  
  [1X2 [33X[0;0YThe families of Lie algebras included in the database[133X[101X
  
  [33X[0;0YHere  we  describe  the  functions  that  access  the classifications of Lie
  algebras  that  are stored in the package. A function below either returns a
  single  Lie  algebra, depending on a list of parameters, or a collection. It
  is  important  to note that two calls of the function [3XNonSolvableLieAlgebra[103X,
  [3XSolvableLieAlgebra[103X,   or   [3XNilpotentLieAlgebra[103X  may  return  isomorphic  Lie
  algebras  even  if  the parameters are different (see the description of the
  parameter  list  for  each  of  the functions). If, however, the output of a
  function  is  a collection, then the members of this collection are pairwise
  non-isomorphic.[133X
  
  [33X[0;0YThe  Lie  algebras  in  the  database  are  stored  in the form of structure
  constant  tables.  Usually  the  size  of  a  family  of Lie algebras in the
  database  is  small  enough  so  that  the entries of the structure constant
  tables  can  be  stored  without  any  compression.  However  the  number of
  nilpotent  Lie  algebras with dimension at least 7 is very large, and so the
  structure  constant  tables  are  compressed  as follows. If [23XL[123X is such a Lie
  algebra,   then  we  fix  a  basis  [23XB=\{b_1,\ldots,b_n\}[123X  and  consider  the
  coefficients  of  the  products  [23X[b_i,b_j][123X  where  [23Xj>i[123X. We concatenate these
  coefficient sequences and consider the long sequence so obtained as a number
  written  in base [23Xp[123X. Then we convert this number to base 62 and write it down
  using  the digits [23X0,\ldots,9,a\ldots,z,A\ldots,Z[123X. Then this string is stored
  in    the   files   [3Xgap/nilpotent/nilpotent_data*.gi[103X.   See   the   function
  [3XReadStringToNilpotentLieAlgebra[103X  in  the file [3Xgap/nilpotent/nilpotent.gi[103X for
  the precise details.[133X
  
  
  [1X2.1 [33X[0;0YNon-solvable Lie algebras[133X[101X
  
  [33X[0;0YThe  package  contains  the  list  of  non-solvable Lie algebras over finite
  fields up to dimension 6. The classification follows the one in [Str].[133X
  
  [1X2.1-1 NonSolvableLieAlgebra[101X
  
  [33X[1;0Y[29X[2XNonSolvableLieAlgebra[102X( [3XF[103X, [3Xpars[103X ) [32X method[133X
  
  [33X[0;0Y[3XF[103X  is  an  arbitrary  finite field, [3Xpars[103X is a list of parameters with length
  between  1  and 4. The output is a non-solvable Lie algebra corresponding to
  the  parameters,  which  is displayed as a string that describes the algebra
  following  [Str].  The  first entry of [3Xpars[103X is the dimension of the algebra,
  and  the  possible  additional entries of [3Xpars[103X describe the algebra if there
  are more algebras with dimension [3Xpars[1][103X.[133X
  
  [33X[0;0YThe possible values of [3Xpars[103X are as follows.[133X
  
  
  [1X2.1-2 [33X[0;0YDimension 1 and 2[133X[101X
  
  [33X[0;0YThere are no non-solvable Lie algebras with dimension less than 3, and so if
  [3Xpars[1][103X is less than 3 then [3XNonSolvableLieAlgebra[103X returns an error message.[133X
  
  
  [1X2.1-3 [33X[0;0YDimension 3[133X[101X
  
  [33X[0;0YThere  is just one non-solvable Lie algebra over an arbitrary finite field [3XF[103X
  (see Section [14X3.2[114X) which is returned by [3XNonSolvableLieAlgebra( F, [3] )[103X.[133X
  
  
  [1X2.1-4 [33X[0;0YDimension 4[133X[101X
  
  [33X[0;0YIf  [3XF[103X has odd characteristic then there is a unique non-solvable Lie algebra
  with    dimension   4   over   [3XF[103X   and   this   algebra   is   returned   by
  [3XNonSolvableLieAlgebra(  F,  [4] )[103X. If [3XF[103X has characteristic 2, then there are
  two distinct Lie algebras and they are returned by [3XNonSolvableLieAlgebra( F,
  [4,i] )[103X for [3Xi=1, 2[103X. See Section [14X3.3[114X for a description of the algebras.[133X
  
  
  [1X2.1-5 [33X[0;0YDimension 5[133X[101X
  
  [33X[0;0YIf  [3XF[103X  has  characteristic  2  then  there  are  5  isomorphism  classes  of
  non-solvable  Lie  algebras  over [3XF[103X and they are described in Section [14X3.4-1[114X.
  The possible values of [3Xpars[103X are as follows.[133X
  
  [30X    [33X[0;6Y[3X[5,1][103X: the Lie algebra in [14X3.4-1[114X(1).[133X
  
  [30X    [33X[0;6Y[3X[5,2,i][103X: [3Xi=0, 1[103X; the Lie algebras in [14X3.4-1[114X(2).[133X
  
  [30X    [33X[0;6Y[3X[5,3,i][103X: [3Xi=0, 1[103X; the Lie algebras in [14X3.4-1[114X(3).[133X
  
  [33X[0;0YIf  the  characteristic  of  [3XF[103X  is  odd, then the list of Lie algebras is as
  follows (see Section [14X3.4-2[114X).[133X
  
  [30X    [33X[0;6Y[3X[5,1,i][103X: [3Xi=1, 0[103X; the Lie algebras that occur in [14X3.4-2[114X(1).[133X
  
  [30X    [33X[0;6Y[3X[5,2][103X: the Lie algebra in [14X3.4-2[114X(2).[133X
  
  [30X    [33X[0;6Y[3X[5,3][103X:  this algebra only exists if the characteristic of [3XF[103X is 3 or 5.
        In  the  former  case the algebra is the one in [14X3.4-2[114X(3), while in the
        latter it is in [14X3.4-2[114X(4).[133X
  
  
  [1X2.1-6 [33X[0;0YDimension 6[133X[101X
  
  [33X[0;0YThe 6-dimensional non-solvable Lie algebras are described in Section [14X3.5[114X. If
  [3XF[103X has characteristic 2, then the possible values of [3Xpars[103X is as follows.[133X
  
  [30X    [33X[0;6Y[3X[6,1][103X: the Lie algebra in [14X3.5-1[114X(1).[133X
  
  [30X    [33X[0;6Y[3X[6,2][103X: the Lie algebra in [14X3.5-1[114X(2).[133X
  
  [30X    [33X[0;6Y[3X[6,3,i][103X: [3Xi=0, 1[103X; the two Lie algebras [14X3.5-1[114X(3).[133X
  
  [30X    [33X[0;6Y[3X[6,4,x][103X:  [3Xx=0,  1,  2,  3[103X  or  [3Xx[103X  is  a  field  element.  In this case
        [3XAllNonSolvableLieAlgebras[103X returns one of the Lie algebras in [14X3.5-1[114X(4).
        If  [3Xx=0,  1,  2,  3[103X then the Lie algebra corresponding to the [3X(x+1)[103X-th
        matrix  of  [14X3.5-1[114X(4)  is returned. If [3Xx[103X is a field element, then a Lie
        algebra is returned which corresponds to the 5th matrix in [14X3.5-1[114X(4).[133X
  
  [30X    [33X[0;6Y[3X[6,5][103X: the Lie algebra in [14X3.5-1[114X(5).[133X
  
  [30X    [33X[0;6Y[3X[6,6,1],  [6,6,2], [6,6,3,x], [6,6,4,x][103X: [3Xx[103X is a field element; the Lie
        algebras  in  [14X3.5-1[114X(6). The third and fourth entries of [3Xpars[103X determine
        the  isomorphism  type  of the radical as a solvable Lie algebra. More
        precisely, if the third argument [3Xpars[3][103X is 1 or 2 then the radical is
        isomorphic  to  [3XSolvableLieAlgebra(  F,[3,pars[3]]  )[103X.  If  the  third
        argument  [3Xpars[3][103X  is  3  or  4  then  the  radical  is  isomorphic to
        [3XSolvableLieAlgebra(  F,[3,pars[3],pars[4]]  )[103X;  see [2XSolvableLieAlgebra[102X
        ([14X2.2-1[114X).[133X
  
  [30X    [33X[0;6Y[3X[6,7][103X: the Lie algebra in [14X3.5-1[114X(7).[133X
  
  [30X    [33X[0;6Y[3X[6,8][103X: the Lie algebra in [14X3.5-1[114X(8).[133X
  
  [33X[0;0YIf  the characteristic of [3XF[103X is odd, then the possible values of [3Xpars[103X are the
  following (see Sections [14X3.5-2[114X, [14X3.5-3[114X, and [14X3.5-4[114X).[133X
  
  [30X    [33X[0;6Y[3X[6,1][103X: the Lie algebra in [14X3.5-2[114X(1).[133X
  
  [30X    [33X[0;6Y[3X[6,2][103X: the Lie algebra in [14X3.5-2[114X(2).[133X
  
  [30X    [33X[0;6Y[3X[6,3,1],  [6,3,2], [6,3,3,x], [6,3,4,x][103X: [3Xx[103X is a field element; the Lie
        algebras  in  [14X3.5-2[114X(3). The third and fourth entries of [3Xpars[103X determine
        the  isomorphism  type  of the radical as a solvable Lie algebra. More
        precisely, if the third argument [3Xpars[3][103X is 1 or 2 then the radical is
        isomorphic  to  [3XSolvableLieAlgebra(  F,[3,pars[3]]  )[103X.  If  the  third
        argument  [3Xpars[3][103X  is  3  or  4  then  the  radical  is  isomorphic to
        [3XSolvableLieAlgebra(  F,[3,pars[3],pars[4]]  )[103X;  see [2XSolvableLieAlgebra[102X
        ([14X2.2-1[114X).[133X
  
  [30X    [33X[0;6Y[3X[6,4][103X: the Lie algebra in [14X3.5-2[114X(4).[133X
  
  [30X    [33X[0;6Y[3X[6,5][103X: the Lie algebra in [14X3.5-2[114X(5).[133X
  
  [30X    [33X[0;6Y[3X[6,6][103X: the Lie algebra in [14X3.5-2[114X(6).[133X
  
  [30X    [33X[0;6Y[3X[6,7][103X: the Lie algebra in [14X3.5-2[114X(7).[133X
  
  [33X[0;0YIf  the  characteristic  is  3  or  5 then there are additional families. In
  characteristic 3, these families are as follows.[133X
  
  [30X    [33X[0;6Y[3X[6,8,x][103X:  [3Xx[103X  is  a  field  element; returns one of the Lie algebras in
        [14X3.5-3[114X(1).[133X
  
  [30X    [33X[0;6Y[3X[6,9][103X: the Lie algebra in [14X3.5-3[114X(2).[133X
  
  [30X    [33X[0;6Y[3X[6,10][103X: the Lie algebra in [14X3.5-3[114X(3).[133X
  
  [30X    [33X[0;6Y[3X[6,11,i][103X: [3Xi=0, 1[103X; one of the two Lie algebras in [14X3.5-3[114X(4).[133X
  
  [30X    [33X[0;6Y[3X[6,12][103X: the first Lie algebra in [14X3.5-3[114X(5).[133X
  
  [30X    [33X[0;6Y[3X[6,13][103X: the second Lie algebra [14X3.5-3[114X(5).[133X
  
  [33X[0;0YIf  the  characteristic  is  5,  then  the  additional  Lie algebras are the
  following.[133X
  
  [30X    [33X[0;6Y[3X[6,8][103X: the Lie algebra in [14X3.5-4[114X(1).[133X
  
  [30X    [33X[0;6Y[3X[6,9][103X: the Lie algebra in [14X3.5-4[114X(2).[133X
  
  [1X2.1-7 AllNonSolvableLieAlgebras[101X
  
  [33X[1;0Y[29X[2XAllNonSolvableLieAlgebras[102X( [3XF[103X, [3Xdim[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XF[103X  is an arbitrary finite field, and [3Xdim[103X is at most 6. A collection is
  returned   whose   members   form   a   complete  and  irredundant  list  of
  representatives  of  the  isomorphism types of the non-solvable Lie algebras
  over  [3XF[103X with dimension [3Xdim[103X. In order to obtain the algebras contained in the
  collection,  one  can  use  the  functions  [3XAsList[103X, [3XEnumerator[103X, [3XIterator[103X, as
  illustrated by the following example.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XL := AllNonSolvableLieAlgebras( GF(4), 4 );[127X[104X
    [4X[28X<Collection of nonsolvable Lie algebras with dimension 4 over GF(2^2)>[128X[104X
    [4X[25Xgap>[125X [27X e := Enumerator( L );[127X[104X
    [4X[28X<enumerator>[128X[104X
    [4X[25Xgap>[125X [27Xfor i in e do Print( Dimension( LieSolvableRadical( i )), "\n" ); od;[127X[104X
    [4X[28X0[128X[104X
    [4X[28X1[128X[104X
    [4X[25Xgap>[125X [27XAsList( L );[127X[104X
    [4X[28X[ W(1;2), W(1;2)^{(1)}+GF(4) ][128X[104X
    [4X[25Xgap>[125X [27XDimension( LieCenter( last[2] ));[127X[104X
    [4X[28X1[128X[104X
  [4X[32X[104X
  
  [33X[0;0YAs  the  output  of  [3XAllNonSolvableLieAlgebras[103X is a collection, the user can
  efficiently  access  the  classification  of  [23Xd[123X-dimensional non-solvable Lie
  algebras  over  a  given  field, even if the classification contains a large
  number  of algebras. For instance, there are 95367431640638 non-solvable Lie
  algebras  over  [23XGF(5^{20})[123X. Clearly one cannot expect to be able to handle a
  list  containing  all  these algebras; it is, however, possible to work with
  the collection of these Lie algebras, as follows.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XL := AllNonSolvableLieAlgebras( GF(5^20), 6 );[127X[104X
    [4X[28X<Collection of nonsolvable Lie algebras with dimension 6 over GF(5^20)>[128X[104X
    [4X[25Xgap>[125X [27Xe := Enumerator( L );[127X[104X
    [4X[28X<enumerator>[128X[104X
    [4X[25Xgap>[125X [27XLength( last );[127X[104X
    [4X[28X95367431640638[128X[104X
    [4X[25Xgap>[125X [27XDimension( LieDerivedSubalgebra( e[462468528345] ));[127X[104X
    [4X[28X5[128X[104X
  [4X[32X[104X
  
  [33X[0;0YWe  note  that  we  could  not  enumerate  the  non-solvable Lie algebras of
  dimension  6  over  finite  fields  of characteristic 3, and so the function
  [3XEnumerator[103X  cannot  be  used  in  that  context.  You  can, however, use the
  functions [3XIterator[103X and [3XAsList[103X as follows.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XL := AllNonSolvableLieAlgebras( GF(3), 6 );[127X[104X
    [4X[28X<Collection of nonsolvable Lie algebras with dimension 6 over GF(3)>[128X[104X
    [4X[25Xgap>[125X [27X e := Iterator( L );[127X[104X
    [4X[28X<iterator>[128X[104X
    [4X[25Xgap>[125X [27Xdims := [];;[127X[104X
    [4X[25Xgap>[125X [27Xfor i in e do Add( dims, Dimension( LieSolvableRadical( i ))); od;[127X[104X
    [4X[25Xgap>[125X [27Xdims;[127X[104X
    [4X[28X[ 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ][128X[104X
    [4X[25Xgap>[125X [27XAsList( L );[127X[104X
    [4X[28X[ sl(2,3)+sl(2,3), sl(2,GF(9)), sl(2,3)+solv([ 1 ]), sl(2,3)+solv([ 2 ]), [128X[104X
    [4X[28X  sl(2,3)+solv([ 3, 0*Z(3) ]), sl(2,3)+solv([ 3, Z(3)^0 ]), [128X[104X
    [4X[28X  sl(2,3)+solv([ 3, Z(3) ]), sl(2,3)+solv([ 4, 0*Z(3) ]), [128X[104X
    [4X[28X  sl(2,3)+solv([ 4, Z(3) ]), sl(2,3)+solv([ 4, Z(3)^0 ]), sl(2,3):(V(1)+V(0)),[128X[104X
    [4X[28X  sl(2,3):V(2), sl(2,3):H, sl(2,3):<x,y,z|[x,y]=y,[x,z]=z>, [128X[104X
    [4X[28X  sl(2,3):V(2,0*Z(3)), sl(2,3):V(2,Z(3)), W(1;1):O(1;1), W(1;1):O(1;1)*, [128X[104X
    [4X[28X  sl(2,3).H(0), sl(2,3).H(1), sl(2,3).(GF(3)+GF(3)+GF(3))(1), [128X[104X
    [4X[28X  sl(2,3).(GF(3)+GF(3)+GF(3))(2) ][128X[104X
  [4X[32X[104X
  
  [1X2.1-8 AllSimpleLieAlgebras[101X
  
  [33X[1;0Y[29X[2XAllSimpleLieAlgebras[102X( [3XF[103X, [3Xdim[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XF[103X  is a finite field, and [3Xdim[103X is either an integer not greater than 6,
  or,  if  [3XF=GF(2)[103X,  then  [3Xdim[103X  is not greater than 9. The output is a list of
  simple  Lie  algebras over [3XF[103X of dimension [3Xdim[103X. If [3Xdim[103X is at most 6, then the
  classification  by Strade [Str] is used. If [3XF=GF(2)[103X and [3Xdim[103X is between 7 and
  9,  then  the  Lie  algebras  in  [VL06] are returned (see Section [14X3.6[114X). The
  algebras  in  the  list are pairwise non-isomorphic. Note that the output of
  this  function  is  a  list  and  not a collection, and the package does not
  contain a function called [3XSimpleLieAlgebra[103X.[133X
  
  
  [1X2.2 [33X[0;0YSolvable and nilpotent Lie algebras[133X[101X
  
  [33X[0;0YThe  package  contains  the  classification  of  solvable  Lie  algebras  of
  dimensions  2,  3  and  4  (taken  from  [dG05]),  and the classification of
  nilpotent   Lie  algebras  of  dimensions  5  and  6  (from  [CdGS11]).  The
  classifications  are  complemented by a function for identifying a given Lie
  algebra  as  a  member  of  the list. This function also returns an explicit
  isomorphism.  In  Section [14X3.7[114X the list is given of the multiplication tables
  of  the  solvable and nilpotent Lie algebras, corresponding to the functions
  in this section.[133X
  
  [1X2.2-1 SolvableLieAlgebra[101X
  
  [33X[1;0Y[29X[2XSolvableLieAlgebra[102X( [3XF[103X, [3Xpars[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XF[103X  is  an  arbitrary  field,  [3Xpars[103X is a list of parameters with length
  between  [9X2[109X  and  [9X4[109X. The first entry of [3Xpars[103X is the dimension of the algebra,
  which  has  to  be  2, 3, or 4. If the dimension is 3, or 4, then the second
  entry  of [3Xpars[103X is the number of the Lie algebra with which it appears in the
  list  of [dG05]. If the dimension is 2, then there are only two (isomorphism
  classes  of)  solvable Lie algebras. In this case, if the second entry is 1,
  then  the  abelian  Lie  algebra  is  returned,  if it is 2, then the unique
  non-abelian  solvable  Lie algebra of dimension 2 is returned. A Lie algebra
  in  the list of [dG05] can have one or two parameters. In that case the list
  [3Xpars[103X also has to contain the parameters.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XSolvableLieAlgebra( Rationals, [4,6,1,2] );[127X[104X
    [4X[28X<Lie algebra of dimension 4 over Rationals>[128X[104X
  [4X[32X[104X
  
  [1X2.2-2 NilpotentLieAlgebra[101X
  
  [33X[1;0Y[29X[2XNilpotentLieAlgebra[102X( [3XF[103X, [3Xpars[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XF[103X  is  an  arbitrary  field,  [3Xpars[103X is a list of parameters with length
  between  [9X2[109X  and  [9X3[109X. The first entry of [3Xpars[103X is the dimension of the algebra,
  which  has  to  be 5 or 6. The second entry of [3Xpars[103X is the number of the Lie
  algebra  with  which it appears in the list of Section [14X3.7[114X. A Lie algebra in
  the  list  of Section [14X3.7[114X can have one parameter. In that case the list [3Xpars[103X
  also has to contain the parameter.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XNilpotentLieAlgebra( GF(3^7), [ 6, 24, Z(3^7)^101 ] );[127X[104X
    [4X[28X<Lie algebra of dimension 6 over GF(3^7)>[128X[104X
  [4X[32X[104X
  
  [1X2.2-3 AllSolvableLieAlgebras[101X
  
  [33X[1;0Y[29X[2XAllSolvableLieAlgebras[102X( [3XF[103X, [3Xdim[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XF[103X  is an arbitrary finite field, and [3Xdim[103X is at most 4. A collection of
  all  solvable  Lie  algebras over [3XF[103X of dimension [3Xdim[103X is returned. The output
  does  not  contain  isomorphic  Lie  algebras.  The  order  in which the Lie
  algebras  appear in the list is always the same. It is possible to construct
  an enumerator from the output collection for all of the valid choices of the
  parameters.  See [3XAllNonSolvableLieAlgebra[103X for a more detailed description of
  usage.[133X
  
  [1X2.2-4 AllNilpotentLieAlgebras[101X
  
  [33X[1;0Y[29X[2XAllNilpotentLieAlgebras[102X( [3XF[103X, [3Xdim[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XF[103X  is a finite field, and [3Xdim[103X not greater than 9. Further, if [3Xdim=9[103X or
  [3Xdim=8[103X,  then  [3XF[103X  must be [3XGF(2)[103X; if [3Xdim=7[103X then [3XF[103X must be one of [3XGF(2)[103X, [3XGF(3)[103X,
  [3XGF(5)[103X  and if [3Xdim≤6[103X then [3XF[103X can be an arbitrary finite field. A collection of
  all  nilpotent  Lie  algebras over [3XF[103X of dimension [3Xdim[103X is returned. If [3Xdim[103X is
  not  greater  than  6  then  the  collection  of  nilpotent  Lie algebras is
  determined  by  [CdGS11],  otherwise  the  classification  can  be  found in
  [Sch05].  The  output does not contain isomorphic Lie algebras. The order in
  which  the  Lie  algebras appear in the collection is always the same. It is
  possible  to  construct  an enumerator from the output collection for all of
  the valid choices of the parameters. See [3XAllNonSolvableLieAlgebra[103X for a more
  detailed description of usage.[133X
  
  [1X2.2-5 NrNilpotentLieAlgebras[101X
  
  [33X[1;0Y[29X[2XNrNilpotentLieAlgebras[102X( [3XF[103X, [3Xdim[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XF[103X is a finite field, and [3Xdim[103X is an integer. The restrictions for [3XF[103X and
  [3Xdim[103X  are  the same as in the function [3XAllNilpotentLieAlgebras[103X. The number of
  nilpotent Lie algebras over [3XF[103X of dimension [3Xdim[103X is returned.[133X
  
  [1X2.2-6 LieAlgebraIdentification[101X
  
  [33X[1;0Y[29X[2XLieAlgebraIdentification[102X( [3XL[103X ) [32X method[133X
  
  [33X[0;0YHere  [3XL[103X  is  a  solvable  Lie  algebra  of  dimension  2,3, or 4, or it is a
  nilpotent  Lie  algebra  of dimension 5 or 6. This function returns a record
  with three fields.[133X
  
  [30X    [33X[0;6Y[3Xname[103X  This  is  a  string  containing  the name of the Lie algebra. It
        starts  with  a capital L if it is a solvable Lie algebra of dimension
        2,3,4.  It starts with a capital N if it is a nilpotent Lie algebra of
        dimension 5 or 6. A name like[133X
  
  "N6_24( GF(3^7), Z(3^7) )"
  
        [33X[0;6Ymeans that the input Lie algebra is isomorphic to the Lie algebra with
        number  24  in  the  list  of  6-dimensional  nilpotent  Lie algebras.
        Furthermore  the  field  is  given and the value of the parameters (if
        there are any).[133X
  
  [30X    [33X[0;6Y[3Xparameters[103X This contains the parameters that appear in the name of the
        algebra.[133X
  
  [30X    [33X[0;6Y[3Xisomorphism[103X This is an isomorphism of the input Lie algebra to the Lie
        algebra from the classification with the given name.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XL:= SolvableLieAlgebra( Rationals, [4,14,3] );[127X[104X
    [4X[28X<Lie algebra of dimension 4 over Rationals>[128X[104X
    [4X[25Xgap>[125X [27X LieAlgebraIdentification( L );[127X[104X
    [4X[28Xrec( isomorphism := CanonicalBasis( <Lie algebra of dimension [128X[104X
    [4X[28X    4 over Rationals> ) -> [ v.3, (-1)*v.2, v.1, (1/3)*v.4 ], [128X[104X
    [4X[28X  name := "L4_14( Rationals, 1/3 )", parameters := [ 1/3 ] )[128X[104X
  [4X[32X[104X
  
  [33X[0;0YIn the example we see that the program finds a different parameter, than the
  one with which the Lie algebra was constructed. The explanation is that some
  parametric  classes  of  Lie  algebras  contain isomorphic Lie algebras, for
  different values of the parameters. In that case the identification function
  makes its own choice.[133X
  
