13.8 CoeffsCyc

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.

Previous Up Top Next
Index