LenstraBase( n, stabilizer, super )
returns a list '[ ' b_1, b_2, ldots, b_m ' ]' of lists, each b_i
consisting of integers such that the elements sum_{j in b_i} 'E(n)'^j
form an integral base of the number field NF( n, stabilizer )
,
see Number Field Records.
super is a list representing a supergroup of the group described by the list stabilizer; the base is chosen such that the group of super acts on it, as far as this is possible.
Note:
The b_i are in general not sets, since for stabilizer = super
,
b_i[1] is always an element of ZumbroichBase( N, 1 )
; this is used
by NF
(see Number Field Records) and Coefficients
(see
Coefficients for Number Fields).
stabilizer must not contain the stabilizer of a proper cyclotomic subfield of Q_n.
gap> LenstraBase( 24, [ 1, 19 ], [ 1, 19 ] ); # a base of [ [ 1, 19 ], [ 8 ], [ 11, 17 ], [ 16 ] ] # $Q_3(\sqrt{6})$, gap> LenstraBase( 24, [ 1, 19 ], [ 1, 5, 19, 23 ] ); # another one [ [ 1, 19 ], [ 5, 23 ], [ 8 ], [ 16 ] ] gap> LenstraBase( 15, [ 1, 4 ], PrimeResidues( 15 ) ); # normal base of [ [ 1, 4 ], [ 2, 8 ], [ 7, 13 ], [ 11, 14 ] ] # $Q_3(\sqrt{5})$
GAP 3.4.4