  
  [1X3 [33X[0;0YUser Functions[133X[101X
  
  [33X[0;0Y[5XQaoS[105X  provides some user functions to obtain information from the databases.
  Currently,  we  support  queries  for transitive groups and algebraic number
  fields.  The  corresponding  commands  are  [2XQaosTransitiveGroup[102X  ([14X3.1-1[114X) and
  [2XQaosNumberField[102X ([14X3.1-2[114X).[133X
  
  
  [1X3.1 [33X[0;0YRetrieve objects matching a query[133X[101X
  
  [1X3.1-1 QaosTransitiveGroup[101X
  
  [29X[2XQaosTransitiveGroup[102X( [3Xquery[103X[, [3Xoptarg[103X] ) [32X function
  
  [33X[0;0YReturn transitive groups matching [3Xquery[103X. The amount of results is limited by
  the  global variable [2XQaosDefaultLimit[102X ([14X3.1-3[114X). Optional argument [3Xoptarg[103X is a
  record with some of the following components:[133X
  
  [30X    [33X[0;6Y[10XAction[110X (string)[133X
  
        [30X    [33X[0;12Ydetermine an action to perform on [3Xquery[103X[133X
  
        [30X    [33X[0;12Ydefault value: "query"[133X
  
        [30X    [33X[0;12Ypossible values: "query", "count"[133X
  
  [30X    [33X[0;6Y[10XColGroups[110X (list of strings)[133X
  
        [30X    [33X[0;12Ydetermine  which  result  groups  should be returned; results of
              [5XQaoS[105X  are  usually grouped by a so-called `column group'. In the
              web  interface these column groups are choosable by checking the
              corresponding name under the text field for the query.[133X
  
        [30X    [33X[0;12Ydefault value: ["size","props","perm-struct"][133X
  
        [30X    [33X[0;12Ypossible values: combinations of "size", "props", "perm-struct",
              "fp-struct"[133X
  
  [30X    [33X[0;6Y[10XLimit[110X (integer/string)[133X
  
        [30X    [33X[0;12Ydetermine how many results are retrieved (maximally)[133X
  
        [30X    [33X[0;12Ydefault value: [2XQaosDefaultLimit[102X ([14X3.1-3[114X)[133X
  
        [30X    [33X[0;12Ypossible values: any positive integer or "all"[133X
  
  [30X    [33X[0;6Y[10XOffset[110X (integer/string)[133X
  
        [30X    [33X[0;12Ydetermine  an  offset on the set of results, this may be used to
              sequentially retrieve blocks of results.[133X
  
        [30X    [33X[0;12Ydefault value: 0[133X
  
        [30X    [33X[0;12Ypossible values: any non-negative integer[133X
  
  [1X3.1-2 QaosNumberField[101X
  
  [29X[2XQaosNumberField[102X( [3Xquery[103X[, [3Xoptarg[103X] ) [32X function
  
  [33X[0;0YReturn number fields matching [3Xquery[103X. The amount of results is limited by the
  global  variable  [2XQaosDefaultLimit[102X  ([14X3.1-3[114X).  Optional  argument [3Xoptarg[103X is a
  record with some of the following components:[133X
  
  [30X    [33X[0;6Y[10XAction[110X (string)[133X
  
        [30X    [33X[0;12Ydetermine an action to perform on [3Xquery[103X[133X
  
        [30X    [33X[0;12Ydefault value: "query"[133X
  
        [30X    [33X[0;12Ypossible values: "query", "count"[133X
  
  [30X    [33X[0;6Y[10XColGroups[110X (list of strings)[133X
  
        [30X    [33X[0;12Ydetermine  which  result  groups  should be returned; results of
              [5XQaoS[105X  are  usually grouped by a so-called `column group'. In the
              web  interface these column groups are choosable by checking the
              corresponding name under the text field for the query.[133X
  
        [30X    [33X[0;12Ydefault value: ["size","struct","clsgroup","galgroup"][133X
  
        [30X    [33X[0;12Ypossible  values:  combinations of "size", "struct", "clsgroup",
              "galgroup", "galprops"[133X
  
  [30X    [33X[0;6Y[10XLimit[110X (integer/string)[133X
  
        [30X    [33X[0;12Ydetermine how many results are retrieved (maximally)[133X
  
        [30X    [33X[0;12Ydefault value: [2XQaosDefaultLimit[102X ([14X3.1-3[114X)[133X
  
        [30X    [33X[0;12Ypossible values: any positive integer or "all"[133X
  
  [30X    [33X[0;6Y[10XOffset[110X (integer/string)[133X
  
        [30X    [33X[0;12Ydetermine  an  offset on the set of results, this may be used to
              sequentially retrieve blocks of results.[133X
  
        [30X    [33X[0;12Ydefault value: 0[133X
  
        [30X    [33X[0;12Ypossible values: any non-negative integer[133X
  
  [1X3.1-3 QaosDefaultLimit[101X
  
  [29X[2XQaosDefaultLimit[102X[32X global variable
  
  [33X[0;0YAn  Integer or String. Determine the (maximal) amount of results returned in
  a  query.  Usually,  this  can  be  overridden  with  the [10XLimit[110X-component in
  optargs.  The  default value is 25. The value can be any positive integer or
  the  string  "all",  in  which  case  no  limit  is  set and all results are
  returned.  [13XCAUTION[113X:  Setting this variable to "all" may result in exhaustive
  use  of  memory,  network bandwidth, and time. Therefore, always consider to
  perform  the  count action on a query before loading all of the results. The
  database  of  number  fields  contains  more  than 1.35 million number field
  objects.  Downloading  them  all means retrieving a string of approx. 1.8 GB
  length!!![133X
  
  [33X[0;0YThe  following  examples  show  their  usage: Query for transitive groups of
  degree 4.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XQaosTransitiveGroup("d4");[127X[104X
    [4X[28X#I Retrieved 5 Transitive Groups.[128X[104X
    [4X[28X#I (C) 2004-2005 QaoS developers <kantdb@math.tu-berlin.de>,[128X[104X
    [4X[28X#I The Kant Project <kant@math.tu-berlin.de>[128X[104X
    [4X[28X#I qaos--dev--1.0--patch-32[128X[104X
    [4X[28X#I 2005-08-29 07:54:18 UTC[128X[104X
    [4X[28X<collection from database: 5 transitive groups; "d4">[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YCount transitive groups of degree 8.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XQaosTransitiveGroup("d8",rec(Action:="count"));[127X[104X
    [4X[28X#I (C) 2004-2005 QaoS developers <kantdb@math.tu-berlin.de>,[128X[104X
    [4X[28X#I The Kant Project <kant@math.tu-berlin.de>[128X[104X
    [4X[28X#I qaos--dev--1.0--patch-33[128X[104X
    [4X[28X#I 2005-08-29 10:04:49 UTC[128X[104X
    [4X[28X50 transitive group satisfy "d8"[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YRetrieve the first 25 transitive groups of degree 8.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27Xq1:=QaosTransitiveGroup("d8");[127X[104X
    [4X[28X#I Retrieved 25 Transitive Groups.[128X[104X
    [4X[28X#I (C) 2004-2005 QaoS developers <kantdb@math.tu-berlin.de>,[128X[104X
    [4X[28X#I The Kant Project <kant@math.tu-berlin.de>[128X[104X
    [4X[28X#I qaos--dev--1.0--patch-33[128X[104X
    [4X[28X#I 2005-08-29 10:08:50 UTC[128X[104X
    [4X[28X<collection from database: 25 transitive groups; "d8">[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YNow retrieve the next 25 results.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27Xq2:=QaosTransitiveGroup("d8",rec(Offset:=25));[127X[104X
    [4X[28X#I Retrieved 25 Transitive Groups.[128X[104X
    [4X[28X#I (C) 2004-2005 QaoS developers <kantdb@math.tu-berlin.de>,[128X[104X
    [4X[28X#I The Kant Project <kant@math.tu-berlin.de>[128X[104X
    [4X[28X#I qaos--dev--1.0--patch-33[128X[104X
    [4X[28X#I 2005-08-29 10:09:41 UTC[128X[104X
    [4X[28X<collection from database: 25 transitive groups; "d8">[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YRetrieve number fields of degree 4.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XQaosNumberField("d4");[127X[104X
    [4X[28X#I Retrieved 25 Algebraic Number Fields.[128X[104X
    [4X[28X#I (C) 2004-2005 QaoS developers <kantdb@math.tu-berlin.de>,[128X[104X
    [4X[28X#I The Kant Project <kant@math.tu-berlin.de>[128X[104X
    [4X[28X#I qaos--dev--1.0--patch-32[128X[104X
    [4X[28X#I 2005-08-29 07:55:11 UTC[128X[104X
    [4X[28X<collection from database: 25 number fields; "d4">[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YWhen  either  of these functions is called with no arguments a short general
  help is displayed:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XQaosTransitiveGroup();[127X[104X
    [4X[28XQaosTransitiveGroup(<query> [, <optarg>]) -> <result>[128X[104X
    [4X[28X [128X[104X
    [4X[28XSearches the Algebraic Objects Database in Berlin.[128X[104X
    [4X[28XThe query string equals the keyword search method in the web surface.[128X[104X
    [4X[28XSee[128X[104X
    [4X[28X<URL>http://qaos.math.tu-berlin.de/qaos/query.scm?type=trnsg&action=Help</URL>[128X[104X
    [4X[28Xfor more information about the syntax and keywords.[128X[104X
    [4X[28X [128X[104X
    [4X[28XNote: You must have `curl' (see <URL>http://curl.haxx.se</URL>) installed and properly[128X[104X
    [4X[28Xconfigured in order to use &QaoS; from within &GAP;.[128X[104X
    [4X[28X [128X[104X
    [4X[28Xtrue[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YIn  this  manual  we  also  refer to the help screen of the web interface to
  obtain more detailed information about the query string.[133X
  
  
  [1X3.2 [33X[0;0YExamine the contents of a database collection[133X[101X
  
  [33X[0;0YIn  order  to  actually  see  the  information  there  is  a function called
  [2XQaosResult[102X ([14X3.2-2[114X) which displays a list of retrieved objects.[133X
  
  [1X3.2-1 QaosResult[101X
  
  [29X[2XQaosResult[102X( [3Xdatabase-collection[103X ) [32X function
  
  [33X[0;0YReturn  the  list of retrieved objects in [3Xdatabase-collection[103X. This function
  actually reveals the result of a query.[133X
  
  [1X3.2-2 QaosResult[101X
  
  [29X[2XQaosResult[102X( [3Xdatabase-count[103X ) [32X function
  
  [33X[0;0YReturn  the (non-negative) integer of a count query (see [10XAction[110X-component in
  optarg record).[133X
  
  [33X[0;0YLet  us  examine  the  groups behind a query for degree 8 abelian transitive
  groups.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XQ:=QaosTransitiveGroup("d8 abelian");[127X[104X
    [4X[28X#I Retrieved 3 Transitive Groups.[128X[104X
    [4X[28X#I (C) 2004-2005 QaoS developers <kantdb@math.tu-berlin.de>,[128X[104X
    [4X[28X#I The Kant Project <kant@math.tu-berlin.de>[128X[104X
    [4X[28X#I qaos--dev--1.0--patch-32[128X[104X
    [4X[28X#I 2005-08-29 08:01:30 UTC[128X[104X
    [4X[28X<collection from database: 3 transitive groups; "d8 abelian">[128X[104X
    [4X[28Xgap>[128X[104X
    [4X[25Xgap>[125X [27XQaosResult(Q);[127X[104X
    [4X[28X[ <transitive group from database: C(8) = 8; id 39>,[128X[104X
    [4X[28X  <transitive group from database: 4[x]2; id 40>,[128X[104X
    [4X[28X  <transitive group from database: E(8) = 2[x]2[x]2; id 41> ][128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YTo  use  the  retrieved group objects in [5XGAP[105X you may use the [2XAsGroup[102X ([14X3.2-3[114X)
  operation on a result.[133X
  
  [1X3.2-3 AsGroup[101X
  
  [29X[2XAsGroup[102X( [3Xdatabase-group-object[103X ) [32X function
  
  [33X[0;0YReturn   the   [5XGAP[105X   group  object  representing  [3Xdatabase-group-object[103X.  If
  [3Xdatabase-group-object[103X cannot be turned into a group, return [9Xfail[109X.[133X
  
  [33X[0;0YFrom the above example, let us [5XGAP[105X-ify the third group object.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XAsGroup(QaosResult(Q)[3]);[127X[104X
    [4X[28XGroup([ (1,8)(2,3)(4,5)(6,7), (1,3)(2,8)(4,6)(5,7), (1,5)(2,6)(3,7)(4,8) ])[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YFor number field objects the corresponding operation is [2XAsField[102X ([14X3.2-4[114X).[133X
  
  [1X3.2-4 AsField[101X
  
  [29X[2XAsField[102X( [3Xdatabase-field-object[103X ) [32X function
  
  [33X[0;0YReturn   the   [5XGAP[105X   field  object  representing  [3Xdatabase-field-object[103X.  If
  [3Xdatabase-field-object[103X cannot be turned into a field, return [9Xfail[109X.[133X
  
  [33X[0;0YConsider following example for number fields (number fields of degree 5 with
  absolute discrimnant between 100000 and 120000 and non-trivial class group):[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XR:=QaosNumberField("d5 |disc| >=100000 |disc| <=120000 cn>1");[127X[104X
    [4X[28X#I Retrieved 18 Algebraic Number Fields.[128X[104X
    [4X[28X#I (C) 2004-2005 QaoS developers <kantdb@math.tu-berlin.de>,[128X[104X
    [4X[28X#I The Kant Project <kant@math.tu-berlin.de>[128X[104X
    [4X[28X#I qaos--dev--1.0--patch-32[128X[104X
    [4X[28X#I 2005-08-29 08:32:35 UTC[128X[104X
    [4X[28X<collection from database: 18 number fields; "d5 |disc| >=100000 |disc| <=120000 cn>1">[128X[104X
    [4X[25Xgap>[125X [27XQaosResult(R);[127X[104X
    [4X[28X[ <number field from database: x_1^5+x_1^4-2*x_1^2+7*x_1+1; id 843712>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4+2*x_1^3-4*x_1^2+2*x_1-1; id 843791>,[128X[104X
    [4X[28X  <number field from database: x_1^5+2*x_1^4-2*x_1^3+2*x_1^2+x_1+4; id 843841>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4+4*x_1^3+4*x_1-1; id 843892>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4+x_1^3+4*x_1^2+3*x_1-1; id 843894>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4-3*x_1^3-2*x_1^2+6*x_1-4; id 843897>,[128X[104X
    [4X[28X  <number field from database: x_1^5+2*x_1^3+2*x_1^2+4*x_1+1; id 843930>,[128X[104X
    [4X[28X  <number field from database: x_1^5+2*x_1^4+6*x_1^3+4*x_1^2+4*x_1-1; id 843955>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4-4*x_1^2+2*x_1+1; id 844004>,[128X[104X
    [4X[28X  <number field from database: x_1^5+4*x_1^2+1; id 844011>,[128X[104X
    [4X[28X  <number field from database: x_1^5+2*x_1^4+3*x_1^3+2*x_1^2-3*x_1+1; id 844036>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4+3*x_1^3+2*x_1^2+8*x_1-1; id 844043>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4+5*x_1^3+5*x_1^2+2*x_1+1; id 844062>,[128X[104X
    [4X[28X  <number field from database: x_1^5+2*x_1^4-3*x_1^3+6*x_1^2-3*x_1+1; id 844066>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4-x_1^3-4*x_1^2+5*x_1-1; id 844082>,[128X[104X
    [4X[28X  <number field from database: x_1^5+2*x_1^4-x_1^3-3*x_1^2+4*x_1+1; id 844107>,[128X[104X
    [4X[28X  <number field from database: x_1^5+x_1^4+2*x_1^3+3*x_1^2-2*x_1+1; id 844110>,[128X[104X
    [4X[28X  <number field from database: x_1^5+2*x_1^4-6*x_1^3+5*x_1^2-2*x_1+1; id 844145> ][128X[104X
    [4X[25Xgap>[125X [27XAsField(QaosResult(R)[4]);[127X[104X
    [4X[28X<field in characteristic 0>[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
