n615', 'K12n616', 'K12n618', 'K12n619', 'K12n620', 'K12n621', 'K12n622', 'K12n623', 'K12n625', 'K12n626', 'K12n627', 'K12n628', 'K12n631', 'K12n632', 'K12n633', 'K12n635', 'K12n636', 'K12n637', 'K12n641', 'K12n643', 'K12n645', 'K12n646', 'K12n649', 'K12n651', 'K12n652', 'K12n653', 'K12n654', 'K12n656', 'K12n657', 'K12n658', 'K12n659', 'K12n661', 'K12n662', 'K12n663', 'K12n664', 'K12n666', 'K12n667', 'K12n668', 'K12n669', 'K12n671', 'K12n674', 'K12n675', 'K12n677', 'K12n678', 'K12n679', 'K12n682', 'K12n683', 'K12n684', 'K12n685', 'K12n686', 'K12n687', 'K12n694', 'K12n695', 'K12n698', 'K12n699', 'K12n700', 'K12n701', 'K12n702', 'K12n703', 'K12n704', 'K12n705', 'K12n706', 'K12n707', 'K12n708', 'K12n709', 'K12n710', 'K12n711', 'K12n712', 'K12n713', 'K12n714', 'K12n715', 'K12n716', 'K12n717', 'K12n718', 'K12n719', 'K12n720', 'K12n721', 'K12n722', 'K12n723', 'K12n724', 'K12n725', 'K12n726', 'K12n727', 'K12n728', 'K12n729', 'K12n730', 'K12n731', 'K12n732', 'K12n733', 'K12n734', 'K12n735', 'K12n736', 'K12n737', 'K12n738', 'K12n740', 'K12n741', 'K12n742', 'K12n743', 'K12n744', 'K12n745', 'K12n746', 'K12n747', 'K12n748', 'K12n751', 'K12n752', 'K12n753', 'K12n754', 'K12n755', 'K12n756', 'K12n757', 'K12n758', 'K12n759', 'K12n760', 'K12n761', 'K12n762', 'K12n763', 'K12n765', 'K12n766', 'K12n767', 'K12n768', 'K12n769', 'K12n770', 'K12n771', 'K12n772', 'K12n773', 'K12n774', 'K12n775', 'K12n776', 'K12n777', 'K12n778', 'K12n779', 'K12n780', 'K12n781', 'K12n782', 'K12n783', 'K12n784', 'K12n785', 'K12n786', 'K12n787', 'K12n788', 'K12n789', 'K12n790', 'K12n791', 'K12n792', 'K12n793', 'K12n794', 'K12n795', 'K12n796', 'K12n797', 'K12n798', 'K12n799', 'K12n800', 'K12n802', 'K12n803', 'K12n804', 'K12n805', 'K12n806', 'K12n807', 'K12n811', 'K12n813', 'K12n814', 'K12n816', 'K12n817', 'K12n818', 'K12n819', 'K12n820', 'K12n821', 'K12n822', 'K12n823', 'K12n824', 'K12n825', 'K12n826', 'K12n827', 'K12n828', 'K12n829', 'K12n831', 'K12n832', 'K12n833', 'K12n834', 'K12n836', 'K12n837', 'K12n838', 'K12n839', 'K12n840', 'K12n841', 'K12n842', 'K12n843', 'K12n844', 'K12n845', 'K12n846', 'K12n847', 'K12n848', 'K12n849', 'K12n852', 'K12n853', 'K12n854', 'K12n855', 'K12n856', 'K12n857', 'K12n858', 'K12n859', 'K12n860', 'K12n861', 'K12n862', 'K12n863', 'K12n864', 'K12n865', 'K12n866', 'K12n867', 'K12n869', 'K12n870', 'K12n871', 'K12n872', 'K12n873', 'K12n874', 'K12n875', 'K12n876', 'K12n877', 'K12n878', 'K12n879', 'K12n880', 'K12n881', 'K12n882', 'K12n883', 'K12n884', 'K12n885', 'K12n886', 'K12n887', 'L10n100', 'L10n101', 'L10n102', 'L10n105', 'L10n106', 'L10n109', 'L10n110', 'L10n112', 'L11n100', 'L11n101', 'L11n102', 'L11n104', 'L11n105', 'L11n107', 'L11n110', 'L11n112', 'L11n113', 'L11n114', 'L11n115', 'L11n116', 'L11n117', 'L11n118', 'L11n119', 'L11n121', 'L11n123', 'L11n125', 'L11n126', 'L11n129', 'L11n130', 'L11n133', 'L11n134', 'L11n135', 'L11n137', 'L11n138', 'L11n139', 'L11n140', 'L11n141', 'L11n142', 'L11n144', 'L11n145', 'L11n146', 'L11n147', 'L11n149', 'L11n150', 'L11n151', 'L11n152', 'L11n153', 'L11n154', 'L11n155', 'L11n156', 'L11n157', 'L11n158', 'L11n160', 'L11n161', 'L11n163', 'L11n164', 'L11n167', 'L11n168', 'L11n170', 'L11n171', 'L11n172', 'L11n173', 'L11n174', 'L11n175', 'L11n177', 'L11n178', 'L11n179', 'L11n182', 'L11n183', 'L11n184', 'L11n185', 'L11n186', 'L11n187', 'L11n188', 'L11n190', 'L11n192', 'L11n193', 'L11n194', 'L11n195', 'L11n196', 'L11n198', 'L11n200', 'L11n201', 'L11n202', 'L11n203', 'L11n206', 'L11n207', 'L11n209', 'L11n210', 'L11n211', 'L11n212', 'L11n213', 'L11n214', 'L11n215', 'L11n216', 'L11n217', 'L11n220', 'L11n221', 'L11n223', 'L11n225', 'L11n229', 'L11n230', 'L11n231', 'L11n234', 'L11n238', 'L11n240', 'L11n241', 'L11n242', 'L11n243', 'L11n245', 'L11n246', 'L11n248', 'L11n249', 'L11n250', 'L11n251', 'L11n255', 'L11n257', 'L11n258', 'L11n259', 'L11n260', 'L11n261', 'L11n263', 'L11n265', 'L11n266', 'L11n268', 'L11n271', 'L11n272', 'L11n273', 'L11n274', 'L11n275', 'L11n276', 'L11n277', 'L11n278', 'L11n279', 'L11n280', 'L11n281', 'L11n282', 'L11n283', 'L11n285', 'L11n286', 'L11n287', 'L11n288', 'L11n289', 'L11n290', 'L11n291', 'L11n292', 'L11n295', 'L11n296', 'L11n297', 'L11n298', 'L11n303', 'L11n309', 'L11n310', 'L11n312', 'L11n314', 'L11n316', 'L11n317', 'L11n318', 'L11n319', 'L11n320', 'L11n321', 'L11n322', 'L11n323', 'L11n324', 'L11n325', 'L11n326', 'L11n327', 'L11n328', 'L11n329', 'L11n330', 'L11n331', 'L11n332', 'L11n333', 'L11n335', 'L11n338', 'L11n341', 'L11n343', 'L11n344', 'L11n349', 'L11n351', 'L11n353', 'L11n355', 'L11n356', 'L11n358', 'L11n361', 'L11n362', 'L11n364', 'L11n365', 'L11n369', 'L11n371', 'L11n372', 'L11n373', 'L11n375', 'L11n376', 'L11n377', 'L11n378', 'L11n380', 'L11n382', 'L11n383', 'L11n384', 'L11n386', 'L11n387', 'L11n388', 'L11n389', 'L11n390', 'L11n391', 'L11n393', 'L11n394', 'L11n395', 'L11n398', 'L11n400', 'L11n401', 'L11n402', 'L11n405', 'L11n407', 'L11n409', 'L11n410', 'L11n412', 'L11n413', 'L11n416', 'L11n418', 'L11n419', 'L11n421', 'L11n422', 'L11n424', 'L11n425', 'L11n427', 'L11n429', 'L11n431', 'L11n434', 'L11n435', 'L11n438', 'L11n440', 'L11n442', 'L11n443', 'L11n444', 'L11n445', 'L11n446', 'L11n448', 'L11n450', 'L11n451', 'L11n452', 'L11n453', 'L11n454', 'L11n455', 'L11n456', 'L11n457', 'L11n458', 'L12n103', 'L12n104', 'L12n106', 'L12n107', 'L12n108', 'L12n109', 'L12n110', 'L12n111', 'L12n113', 'L12n115', 'L12n116', 'L12n117', 'L12n118', 'L12n120', 'L12n121', 'L12n122', 'L12n123', 'L12n124', 'L12n125', 'L12n126', 'L12n127', 'L12n128', 'L12n129', 'L12n130', 'L12n131', 'L12n132', 'L12n133', 'L12n134', 'L12n135', 'L12n136', 'L12n137', 'L12n139', 'L12n140', 'L12n141', 'L12n142', 'L12n144', 'L12n145', 'L12n146', 'L12n147', 'L12n149', 'L12n150', 'L12n151', 'L12n152', 'L12n154', 'L12n155', 'L12n158', 'L12n160', 'L12n162', 'L12n164', 'L12n167', 'L12n168', 'L12n169', 'L12n170', 'L12n171', 'L12n172', 'L12n173', 'L12n175', 'L12n176', 'L12n177', 'L12n178', 'L12n180', 'L12n181', 'L12n182', 'L12n183', 'L12n184', 'L12n185', 'L12n187', 'L12n189', 'L12n190', 'L12n191', 'L12n192', 'L12n193', 'L12n194', 'L12n195', 'L12n196', 'L12n197', 'L12n198', 'L12n199', 'L12n200', 'L12n201', 'L12n202', 'L12n203', 'L12n204', 'L12n205', 'L12n206', 'L12n210', 'L12n211', 'L12n212', 'L12n214', 'L12n216', 'L12n218', 'L12n220', 'L12n221', 'L12n223', 'L12n226', 'L12n229', 'L12n232', 'L12n233', 'L12n235', 'L12n241', 'L12n242', 'L12n243', 'L12n244', 'L12n247', 'L12n248', 'L12n251', 'L12n252', 'L12n253', 'L12n254', 'L12n256', 'L12n257', 'L12n258', 'L12n259', 'L12n262', 'L12n263', 'L12n268', 'L12n269', 'L12n270', 'L12n271', 'L12n275', 'L12n276', 'L12n277', 'L12n278', 'L12n279', 'L12n281', 'L12n282', 'L12n284', 'L12n285', 'L12n288', 'L12n289', 'L12n292', 'L12n293', 'L12n295', 'L12n297', 'L12n300', 'L12n301', 'L12n302', 'L12n303', 'L12n305', 'L12n307', 'L12n308', 'L12n309', 'L12n311', 'L12n313', 'L12n314', 'L12n316', 'L12n317', 'L12n318', 'L12n320', 'L12n321', 'L12n322', 'L12n323', 'L12n324', 'L12n325', 'L12n326', 'L12n329', 'L12n330', 'L12n331', 'L12n332', 'L12n333', 'L12n334', 'L12n335', 'L12n336', 'L12n337', 'L12n338', 'L12n340', 'L12n343', 'L12n346', 'L12n348', 'L12n350', 'L12n351', 'L12n352', 'L12n353', 'L12n355', 'L12n356', 'L12n357', 'L12n359', 'L12n360', 'L12n361', 'L12n362', 'L12n363', 'L12n364', 'L12n365', 'L12n366', 'L12n367', 'L12n370', 'L12n372', 'L12n374', 'L12n378', 'L12n380', 'L12n382', 'L12n385', 'L12n386', 'L12n387', 'L12n391', 'L12n392', 'L12n393', 'L12n394', 'L12n397', 'L12n400', 'L12n401', 'L12n403', 'L12n404', 'L12n406', 'L12n407', 'L12n410', 'L12n411', 'L12n414', 'L12n415', 'L12n416', 'L12n417', 'L12n419', 'L12n421', 'L12n423', 'L12n425', 'L12n427', 'L12n428', 'L12n431', 'L12n433', 'L12n435', 'L12n436', 'L12n437', 'L12n438', 'L12n440', 'L12n441', 'L12n445', 'L12n446', 'L12n447', 'L12n449', 'L12n450', 'L12n453', 'L12n454', 'L12n455', 'L12n457', 'L12n459', 'L12n462', 'L12n463', 'L12n466', 'L12n468', 'L12n469', 'L12n472', 'L12n473', 'L12n475', 'L12n477', 'L12n479', 'L12n483', 'L12n484', 'L12n485', 'L12n487', 'L12n488', 'L12n489', 'L12n490', 'L12n491', 'L12n494', 'L12n495', 'L12n496', 'L12n497', 'L12n498', 'L12n499', 'L12n501', 'L12n503', 'L12n507', 'L12n509', 'L12n510', 'L12n512', 'L12n516', 'L12n518', 'L12n519', 'L12n521', 'L12n522', 'L12n524', 'L12n525', 'L12n527', 'L12n528', 'L12n530', 'L12n532', 'L12n533', 'L12n534', 'L12n535', 'L12n536', 'L12n537', 'L12n538', 'L12n540', 'L12n541', 'L12n542', 'L12n543', 'L12n546', 'L12n547', 'L12n550', 'L12n554', 'L12n555', 'L12n557', 'L12n558', 'L12n560', 'L12n562', 'L12n567', 'L12n568', 'L12n570', 'L12n571', 'L12n573', 'L12n578', 'L12n581', 'L12n583', 'L12n584', 'L12n585', 'L12n587', 'L12n588', 'L12n589', 'L12n593', 'L12n595', 'L12n596', 'L12n598', 'L12n599', 'L12n601', 'L12n603', 'L12n604', 'L12n606', 'L12n607', 'L12n610', 'L12n611', 'L12n613', 'L12n615', 'L12n616', 'L12n617', 'L12n618', 'L12n620', 'L12n621', 'L12n622', 'L12n625', 'L12n626', 'L12n627', 'L12n628', 'L12n629', 'L12n630', 'L12n631', 'L12n632', 'L12n633', 'L12n634', 'L12n635', 'L12n636', 'L12n637', 'L12n639', 'L12n640', 'L12n641', 'L12n642', 'L12n643', 'L12n644', 'L12n647', 'L12n648', 'L12n649', 'L12n650', 'L12n654', 'L12n655', 'L12n656', 'L12n657', 'L12n658', 'L12n659', 'L12n661', 'L12n662', 'L12n663', 'L12n664', 'L12n665', 'L12n666', 'L12n667', 'L12n668', 'L12n669', 'L12n670', 'L12n671', 'L12n672', 'L12n674', 'L12n676', 'L12n677', 'L12n682', 'L12n685', 'L12n686', 'L12n688', 'L12n689', 'L12n690', 'L12n691', 'L12n692', 'L12n693', 'L12n694', 'L12n695', 'L12n696', 'L12n698', 'L12n699', 'L12n701', 'L12n702', 'L12n704', 'L12n705', 'L12n710', 'L12n714', 'L12n715', 'L12n716', 'L12n718', 'L12n719', 'L12n720', 'L12n722', 'L12n723', 'L12n725', 'L12n726', 'L12n728', 'L12n729', 'L12n730', 'L12n733', 'L12n734', 'L12n735', 'L12n736', 'L12n737', 'L12n738', 'L12n741', 'L12n742', 'L12n745', 'L12n748', 'L12n749', 'L12n751', 'L12n753', 'L12n754', 'L12n757', 'L12n758', 'L12n760', 'L12n761', 'L12n763', 'L12n765', 'L12n766', 'L12n772', 'L12n773', 'L12n774', 'L12n775', 'L12n777', 'L12n778', 'L12n779', 'L12n782', 'L12n784', 'L12n785', 'L12n786', 'L12n788', 'L12n789', 'L12n790', 'L12n791', 'L12n792', 'L12n793', 'L12n794', 'L12n795', 'L12n797', 'L12n798', 'L12n800', 'L12n801', 'L12n802', 'L12n806', 'L12n810', 'L12n812', 'L12n814', 'L12n815', 'L12n816', 'L12n819', 'L12n820', 'L12n823', 'L12n825', 'L12n826', 'L12n827', 'L12n828', 'L12n832', 'L12n833', 'L12n834', 'L12n835', 'L12n837', 'L12n838', 'L12n839', 'L12n841', 'L12n842', 'L12n843', 'L12n844', 'L12n845', 'L12n846', 'L12n847', 'L12n848', 'L12n849', 'L12n854', 'L12n855', 'L12n858', 'L12n862', 'L12n863', 'L12n864', 'L12n866', 'L12n867', 'L12n869', 'L12n870', 'L12n872', 'L12n874', 'L12n875', 'L12n876', 'L12n878', 'L12n879', 'L12n880', 'L12n882', 'L12n883', 'L12n884', 'L12n886', 'L12n887', 'L12n889', 'L12n890', 'L12n894', 'L12n896', 'L12n897', 'L12n898', 'L12n899', 'L12n900', 'L12n901', 'L12n903', 'L12n904', 'L12n912', 'L12n913', 'L12n914', 'L12n915', 'L12n916', 'L12n917', 'L12n918', 'L12n919', 'L12n921', 'L12n923', 'L12n924', 'L12n926', 'L12n928', 'L12n929', 'L12n931', 'L12n932', 'L12n933', 'L12n936', 'L12n937', 'L12n938', 'L12n939', 'L12n941', 'L12n942', 'L12n943', 'L12n944', 'L12n948', 'L12n949', 'L12n950', 'L12n951', 'L12n953', 'L12n955', 'L12n957', 'L12n958', 'L12n959', 'L12n961', 'L12n962', 'L12n965', 'L12n966', 'L12n967', 'L12n970', 'L12n971', 'L12n972', 'L12n975', 'L12n976', 'L12n977', 'L12n978', 'L12n979', 'L12n981', 'L12n983', 'L12n984', 'L12n986', 'L12n987', 'L12n988', 'L12n990', 'L12n992', 'L12n993', 'L12n994', 'L12n995', 'L12n996', 'L12n998', 'L12n999', 'K13n2028', 'K13n2958', 'K13n3009', 'L12n1000', 'L12n1003', 'L12n1004', 'L12n1005', 'L12n1006', 'L12n1009', 'L12n1010', 'L12n1013', 'L12n1014', 'L12n1015', 'L12n1016', 'L12n1017', 'L12n1018', 'L12n1019', 'L12n1020', 'L12n1022', 'L12n1023', 'L12n1024', 'L12n1026', 'L12n1028', 'L12n1030', 'L12n1031', 'L12n1032', 'L12n1033', 'L12n1035', 'L12n1036', 'L12n1037', 'L12n1038', 'L12n1039', 'L12n1041', 'L12n1042', 'L12n1043', 'L12n1044', 'L12n1045', 'L12n1046', 'L12n1047', 'L12n1048', 'L12n1049', 'L12n1050', 'L12n1051', 'L12n1053', 'L12n1055', 'L12n1056', 'L12n1057', 'L12n1058', 'L12n1059', 'L12n1060', 'L12n1062', 'L12n1063', 'L12n1064', 'L12n1066', 'L12n1068', 'L12n1070', 'L12n1071', 'L12n1073', 'L12n1076', 'L12n1077', 'L12n1078', 'L12n1079', 'L12n1080', 'L12n1081', 'L12n1083', 'L12n1085', 'L12n1086', 'L12n1087', 'L12n1088', 'L12n1089', 'L12n1090', 'L12n1091', 'L12n1094', 'L12n1096', 'L12n1100', 'L12n1104', 'L12n1105', 'L12n1106', 'L12n1107', 'L12n1108', 'L12n1111', 'L12n1112', 'L12n1113', 'L12n1118', 'L12n1119', 'L12n1123', 'L12n1124', 'L12n1125', 'L12n1126', 'L12n1127', 'L12n1128', 'L12n1129', 'L12n1131', 'L12n1132', 'L12n1134', 'L12n1135', 'L12n1137', 'L12n1141', 'L12n1142', 'L12n1144', 'L12n1146', 'L12n1150', 'L12n1151', 'L12n1157', 'L12n1158', 'L12n1161', 'L12n1162', 'L12n1168', 'L12n1170', 'L12n1171', 'L12n1172', 'L12n1173', 'L12n1174', 'L12n1175', 'L12n1177', 'L12n1182', 'L12n1183', 'L12n1184', 'L12n1185', 'L12n1187', 'L12n1189', 'L12n1190', 'L12n1191', 'L12n1193', 'L12n1194', 'L12n1196', 'L12n1203', 'L12n1206', 'L12n1207', 'L12n1208', 'L12n1209', 'L12n1212', 'L12n1213', 'L12n1214', 'L12n1215', 'L12n1216', 'L12n1219', 'L12n1220', 'L12n1221', 'L12n1222', 'L12n1225', 'L12n1227', 'L12n1228', 'L12n1230', 'L12n1232', 'L12n1233', 'L12n1234', 'L12n1236', 'L12n1238', 'L12n1239', 'L12n1241', 'L12n1243', 'L12n1245', 'L12n1246', 'L12n1247', 'L12n1248', 'L12n1250', 'L12n1251', 'L12n1253', 'L12n1255', 'L12n1256', 'L12n1258', 'L12n1261', 'L12n1262', 'L12n1264', 'L12n1266', 'L12n1267', 'L12n1268', 'L12n1269', 'L12n1270', 'L12n1271', 'L12n1274', 'L12n1275', 'L12n1276', 'L12n1280', 'L12n1281', 'L12n1284', 'L12n1285', 'L12n1286', 'L12n1287', 'L12n1288', 'L12n1289', 'L12n1290', 'L12n1291', 'L12n1292', 'L12n1293', 'L12n1294', 'L12n1297', 'L12n1298', 'L12n1303', 'L12n1305', 'L12n1306', 'L12n1307', 'L12n1308', 'L12n1309', 'L12n1315', 'L12n1316', 'L12n1318', 'L12n1322', 'L12n1324', 'L12n1325', 'L12n1328', 'L12n1329', 'L12n1330', 'L12n1331', 'L12n1332', 'L12n1335', 'L12n1337', 'L12n1338', 'L12n1339', 'L12n1341', 'L12n1343', 'L12n1347', 'L12n1348', 'L12n1349', 'L12n1351', 'L12n1352', 'L12n1354', 'L12n1355', 'L12n1356', 'L12n1358', 'L12n1359', 'L12n1364', 'L12n1365', 'L12n1366', 'L12n1371', 'L12n1372', 'L12n1373', 'L12n1380', 'L12n1381', 'L12n1383', 'L12n1384', 'L12n1385', 'L12n1386', 'L12n1387', 'L12n1388', 'L12n1389', 'L12n1390', 'L12n1391', 'L12n1392', 'L12n1393', 'L12n1394', 'L12n1395', 'L12n1396', 'L12n1397', 'L12n1399', 'L12n1400', 'L12n1401', 'L12n1403', 'L12n1407', 'L12n1408', 'L12n1409', 'L12n1411', 'L12n1412', 'L12n1413', 'L12n1414', 'L12n1417', 'L12n1418', 'L12n1419', 'L12n1421', 'L12n1422', 'L12n1423', 'L12n1424', 'L12n1425', 'L12n1426', 'L12n1427', 'L12n1430', 'L12n1431', 'L12n1432', 'L12n1434', 'L12n1435', 'L12n1437', 'L12n1438', 'L12n1439', 'L12n1440', 'L12n1442', 'L12n1443', 'L12n1444', 'L12n1445', 'L12n1446', 'L12n1448', 'L12n1449', 'L12n1450', 'L12n1451', 'L12n1452', 'L12n1453', 'L12n1454', 'L12n1455', 'L12n1457', 'L12n1459', 'L12n1461', 'L12n1464', 'L12n1465', 'L12n1466', 'L12n1467', 'L12n1468', 'L12n1469', 'L12n1470', 'L12n1471', 'L12n1472', 'L12n1473', 'L12n1475', 'L12n1476', 'L12n1477', 'L12n1478', 'L12n1479', 'L12n1480', 'L12n1481', 'L12n1482', 'L12n1483', 'L12n1484', 'L12n1485', 'L12n1486', 'L12n1487', 'L12n1488', 'L12n1489', 'L12n1491', 'L12n1492', 'L12n1494', 'L12n1495', 'L12n1497', 'L12n1498', 'L12n1499', 'L12n1500', 'L12n1503', 'L12n1504', 'L12n1506', 'L12n1509', 'L12n1510', 'L12n1511', 'L12n1512', 'L12n1513', 'L12n1515', 'L12n1516', 'L12n1517', 'L12n1518', 'L12n1520', 'L12n1521', 'L12n1522', 'L12n1523', 'L12n1524', 'L12n1527', 'L12n1528', 'L12n1530', 'L12n1531', 'L12n1532', 'L12n1534', 'L12n1535', 'L12n1537', 'L12n1539', 'L12n1541', 'L12n1543', 'L12n1544', 'L12n1545', 'L12n1547', 'L12n1549', 'L12n1551', 'L12n1554', 'L12n1555', 'L12n1556', 'L12n1557', 'L12n1559', 'L12n1561', 'L12n1562', 'L12n1564', 'L12n1565', 'L12n1567', 'L12n1569', 'L12n1571', 'L12n1572', 'L12n1573', 'L12n1574', 'L12n1575', 'L12n1576', 'L12n1577', 'L12n1578', 'L12n1579', 'L12n1580', 'L12n1581', 'L12n1582', 'L12n1583', 'L12n1584', 'L12n1585', 'L12n1586', 'L12n1587', 'L12n1588', 'L12n1589', 'L12n1590', 'L12n1591', 'L12n1592', 'L12n1593', 'L12n1594', 'L12n1595', 'L12n1597', 'L12n1598', 'L12n1599', 'L12n1600', 'L12n1602', 'L12n1603', 'L12n1605', 'L12n1606', 'L12n1608', 'L12n1610', 'L12n1611', 'L12n1612', 'L12n1613', 'L12n1616', 'L12n1617', 'L12n1618', 'L12n1619', 'L12n1624', 'L12n1626', 'L12n1627', 'L12n1628', 'L12n1630', 'L12n1632', 'L12n1633', 'L12n1636', 'L12n1637', 'L12n1639', 'L12n1640', 'L12n1641', 'L12n1646', 'L12n1647', 'L12n1649', 'L12n1650', 'L12n1652', 'L12n1653', 'L12n1654', 'L12n1655', 'L12n1656', 'L12n1657', 'L12n1658', 'L12n1660', 'L12n1661', 'L12n1662', 'L12n1663', 'L12n1664', 'L12n1665', 'L12n1666', 'L12n1667', 'L12n1668', 'L12n1671', 'L12n1673', 'L12n1674', 'L12n1675', 'L12n1677', 'L12n1678', 'L12n1680', 'L12n1681', 'L12n1683', 'L12n1684', 'L12n1685', 'L12n1686', 'L12n1687', 'L12n1688', 'L12n1689', 'L12n1690', 'L12n1691', 'L12n1693', 'L12n1695', 'L12n1696', 'L12n1698', 'L12n1700', 'L12n1703', 'L12n1705', 'L12n1708', 'L12n1709', 'L12n1711', 'L12n1712', 'L12n1713', 'L12n1714', 'L12n1718', 'L12n1720', 'L12n1721', 'L12n1723', 'L12n1725', 'L12n1728', 'L12n1729', 'L12n1732', 'L12n1733', 'L12n1736', 'L12n1738', 'L12n1740', 'L12n1743', 'L12n1747', 'L12n1748', 'L12n1749', 'L12n1750', 'L12n1751', 'L12n1752', 'L12n1753', 'L12n1754', 'L12n1757', 'L12n1761', 'L12n1762', 'L12n1763', 'L12n1765', 'L12n1766', 'L12n1768', 'L12n1770', 'L12n1771', 'L12n1772', 'L12n1773', 'L12n1774', 'L12n1776', 'L12n1777', 'L12n1779', 'L12n1781', 'L12n1783', 'L12n1784', 'L12n1788', 'L12n1789', 'L12n1792', 'L12n1794', 'L12n1796', 'L12n1798', 'L12n1800', 'L12n1801', 'L12n1802', 'L12n1803', 'L12n1804', 'L12n1805', 'L12n1806', 'L12n1807', 'L12n1808', 'L12n1810', 'L12n1811', 'L12n1812', 'L12n1813', 'L12n1814', 'L12n1815', 'L12n1816', 'L12n1817', 'L12n1819', 'L12n1820', 'L12n1822', 'L12n1823', 'L12n1824', 'L12n1825', 'L12n1826', 'L12n1827', 'L12n1830', 'L12n1831', 'L12n1832', 'L12n1833', 'L12n1834', 'L12n1835', 'L12n1836', 'L12n1838', 'L12n1839', 'L12n1840', 'L12n1842', 'L12n1843', 'L12n1844', 'L12n1845', 'L12n1846', 'L12n1849', 'L12n1850', 'L12n1851', 'L12n1852', 'L12n1853', 'L12n1854', 'L12n1855', 'L12n1856', 'L12n1857', 'L12n1858', 'L12n1859', 'L12n1860', 'L12n1861', 'L12n1863', 'L12n1864', 'L12n1865', 'L12n1867', 'L12n1869', 'L12n1871', 'L12n1872', 'L12n1873', 'L12n1874', 'L12n1875', 'L12n1878', 'L12n1879', 'L12n1881', 'L12n1883', 'L12n1886', 'L12n1887', 'L12n1890', 'L12n1891', 'L12n1893', 'L12n1895', 'L12n1897', 'L12n1900', 'L12n1901', 'L12n1902', 'L12n1904', 'L12n1905', 'L12n1906', 'L12n1907', 'L12n1908', 'L12n1909', 'L12n1911', 'L12n1914', 'L12n1915', 'L12n1916', 'L12n1917', 'L12n1918', 'L12n1919', 'L12n1920', 'L12n1921', 'L12n1922', 'L12n1924', 'L12n1926', 'L12n1930', 'L12n1932', 'L12n1934', 'L12n1935', 'L12n1936', 'L12n1938', 'L12n1939', 'L12n1942', 'L12n1944', 'L12n1945', 'L12n1946', 'L12n1947', 'L12n1949', 'L12n1950', 'L12n1951', 'L12n1954', 'L12n1955', 'L12n1956', 'L12n1957', 'L12n1958', 'L12n1960', 'L12n1962', 'L12n1963', 'L12n1964', 'L12n1965', 'L12n1967', 'L12n1970', 'L12n1971', 'L12n1972', 'L12n1973', 'L12n1974', 'L12n1975', 'L12n1976', 'L12n1980', 'L12n1981', 'L12n1983', 'L12n1984', 'L12n1989', 'L12n1990', 'L12n1991', 'L12n1994', 'L12n1999', 'L12n2000', 'L12n2001', 'L12n2002', 'L12n2004', 'L12n2005', 'L12n2006', 'L12n2008', 'L12n2010', 'L12n2012', 'L12n2013', 'L12n2014', 'L12n2015', 'L12n2016', 'L12n2017', 'L12n2018', 'L12n2019', 'L12n2021', 'L12n2022', 'L12n2023', 'L12n2024', 'L12n2025', 'L12n2028', 'L12n2029', 'L12n2030', 'L12n2032', 'L12n2034', 'L12n2035', 'L12n2036', 'L12n2037', 'L12n2038', 'L12n2039', 'L12n2041', 'L12n2042', 'L12n2044', 'L12n2045', 'L12n2046', 'L12n2048', 'L12n2049', 'L12n2051', 'L12n2052', 'L12n2053', 'L12n2055', 'L12n2057', 'L12n2058', 'L12n2061', 'L12n2062', 'L12n2063', 'L12n2064', 'L12n2066', 'L12n2068', 'L12n2070', 'L12n2071', 'L12n2072', 'L12n2073', 'L12n2074', 'L12n2075', 'L12n2076', 'L12n2078', 'L12n2079', 'L12n2080', 'L12n2083', 'L12n2084', 'L12n2090', 'L12n2093', 'L12n2094', 'L12n2096', 'L12n2097', 'L12n2098', 'L12n2099', 'L12n2100', 'L12n2102', 'L12n2103', 'L12n2105', 'L12n2107', 'L12n2108', 'L12n2111', 'L12n2113', 'L12n2115', 'L12n2117', 'L12n2118', 'L12n2119', 'L12n2120', 'L12n2121', 'L12n2122', 'L12n2123', 'L12n2124', 'L12n2125', 'L12n2126', 'L12n2128', 'L12n2130', 'L12n2132', 'L12n2134', 'L12n2135', 'L12n2137', 'L12n2138', 'L12n2142', 'L12n2143', 'L12n2145', 'L12n2146', 'L12n2147', 'L12n2148', 'L12n2149', 'L12n2151', 'L12n2152', 'L12n2154', 'L12n2155', 'L12n2157', 'L12n2158', 'L12n2159', 'L12n2160', 'L12n2161', 'L12n2162', 'L12n2164', 'L12n2165', 'L12n2166', 'L12n2167', 'L12n2169', 'L12n2172', 'L12n2173', 'L12n2175', 'L12n2177', 'L12n2180', 'L12n2181', 'L12n2183', 'L12n2185', 'L12n2187', 'L12n2190', 'L12n2192', 'L12n2193', 'L12n2194', 'L12n2195', 'L12n2200', 'L12n2204', 'L12n2208', 'L12n2211', 'L12n2215', 'L12n2216', 'L12n2218', 'L12n2220', 'L12n2222', 'L12n2223', 'L12n2225', 'L12n2226', 'L12n2227', 'L12n2228', 'L12n2229', 'L12n2231', 'L12n2233', 'L12n2234', 'L12n2235', 'L12n2236', 'L12n2237', 'L12n2238', 'L12n2239', 'L12n2240', 'L12n2241', 'L12n2242', 'L12n2243', 'L12n2244', 'L12n2245', 'L12n2247', 'L12n2248', 'L12n2252', 'L12n2254', 'L13n4413']
len(QA)
Out[2]:
2752
In [3]:
QA=[snappy.Manifold(link) for link in QA]
In [4]:
def replace_strands(PD,sold,snew):
    '''Replaces the strand sold by the strand snew in the PD code.'''
    PD_new=PD.copy()
    PD_new=[tuple([snew if x==sold else x for x in c]) for c in PD]
    return PD_new 

def smoothings(PD,cros):
    '''
    Returns the smoothings of that crossing.
    '''
    (a,b,c,d)=cros
    PD_0=PD.copy()
    PD_0.remove(cros)
    PD_infty=PD.copy()
    PD_infty.remove(cros)
    PD_0=replace_strands(PD_0,b,a)
    PD_0=replace_strands(PD_0,d,c)
    PD_infty=replace_strands(PD_infty,d,a)
    PD_infty=replace_strands(PD_infty,c,b)
    return [PD_0,PD_infty]
    
def is_QA(D):
    '''
    Returns true if the diagram D is quasi-alternating and false if it is unclear.
    '''
    D.simplify('global')
    if D.is_alternating():
        return True
    if D.exterior() in QA:
        return True
    PD=D.PD_code()
    if len(PD)<13:
        return False
    det=D.determinant()
    for cros in PD:
        [PD0,PDinfty]=smoothings(PD,cros)
        L0=snappy.Link(PD0)
        Linfty=snappy.Link(PDinfty)
        try:
            det0=L0.determinant(method='goeritz')
        except ValueError:
            try:
                det0=L0.determinant(method='wirt')
            except ValueError:
                try:
                    det0=L0.determinant(method='color')
                except ValueError:
                    det0=0
        try:
            detinfty=Linfty.determinant(method='goeritz')
        except ValueError:
            try:
                detinfty=Linfty.determinant(method='wirt')
            except ValueError:
                try:
                    detinfty=Linfty.determinant(method='color')
                except ValueError:
                    detinffty=0
        if det0+detinfty==det:
            if is_QA(L0)==True:
                if is_QA(Linfty)==True:
                    return True
    return False

We know that:

v2871(2,1)=DBC(K14n8212)

t09882(-2,1)=DBC(K14n11995)

o9_32044(-3,1)=DBC(K15n42102)

o9_32964(-4,1)=DBC(Braid(-1, 2, -3, -3, 2, 4, 2, 5, 3, 3, -4, -3, 2, -3, -2, -4, -2, -5, 1, -2, 3, -4, 3, 2, 3))

We show that they are all QA.

In [5]:
is_QA(snappy.Link('K14n8212'))
Out[5]:
True
In [6]:
is_QA(snappy.Link('K14n11995'))
Out[6]:
True
In [7]:
word=[-1, -2, -2, -2, 3, 2, -4, -3, 5, 2, 4, 1, -3, -4, 3, -2, 3, -4, -5, 4, 3, 2, 3]
D=snappy.Link(braid_closure=word)
print(D.exterior().identify())

[K15n42102(0,0)]
In [8]:
D=snappy.Link('K15n42102')
In [9]:
is_QA(D)
Out[9]:
True
In [2]:
word=[-1, 2, -3, -3, 2, 4, 2, 5, 3, 3, -4, -3, 2, -3, -2, -4, -2, -5, 1, -2, 3, -4, 3, 2, 3]
D=snappy.Link(braid_closure=word)
print(D.exterior().identify())

[]
In [11]:
is_QA(D)
Out[11]:
True

We will identify this branching set as a 17-crossing knot in Burton's list.

In [3]:
D.simplify('global')
Out[3]:
True
In [4]:
D.sage_link().plot()
Out[4]:
In [5]:
D
Out[5]:
<Link: 1 comp; 17 cross>
In [6]:
D.simplify('global')
Out[6]:
False
In [9]:
E=D.exterior()
In [10]:
E.identify()
Out[10]:
[]
In [12]:
import snappy
import csv
import pickle
import time
In [13]:
def change_notation(dt_code):
    """
    Changes Dowker-Thistlewait notation from alphabetical to numerical
    Input:
        dt_code (string): alphabetical DT notation
    Return:
        (string): numerical DT notation
    """
    alpha = "abcdefghijklmnopqrstuvwxyz"
    Alpha = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    result = []
    for letter in dt_code:
        if letter in alpha:
            result.append(2* (alpha.index(letter) + 1))
        elif letter in Alpha:
            result.append(-2 * (Alpha.index(letter) + 1))
        else:
            print(dt_code)
    return "DT: " + str([tuple(result)])
In [20]:
start_time = time.time()
count=0
with open('17n-hyp.csv', 'r') as file:
    reader = csv.reader(file)
    for row in reader:
        try:
            K=snappy.Link(change_notation(row[2])).exterior()
            if K.is_isometric_to(E):
                print(K)
                print(row)
                break
        except IndexError:
            pass

print('Time taken: %s minutes ' % ((time.time() - start_time)/60))   

dt_code
unnamed link(0,0)
['17nh_0008151', 'rabcdbefghijklmnoeamhijgpqndcoqpfklllvlzfTEWEma', 'iMNgpJdloKEqCBhaf']
Time taken: 0.20573570330937704 minutes