# GAP code for the lmfdb family of higher genus curves 8.5-1.0.5-5-5-5-5-5 # 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:=[5,1]; signature:=[0,5,5,5,5,5,5]; genus:=8; r:=Length(signature)-1; g0:=signature[1]; dim:=3*g0-3+r; # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [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:=1; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [4, 5, 1, 2, 3], [4, 5, 1, 2, 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:=2; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [4, 5, 1, 2, 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:=3; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [5, 1, 2, 3, 4], [5, 1, 2, 3, 4], [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:=4; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [3, 4, 5, 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:=5; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [4, 5, 1, 2, 3], [5, 1, 2, 3, 4], [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:=6; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [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:=7; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [5, 1, 2, 3, 4], [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:=8; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [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:=9; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [4, 5, 1, 2, 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:=10; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[2, 3, 4, 5, 1], [4, 5, 1, 2, 3], [5, 1, 2, 3, 4], [5, 1, 2, 3, 4], [5, 1, 2, 3, 4], [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:=11; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [4, 5, 1, 2, 3], [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:=12; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [4, 5, 1, 2, 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:=13; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[3, 4, 5, 1, 2], [3, 4, 5, 1, 2], [5, 1, 2, 3, 4], [5, 1, 2, 3, 4], [5, 1, 2, 3, 4], [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:=14; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[3, 4, 5, 1, 2], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [5, 1, 2, 3, 4], [5, 1, 2, 3, 4], [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:=15; gen_vect_label:=1; is_hyperelliptic:=false; 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) ); # Here we add an action to data. gen_vectors:=[[4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [4, 5, 1, 2, 3], [5, 1, 2, 3, 4], [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:=16; gen_vect_label:=1; is_hyperelliptic:=false; 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) );