RepresentativeOperation( G, d, e )
RepresentativeOperation( G, d, e, operation )
RepresentativeOperation returns a representative of the point e in
the orbit of the point d under the group G. If d = e then
G.identity, otherwise it is not
specified which group element
RepresentativeOperation will return if
there are several that map d to e. If e is not in the orbit of d
An element g of G is called a representative for the point e in the orbit of d under G if g maps d to e, i.e., d^g = e. Note that the set of such representatives that map d to e forms a right coset of the stabilizer of d in G (see Stabilizer).
RepresentativeOperation accepts a function operation of two arguments
d and g as optional third argument, which specifies how the elements
of G operate (see Other Operations).
gap> g := Group( (1,2,3)(6,7), (3,4,5)(7,8) );; gap> RepresentativeOperation( g, 1, 5 ); (1,5,4,3,2)(6,8,7) gap> RepresentativeOperation( g, 1, 6 ); false gap> RepresentativeOperation( g, [1,2,3], [3,4,5], OnSets ); (1,3,5,2,4) gap> RepresentativeOperation( g, [1,2,3,4], [3,4,5,2], OnTuples ); false
G.operations.RepresentativeOperation( G, d, e, operation )
and returns the value. Note that the fourth argument is not optional for functions called this way.
The default function called this way is
GroupOper.RepresentativeOperation, which starts a normal orbit
calculation to compute the orbit of d under G, and remembers for each
point how it was obtained, i.e., which generator of G took which orbit
point to this new point. When the point e appears this information can
be traced back to write down the representative of e as a word in the
generators. Special categories of groups overlay this default function
with more efficient functions.
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