Math.Projects.ChevalleyGroup.Classical
- sl :: FiniteField k => Int -> [k] -> [[[k]]]
- l :: (FiniteField k, Ord k) => Int -> [k] -> [Permutation [k]]
- sp2 :: FiniteField k => Int -> [k] -> [[[k]]]
- s2 :: (FiniteField k, Ord k) => Int -> [k] -> [Permutation [k]]
Documentation
sl :: FiniteField k => Int -> [k] -> [[[k]]]Source
The special linear group SL(n,Fq), generated by elementary transvections, returned as matrices
l :: (FiniteField k, Ord k) => Int -> [k] -> [Permutation [k]]Source
The projective special linear group PSL(n,Fq) == A(n,Fq) == SL(n,Fq)/Z, returned as permutations of the points of PG(n-1,Fq). This is a finite simple group provided n>2 or q>3.
sp2 :: FiniteField k => Int -> [k] -> [[[k]]]Source
The symplectic group Sp(2n,Fq), returned as matrices
s2 :: (FiniteField k, Ord k) => Int -> [k] -> [Permutation [k]]Source
The projective symplectic group PSp(2n,Fq) == Cn(Fq) == Sp(2n,Fq)/Z, returned as permutations of the points of PG(2n-1,Fq). This is a finite simple group for n>1, except for PSp(4,F2).