sigma-ij-0.2.0.2: Thom polynomials of second order Thom-Boardman singularities

Math.ThomPoly.SigmaIJ

Contents

Description

Calculates the Thom polynomial of Sigma^{ij} with localization and the substitution trick

Synopsis

# Sigma^{ij}

data SigmaIJ Source #

Constructors

 SigmaIJ Fields_i :: !Intthe index i_j :: !Intthe index j_n :: !Intthe source dimension n

Instances

 Source # Methods(==) :: SigmaIJ -> SigmaIJ -> Bool #(/=) :: SigmaIJ -> SigmaIJ -> Bool # Source # MethodsshowList :: [SigmaIJ] -> ShowS # Source # Methodssolve :: CoeffRing coeff => Proxy * coeff -> Batch -> SigmaIJ -> FreeMod Schur (FieldOfFractions coeff) Source #

smallestIJ :: (Int, Int) -> SigmaIJ Source #

We need n >= mu with this method

The codimension of Sigma^{i,j}(n,m)

calcMu :: (Int, Int) -> Int Source #

computes the (shifted) algebraic multiplicity mu = i + (j o i)

Signed pairs of partitions appearing in the Thom polynomial of Sigma^{ij}

data Fixpoint2 Source #

A fixed point

Constructors

 Fix2 Fields_ii :: [Int] _jj :: [Int] _ioj :: [(Int, Int)] _kk :: [Int] _ss :: [Int] _rr :: [Int]

Instances

 Source # MethodsshowList :: [Fixpoint2] -> ShowS #

o :: Int -> Int -> Int Source #

dimension of a "half-symmetric tensor product"

oo :: [Int] -> [Int] -> [(Int, Int)] Source #

"half-symmetric tensor product"

length (js oo is) == (length js) o (length is)

sigmaij' :: forall coeff. CoeffRing coeff => Proxy coeff -> SigmaIJ -> [(Partition, Partition)] -> FreeMod Schur (FieldOfFractions coeff) Source #