# GAP code for the lmfdb family of higher genus curves 4.32-19.0.2-4-16 # The results are stored in a list of records called 'data' # WARNING: The conjugacy class numbers may not be the same as those listed in lmfdb.org, as numberings in Magma and GAP may differ. If you need to connect this data to that posted on lmfdb.org, compare the variables 'passport_label' and 'gen_vector_labels'. data:=[]; # Generate data which is the same for all entries. gp_id:=[32,19]; signature:=[0,2,4,16]; genus:=4; r:=Length(signature)-1; g0:=signature[1]; dim:=3*g0-3+r; # Here we add an action to data. gen_vectors:=[[9, 10, 12, 11, 15, 16, 13, 14, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [18, 17, 19, 20, 24, 23, 22, 21, 30, 29, 31, 32, 26, 25, 27, 28, 1, 2, 4, 3, 7, 8, 5, 6, 13, 14, 16, 15, 9, 10, 12, 11], [25, 26, 27, 28, 29, 30, 31, 32, 23, 24, 22, 21, 17, 18, 19, 20, 10, 9, 12, 11, 14, 13, 16, 15, 8, 7, 5, 6, 2, 1, 4, 3]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=1; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=PermList([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]); is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list,genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal) ); # Here we add an action to data. gen_vectors:=[[9, 10, 12, 11, 15, 16, 13, 14, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [19, 20, 17, 18, 22, 21, 23, 24, 31, 32, 29, 30, 27, 28, 25, 26, 4, 3, 2, 1, 5, 6, 8, 7, 16, 15, 14, 13, 12, 11, 10, 9], [27, 28, 26, 25, 31, 32, 30, 29, 22, 21, 24, 23, 19, 20, 18, 17, 12, 11, 9, 10, 16, 15, 13, 14, 5, 6, 7, 8, 4, 3, 1, 2]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=2; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=PermList([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]); is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list,genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal) ); # Here we add an action to data. gen_vectors:=[[9, 10, 12, 11, 15, 16, 13, 14, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [17, 18, 20, 19, 23, 24, 21, 22, 29, 30, 32, 31, 25, 26, 28, 27, 2, 1, 3, 4, 8, 7, 6, 5, 14, 13, 15, 16, 10, 9, 11, 12], [26, 25, 28, 27, 30, 29, 32, 31, 24, 23, 21, 22, 18, 17, 20, 19, 9, 10, 11, 12, 13, 14, 15, 16, 7, 8, 6, 5, 1, 2, 3, 4]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=3; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=PermList([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]); is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list,genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal) ); # Here we add an action to data. gen_vectors:=[[9, 10, 12, 11, 15, 16, 13, 14, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [20, 19, 18, 17, 21, 22, 24, 23, 32, 31, 30, 29, 28, 27, 26, 25, 3, 4, 1, 2, 6, 5, 7, 8, 15, 16, 13, 14, 11, 12, 9, 10], [28, 27, 25, 26, 32, 31, 29, 30, 21, 22, 23, 24, 20, 19, 17, 18, 11, 12, 10, 9, 15, 16, 14, 13, 6, 5, 8, 7, 3, 4, 2, 1]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=4; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=PermList([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]); is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list,genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal) );