HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

Math.Projects.ChevalleyGroup.Classical

Synopsis

# Documentation

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

numPtsPG :: (Integral a, Integral b) => 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 :: (Enum b, Eq b, Num b, Num a) => b -> (b, b) -> a -> [[a]] 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 a, Integral b) => b -> a -> a Source #

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

omegaeven :: FiniteField a => Int -> p -> [[[a]]] Source #

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

omegaodd :: (Foldable t, FiniteField a1) => Int -> t a2 -> [[[a1]]] Source #

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

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