| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Math.RootLoci.CSM.Equivariant.PushForward
Description
Compute the pushforward maps pi_* and delta_* between the
GL2-equivariant cohomology rings
Recall that:
Delta_nu : Q^d -> Q^n
pi : Q^n -> P^n
and Q^n = P^1 x P^1 x ... x P^1.
Synopsis
- tau :: ChernBase base => Int -> ZMod base
- tauEta :: ChernBase base => Int -> ZMod (Eta base)
- delta_star_ :: ChernBase base => Partition -> ZMod (Omega base) -> ZMod (Eta base)
- delta_star :: ChernBase base => SetPartition -> ZMod (Omega base) -> ZMod (Eta base)
- delta_star' :: ChernBase base => [[Int]] -> ZMod (Omega base) -> ZMod (Eta base)
- pi_star_table :: Int -> Array Int (ZMod (Gam AB))
- compute_pi_star :: Int -> ZMod (Eta AB) -> ZMod (Gam AB)
- pi_star :: forall base. ChernBase base => Int -> ZMod (Eta base) -> ZMod (Gam base)
- piStarTableAff :: ChernBase base => Int -> Array Int (ZMod base)
- piStarTableProj :: ChernBase base => Int -> Array Int (ZMod (Gam base))
The function tau
pushforward along the diagonal map Delta_{nu} : Q^d -> Q^n
delta_star :: ChernBase base => SetPartition -> ZMod (Omega base) -> ZMod (Eta base) Source #
delta_star' :: ChernBase base => [[Int]] -> ZMod (Omega base) -> ZMod (Eta base) Source #
We can give an explicit indexing scheme (set partition), instead of the linear indexing used above. This will be useful when computing the "open" part
pushforward along the order-forgetting map pi : Q^n -> P^n
pi_star_table :: Int -> Array Int (ZMod (Gam AB)) Source #
Table of pi_*( eta_1*eta_2*...*eta_k ), computed by breaking the symmetry.
Slow implementation of pi_star, using pi_star_table
Arguments
| :: forall base. ChernBase base | |
| => Int | the number of points |
| -> ZMod (Eta base) | |
| -> ZMod (Gam base) |
However it should faster to just use the recursion for the P_j(m) polynomials,
which this function does.