HaskellForMaths-0.4.5: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None

Math.Projects.ChevalleyGroup.Classical

Synopsis

- numPtsAG :: (Integral b, Num a) => b -> a -> a
- numPtsPG :: (Integral a, Integral b) => b -> a -> a
- sl :: FiniteField k => Int -> [k] -> [[[k]]]
- elemTransvection :: (Enum t1, Eq t1, Num t1, Num t) => t1 -> (t1, t1) -> t -> [[t]]
- l :: (FiniteField k, Ord k) => Int -> [k] -> [Permutation [k]]
- orderL :: Integral a => a -> a -> a
- sp2 :: FiniteField k => Int -> [k] -> [[[k]]]
- s2 :: (FiniteField k, Ord k) => Int -> [k] -> [Permutation [k]]
- s :: (Ord k, FiniteField k) => Int -> [k] -> [Permutation [k]]
- orderS2 :: (Integral a, Integral b) => b -> a -> a
- orderS :: (Integral b, Integral a) => b -> a -> a
- omegaeven :: FiniteField t1 => Int -> t -> [[[t1]]]
- d :: (Ord a, FiniteField a) => Int -> [a] -> [Permutation [a]]
- omegaodd :: FiniteField t => Int -> [a] -> [[[t]]]
- b :: (Ord a, FiniteField a) => Int -> [a] -> [Permutation [a]]
- o :: (Ord a, FiniteField a) => Int -> [a] -> [Permutation [a]]

# Documentation

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

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

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

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

elemTransvection :: (Enum t1, Eq t1, Num t1, Num t) => 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 -> aSource

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

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

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

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

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

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

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

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