Add ConformalSymplecticGroup
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... and add some generalizations.
- Add `ConformalSymplecticGroup`, essentially analogous to
the implementation of `SymplecticGroup`, that is,
- introduce a plain function `ConformalSymplecticGroup`
and a constructor `ConformalSymplecticGroupCons`,
- install various methods for `ConformalSymplecticGroupCons`,
- introduce a property `IsFullSubgroupGLRespectingBilinearFormUpToScalars`
that is set in the groups returned by `ConformalSymplecticGroup`,
- install a `\in` method for a matrix and a group in
`IsFullSubgroupGLRespectingBilinearFormUpToScalars`,
- add tests for the new code.
- In `ConformalSymplecticGroup`, `GeneralLinearGroup`, `SpecialLinearGroup`,
and `SymplecticGroup`, support a filter that determines the
representation of the matrices constructed as generators of the groups
and as matrices of the invariant forms.
(Note that `ConformalSymplecticGroup` and `SymplecticGroup` call
`GeneralLinearGroup` and `SpecialLinearGroup`, respectively, for `n = 2`.)
For that, an "experimental" global option `ConstructingFilter` is used.
Currently `IsPlistRep` is the default value, `IsPlistRepMAtrix` is
another possible value.
(Eventually we want to support such a filter also for the other classical
groups.)
- Change the delegation between methods of `SymplecticGroup`:
Do not delegate from the variant where a finite field is given
to the variant with given size of the field, but the other way round.
This way, it will be possible to use elements from
`StandardFiniteField( p, n )` instead of `GF( p, n )` in the matrices.
(Eventually we want to change this also for the other classical groups.)
Once we decide about the setup that we want for `ConformalSymplecticGroup`,
implementations for other conformal classical group can be added,
and the relevant methods in the Forms package can be adjusted and extended
accordingly.
ThomasBreuer
added
kind: enhancement
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... and add some generalizations.
Add
ConformalSymplecticGroup, essentially analogous to the implementation ofSymplecticGroup, that is,ConformalSymplecticGroupand a constructorConformalSymplecticGroupCons,ConformalSymplecticGroupCons,IsFullSubgroupGLRespectingBilinearFormUpToScalarsthat is set in the groups returned byConformalSymplecticGroup,\inmethod for a matrix and a group inIsFullSubgroupGLRespectingBilinearFormUpToScalars,In
ConformalSymplecticGroup,GeneralLinearGroup,SpecialLinearGroup, andSymplecticGroup, support a filter that determines the representation of the matrices constructed as generators of the groups and as matrices of the invariant forms. (Note thatConformalSymplecticGroupandSymplecticGroupcallGeneralLinearGroupandSpecialLinearGroup, respectively, forn = 2.) For that, an "experimental" global optionConstructingFilteris used. CurrentlyIsPlistRepis the default value,IsPlistRepMAtrixis another possible value. (Eventually we want to support such a filter also for the other classical groups.)Change the delegation between methods of
SymplecticGroup: Do not delegate from the variant where a finite field is given to the variant with given size of the field, but the other way round. This way, it will be possible to use elements fromStandardFiniteField( p, n )instead ofGF( p, n )in the matrices. (Eventually we want to change this also for the other classical groups.)Once we decide about the setup that we want for
ConformalSymplecticGroup, implementations for other conformal classical group can be added, and the relevant methods in the Forms package can be adjusted and extended accordingly.