25.22 RightCoset for Ag Groups

AgGroupOps.Coset( G )

A coset C = <G>{*}x is represented as record with the following components.

representative:

contains the representative x.

group:

contains the group G.

isDomain:

is true.

isRightCoset:

is true.

isFinite:

is true.

operations:

contains the operations record RightCosetAgGroupOps.

RightCosetAgGroupOps.<( C1, C2 )

If C1 and C2 do not have a common group or if one argument is no coset then the functions uses DomainOps.< in order to compare C1 and C2. Note that this will compute the set of elements of C1 and C2.

If C1 and C2 have a common group then AgGroupCosetOps.< will use SiftedAgWord (see SiftedAgWord) and ConjugateSubgroup (see ConjugateSubgroup) in order to compare C1 and C2. It does not compute the set of elements of C1 and C2.

Previous Up Top Next
Index