HaskellForMaths-0.4.7: Combinatorics, group theory, commutative algebra, non-commutative algebra

Math.Projects.ChevalleyGroup.Classical

Synopsis

# Documentation

numPtsAG :: (Num a, Integral b) => b -> a -> a Source

numPtsPG :: (Integral b, Integral a) => b -> a -> a Source

sl :: FiniteField k => Int -> [k] -> [[[k]]] Source

The special linear group SL(n,Fq), generated by elementary transvections, returned as matrices

elemTransvection :: (Num t1, Num t, Eq t1, Enum t1) => t1 -> (t1, t1) -> t -> [[t]] Source

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.

orderL :: Integral a => a -> a -> a Source

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).

s :: (FiniteField k, Ord k) => Int -> [k] -> [Permutation [k]] Source

orderS2 :: (Integral b, Integral a) => b -> a -> a Source

orderS :: (Integral b, Integral a) => b -> a -> a Source

omegaeven :: FiniteField t1 => Int -> t -> [[[t1]]] Source

d :: (FiniteField a, Ord a) => Int -> [a] -> [Permutation [a]] Source

omegaodd :: FiniteField t => Int -> [a] -> [[[t]]] Source

b :: (FiniteField a, Ord a) => Int -> [a] -> [Permutation [a]] Source

o :: (FiniteField a, Ord a) => Int -> [a] -> [Permutation [a]] Source