gap> RCWAInfo(3);
gap> a := RcwaMapping([[3,0,2],[3, 1,4],[3,0,2],[3,-1,4]]);;
gap> T := RcwaMapping([[1,0,2],[3,1,2]]);;
gap> v := RcwaMapping([[-1,2,1],[1,-1,1],[1,-1,1]]);;
gap> Order(a);
#I  The mapping IntegralRcwaMapping( [ [ 3, 0, 2 ], [ 3, 1, 4 ], [ 3, 0, 2 ], 
  [ 3, -1, 4 ] 
 ] ) has a cycle longer than 2 times the square of its modulus, hence we claim\
 its order is infinite, although the validity of this criterium has not been p\
roved so far.
infinity
gap> IsTame(T);
#I  The 4th power of IntegralRcwaMapping( [ [ 1, 0, 2 ], [ 3, 1, 2 ] 
 ] ) has Modulus 
16; this is larger than the square of the modulus of the base, so we claim the\
 mapping is wild, although the validity of this criterium has not yet been pro\
ved.
false
gap> StandardizingConjugator(v);
#I  StandardConjugate for IntegralRcwaMapping( 
[ [ -1, 2, 1 ], [ 1, -1, 1 ], [ 1, -1, 1 ] ] )
#I  A set of representatives for the series of `halved' cycles is [ rec(
      pts := [ 3, -1, -2, -3, 5, 4 ],
      HalvedAt := 0 ) ].
#I  A set of representatives for the series of `not halved' cycles is [  ].
#I  The cycle type is [ [ 6 ], [  ] ].
#I  [Preimage, image] - pairs defining a standardizing conjugator are 
[ [ 0, 0 ], [ 2, 1 ], [ 1, 2 ], [ 0, 0 ], [ 2, 1 ], [ 1, 2 ], [ 3, -3 ], 
  [ -1, -2 ], [ -2, -1 ], [ -3, 3 ], [ 5, 4 ], [ 4, 5 ] ].
<integral rcwa mapping with modulus 3>