CoeffsCyc( z, n )
If z is a cyclotomic which is contained in Q_n, CoeffsCyc( z,
n )
returns a list cfs of length n where the entry at position
i is the coefficient of 'E(<n>)'^{i-1} in the internal
representation of z as element of the cyclotomic field Q_n (see
More about Cyclotomics, ZumbroichBase):
<z> = <cfs>[1] + <cfs>[2] 'E(<n>)'^1 + ldots + <cfs>[n]
'E(<n>)'^{n-1}.
Note that all positions which do not belong to base elements of Q_n contain zeroes.
gap> CoeffsCyc( E(5), 5 ); CoeffsCyc( E(5), 15 ); [ 0, 1, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0 ] gap> CoeffsCyc( 1+E(3), 9 ); CoeffsCyc( E(5), 7 ); [ 0, 0, 0, 0, 0, 0, -1, 0, 0 ] Error, no representation of <z> in 7th roots of unity
CoeffsCyc
calls the internal function COEFFSCYC
:
COEFFSCYC( z )
is equivalent to CoeffsCyc( z, NofCyc( z ) )
, see NofCyc.
GAP 3.4.4