ConsiderSmallerPowermaps( tbl, prime_powermap, prime )
ConsiderSmallerPowermaps( tbl, prime_powermap, prime, "quick" )
Maps and Parametrized Maps) that is an approximation of the prime-th powermap of the character table tbl:
If <prime> > '<tbl>.orders[i]' for a class i
, try to improve
prime_powermap at class i
using that for g in class i
,
g_i^{<prime>} = g_i^{<prime> 'mod <tbl>.orders[i]'} holds;
so if the (prime mod tbl.orders[i])
-th powermap at class i
is
determined by the maps stored in tbl.powermap
, this information is
used.
If "quick"
is specified, only those classes are considered for which
prime_powermap is ambiguous.
If there are classes for which no image is possible, false
is returned,
otherwise true
.
Note: If tbl.orders
is unbound, true
is returned without tests.
gap> t:= CharTable( "3.A6" );; init:= InitPowermap( t, 5 );; gap> Indeterminateness( init ); 4096 gap> ConsiderSmallerPowermaps( t, init, 5 );; gap> Indeterminateness( init ); 256
ConsiderSmallerPowermaps
is used by Powermap Powermap
.
GAP 3.4.4