Safe Haskell	None
Language	Haskell2010

Math.ThomPoly.SigmaIJ

Contents

Description

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

Synopsis

Documentation

`Sigma^{ij}`

Constructors

SigmaIJ
Fields _i :: !Int the index `i` _j :: !Int the index `j` _n :: !Int the source dimension `n`

Instances

Eq SigmaIJ Source #
Methods (==) :: SigmaIJ -> SigmaIJ -> Bool # (/=) :: SigmaIJ -> SigmaIJ -> Bool #
Show SigmaIJ Source #
Methods showsPrec :: Int -> SigmaIJ -> ShowS # show :: SigmaIJ -> String # showList :: [SigmaIJ] -> ShowS #
Problem SigmaIJ Source #
Methods baseFName :: SigmaIJ -> String Source # calcStats :: SigmaIJ -> Stats Source # solve :: CoeffRing coeff => Proxy * coeff -> Batch -> SigmaIJ -> FreeMod Schur (FieldOfFractions coeff) Source #

We need n >= mu with this method

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

There is a sign in the localization formula.

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

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

A fixed point

Constructors

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

Instances

Show Fixpoint2 Source #
Methods showsPrec :: Int -> Fixpoint2 -> ShowS # show :: Fixpoint2 -> String # showList :: [Fixpoint2] -> ShowS #

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)