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Maple interface to the QaoS databases
by Sebastian Freundt and Sebastian Pauli 

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# Maple interface to the QaoS databases
module Qaos( )

   # QaosNumberField(query::string [,limit::integer])::list(qaosnumberfield)
   # QaosNumberField([limit::integer])::list(qaosnumberfield)
   #  

   # Searches the KANT number field database in Berlin. Returns at most
   # 'limit' matches. The string 'query' is made up of terms of the form
   # invariant=value, where invariant is one of:
   #
   # degree or deg,
   # classnumber or classnum or class,
   # real signature or sig-real or rsig,
   # imaginary signature or sig-im or isig,
   # discriminant or disc,
   # regulator or reg, or
   # galoisgroup or galgrp.
   #
   # If value is a number then >, <, >=,, <= or <> can be used instead of =.
   # You can omit the relation if you want it to be =. The Galois group may be
   # enclosed in single quotes, e.g. galoisgroup='S5' or galgrp is 's5'.
   # Several terms are implied to be connected by AND, e.g. degree=3 cls 2
   # |disc| <= 9876.
   #
   # Called without an argument NumberFieldQuery returns more fields matching
   # the previous search query.
   #
   # The procedure DefiningPolynomial returns a defining polynomial of a
   # field. The invariants of the returned fields can be accessed withh the
   # procedure: ClassGroup, ClassNumber, Degree, Discriminant, GaloisGroup,
   # Regulator, Signature
   #
   # Properties of the Galois group can be obtained with the procedures:
   # IsAbelian, IsMetaAbelian, IsSimple, IsSolvable, IsSuperSolvable,
   # IsCyclic, IsPrimitive, IsNilpotent
   #
   # You must have 'curl' installed and properly configured in order to use
   # the database.
   QaosNumberField( )

   # The defining polynomial of a number field from the KANT database.
   DefiningPolynomial( q::qaosnumberfield )

   # The regulator of a number field from the KANT database.
   Regulator( q::qaosnumberfield )

   # A name of the Galois group of a number field from the KANT database.
   GaloisGroup( q::qaosnumberfield )

   # The signature [r_1,r_2] of a number field from the KANT database.
   Signature( q::qaosnumberfield )

   Degree( )

   # The discriminant of a number field from the KANT database.
   Discriminant( q::qaosnumberfield )

   # The class number of a number field from the KANT database.
   ClassNumber( q::qaosnumberfield )

   # The class group of a number field from the KANT database.
   ClassGroup( q::qaosnumberfield )

   # QaosTransitiveGroup(query::string[,limit::integer])::list(qaostransitivegroup)
   # QaosTransitiveGroup([limit::integer])::list(qaostransitivegroup)
   #
   # Searches the QaoS transitive group database in Berlin. Returns at most
   # 'limit' matches. The string 'query' is made up of terms of the form
   # invariant=value, where invariant is one of:
   #
   # Keywords with integer values, Syntax: keyword integer
   #
   # d, deg, degr, degree: The degree of the transitive group
   # o, ord, order: The order of the transitive group
   # of, ord fac, order factor: A factor of the order of the transitive group
   # n, num, numb: The number of the transitive group in the tn nomenclature
   # csl, compser len, compseries length: The length of the composition series
   # lcsl, lcentser len, lowercentralseries length: The length of the lower
   # central series
   #
   # Keywords with string values, Syntax: keyword 'string'
   #
   # name: The name of the transitive group, either a trivial name or a name
   # in the tn nomenclature
   #
   # Keywords with boolean values, Syntax: keyword | not keyword
   #
   # a ab abel abelian: The abelian property of the group
   # ma metab metabel metabelian: The metabelian property of the group
   # c cyc cyclic: The cyclic property of the group
   # p pr prim primitive: The primitive property of the group
   # si sim simp simple: The simple property of the group
   # s sol solv solvable: The solvable property of the group
   # ss supsol supsolv supersolvable: The supersolvable property of the group
   # np nilp nilpot nilpotent: The nilpotent property of the group
   #
   # If value is a number then >, <, >=, <= or != can be used instead of =.
   # You can omit the relation if you want it to be =.
   #
   # Called without an argument QaosTransitiveGroup returns more groups
   # matching the previous search query.
   #
   # The procedure PermutationGroup converts groups from the database to
   # permutation groups. The invariants of the returned groups can be accessed
   # withh the procedure: GroupOrder, IsAbelian, IsMetaAbelian, IsSimple,
   # IsSolvable, IsSuperSolvable, IsCyclic, IsPrimitive, IsNilpotent,
   # TransitiveGroupIdentification, LengthCompositionSeries.
   #
   # You must have 'curl' installed and properly configured in order to use
   # the database.
   QaosTransitiveGroup( )

   # Convert a transitive group from the QaoS database into a permutation
   # group.
   PermutationGroup( q::qaostransitivegroup )

   GroupOrder( q::qaostransitivegroup )

   IsAbelian( )

   IsMetaAbelian( )

   IsSimple( )

   IsSolvable( )

   IsSuperSolvable( )

   IsCyclic( )

   IsPrimitive( )

   IsNilpotent( )

   LengthCompositionSeries( q::qaostransitivegroup )

   TransitiveGroupIdentification( q::qaostransitivegroup )

   LengthLowerCentralSeries( q::qaostransitivegroup )

 

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