Exponents( U, u )
Exponents( U, u, F )
Exponents
returns the exponent vector of an ag word u with respect to
an induced generating system of U as list of integers if no field F
is given. Otherwise the product of the exponent vector and F.one
is
returned. Note that u must be an element of U.
Let (u_1, ..., u_r) be an induced generating system of U. Then u can be uniquely written as u_1^{nu_1}* ...* u_r^{nu_r} for integer nu_i. The exponent vector of u is [nu_1, ..., nu_r].
Factor Groups of Ag Groups for details.
Note that Exponents
adds a record component U.shiftInfo
. This
entry is used by subsequent calls with the same ag group in order to
speed up computation. If you ever change the component U.igs
by
hand, not using Normalize
, you must unbind the component
U.shiftInfo
, otherwise all following results of Exponents
will be
corrupted. In case U is a parent group you can use ExponentsAgWord
(see ExponentsAgWord), which is slightly faster but requires a parent
group U.
Note that you you may get a weird error message if u is no element of U. So it is strictly required that u is an element of U.
Note that Exponents
uses ExponentsAgWord
but not ExponentAgWord
, so
for records that mimic agwords Exponents
may be used in
ExponentAgWord
.
gap> v4 := AgSubgroup( s4, [ c, d ], true ); Subgroup( s4, [ c, d ] ) gap> Exponents( v4, c * d ); [ 1, 1 ] gap> Exponents( s4 mod v4, a * b^2 * c * d ); [ 1, 2 ]
GAP 3.4.4