Math.RootLoci.Motivic.Abstract

The abstract motivic algorithm

See: B. Komuves: Motivic characteristic classes of discriminant strata

TODO: caching of results (otherwise it is very slow)

The abstract algorithm

symn :: Num c => Dim -> FreeMod c SingleLam

The (abstract) class of Sym^n(X)

open :: Dim -> ZMod SingleLam

The open stratum X(1,1,...,1)

zeros :: Int -> ZMod MultiLam

xlam :: Partition -> ZMod SingleLam

The open stratum X(lambda)

dvec :: [Dim] -> ZMod MultiLam

The open stratum D(n1,n2,...)

dvecSorted :: [Dim] -> ZMod MultiLam

The open stratum D(n1,n2,...), assuming n1 >= n2 >= n3 >= ...

Data types and instances

newtype Var

A variable, implemented as a de Bruijn level (indexing starts from 0)

Constructors

DeBruijn Int

Instances

Eq Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

(==) :: Var -> Var -> Bool

(/=) :: Var -> Var -> Bool

Ord Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

compare :: Var -> Var -> Ordering

(<) :: Var -> Var -> Bool

(<=) :: Var -> Var -> Bool

(>) :: Var -> Var -> Bool

(>=) :: Var -> Var -> Bool

max :: Var -> Var -> Var

min :: Var -> Var -> Var

Show Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

showsPrec :: Int -> Var -> ShowS

show :: Var -> String

showList :: [Var] -> ShowS

Pretty Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

pretty :: Var -> String

prettyInParens :: Var -> String

Rename Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> Var -> Var

Shift Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

shift :: Int -> Var -> Var

Pretty (Var, Int)

Defined in Math.RootLoci.Motivic.Abstract

Methods

pretty :: (Var, Int) -> String

prettyInParens :: (Var, Int) -> String

Omega (Var, Int)

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> (Var, Int) -> (Var, Int)

Rename (Var, Int)

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> (Var, Int) -> (Var, Int)

newtype Bindings

We use de Bruijn levels to index the bound variables, and ecah bound variables has a dimension

Constructors

Bindings [Dim]

Instances

Eq Bindings

Defined in Math.RootLoci.Motivic.Abstract

Methods

(==) :: Bindings -> Bindings -> Bool

(/=) :: Bindings -> Bindings -> Bool

Ord Bindings

Defined in Math.RootLoci.Motivic.Abstract

Methods

compare :: Bindings -> Bindings -> Ordering

(<) :: Bindings -> Bindings -> Bool

(<=) :: Bindings -> Bindings -> Bool

(>) :: Bindings -> Bindings -> Bool

(>=) :: Bindings -> Bindings -> Bool

max :: Bindings -> Bindings -> Bindings

min :: Bindings -> Bindings -> Bindings

Show Bindings

Defined in Math.RootLoci.Motivic.Abstract

Methods

showsPrec :: Int -> Bindings -> ShowS

show :: Bindings -> String

showList :: [Bindings] -> ShowS

Pretty Bindings

Defined in Math.RootLoci.Motivic.Abstract

Methods

pretty :: Bindings -> String

prettyInParens :: Bindings -> String

Cross Bindings

Defined in Math.RootLoci.Motivic.Abstract

Methods

cross :: Bindings -> Bindings -> Bindings

crossMany :: [Bindings] -> Bindings

crossInterleave :: Bindings -> Bindings -> Bindings

Empty Bindings

Defined in Math.RootLoci.Motivic.Abstract

Methods

empty :: Bindings

numberOfBoundVariables :: Bindings -> Int

dimensionTable :: Bindings -> Map Var Dim

newtype Single

An expression living on Sym^n(X), with free variables

Constructors

Single [(Var, Int)]

Instances

Eq Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

(==) :: Single -> Single -> Bool

(/=) :: Single -> Single -> Bool

Ord Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

compare :: Single -> Single -> Ordering

(<) :: Single -> Single -> Bool

(<=) :: Single -> Single -> Bool

(>) :: Single -> Single -> Bool

(>=) :: Single -> Single -> Bool

max :: Single -> Single -> Single

min :: Single -> Single -> Single

Show Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

showsPrec :: Int -> Single -> ShowS

show :: Single -> String

showList :: [Single] -> ShowS

Pretty Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

pretty :: Single -> String

prettyInParens :: Single -> String

Omega Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> Single -> Single

Normalize Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: Single -> Single

Empty Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

empty :: Single

Rename Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> Single -> Single

Shift Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

shift :: Int -> Single -> Single

Psi Multi Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: Multi -> Single

SingleToMulti Single Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

singleToMulti :: Single -> Multi

unSingle :: Single -> [(Var, Int)]

newtype Multi

An expression living on Sym^{n_1}(X) x ... x Sym^{n_r}(X), with free variables

Constructors

Multi [Single]

Instances

Eq Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

(==) :: Multi -> Multi -> Bool

(/=) :: Multi -> Multi -> Bool

Ord Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

compare :: Multi -> Multi -> Ordering

(<) :: Multi -> Multi -> Bool

(<=) :: Multi -> Multi -> Bool

(>) :: Multi -> Multi -> Bool

(>=) :: Multi -> Multi -> Bool

max :: Multi -> Multi -> Multi

min :: Multi -> Multi -> Multi

Show Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

showsPrec :: Int -> Multi -> ShowS

show :: Multi -> String

showList :: [Multi] -> ShowS

Pretty Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

pretty :: Multi -> String

prettyInParens :: Multi -> String

Theta Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

theta :: Multi -> Multi

Permute Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

permute :: Permutation -> Multi -> Multi

ExtendToCommonSize Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

extendToCommonSize :: (Multi, Multi) -> (Multi, Multi)

PsiEvenOdd Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

psiEvenOdd :: Multi -> Multi

Omega123 Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega123 :: Multi -> Multi

Omega Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> Multi -> Multi

Cross Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

cross :: Multi -> Multi -> Multi

crossMany :: [Multi] -> Multi

crossInterleave :: Multi -> Multi -> Multi

SuperNormalize Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

superNormalize :: Multi -> Multi

Normalize Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: Multi -> Multi

Empty Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

empty :: Multi

Rename Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> Multi -> Multi

Shift Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

shift :: Int -> Multi -> Multi

Psi Multi Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: Multi -> Single

SingleToMulti Single Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

singleToMulti :: Single -> Multi

data SingleLam

A lambda expression living on Sym^n(X), with variables bound to Sym^d(X) with different dimensions

Constructors

SingleLam !Bindings !Single

Instances

Eq SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

(==) :: SingleLam -> SingleLam -> Bool

(/=) :: SingleLam -> SingleLam -> Bool

Ord SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

compare :: SingleLam -> SingleLam -> Ordering

(<) :: SingleLam -> SingleLam -> Bool

(<=) :: SingleLam -> SingleLam -> Bool

(>) :: SingleLam -> SingleLam -> Bool

(>=) :: SingleLam -> SingleLam -> Bool

max :: SingleLam -> SingleLam -> SingleLam

min :: SingleLam -> SingleLam -> SingleLam

Show SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

showsPrec :: Int -> SingleLam -> ShowS

show :: SingleLam -> String

showList :: [SingleLam] -> ShowS

Pretty SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

pretty :: SingleLam -> String

prettyInParens :: SingleLam -> String

Pontrjagin SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

pontrjaginOne :: SingleLam

pontrjaginMul :: SingleLam -> SingleLam -> SingleLam

Omega SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> SingleLam -> SingleLam

Normalize SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: SingleLam -> SingleLam

Empty SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

empty :: SingleLam

Degree SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Associated Types

type MultiDegree SingleLam

Methods

totalDegree :: SingleLam -> Int

multiDegree :: SingleLam -> MultiDegree SingleLam

Psi MultiLam SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: MultiLam -> SingleLam

SingleToMulti SingleLam MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

singleToMulti :: SingleLam -> MultiLam

(Eq c, Num c) => Psi [FreeMod c SingleLam] (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: [FreeMod c SingleLam] -> FreeMod c SingleLam

(Eq c, Num c) => Omega (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> FreeMod c SingleLam -> FreeMod c SingleLam

(Eq c, Num c) => Normalize (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: FreeMod c SingleLam -> FreeMod c SingleLam

(Eq c, Num c) => Psi (FreeMod c MultiLam) (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: FreeMod c MultiLam -> FreeMod c SingleLam

(Eq c, Num c) => SingleToMulti (FreeMod c SingleLam) (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

singleToMulti :: FreeMod c SingleLam -> FreeMod c MultiLam

type MultiDegree SingleLam

Defined in Math.RootLoci.Motivic.Abstract

type MultiDegree SingleLam = Int

data MultiLam

A lambda expression living on Sym^{n_1}(X) x ... x Sym^{n_r}(X), with variables bound to Sym^d(X) with different dimensions

Constructors

MultiLam !Bindings !Multi

Instances

Eq MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

(==) :: MultiLam -> MultiLam -> Bool

(/=) :: MultiLam -> MultiLam -> Bool

Ord MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

compare :: MultiLam -> MultiLam -> Ordering

(<) :: MultiLam -> MultiLam -> Bool

(<=) :: MultiLam -> MultiLam -> Bool

(>) :: MultiLam -> MultiLam -> Bool

(>=) :: MultiLam -> MultiLam -> Bool

max :: MultiLam -> MultiLam -> MultiLam

min :: MultiLam -> MultiLam -> MultiLam

Show MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

showsPrec :: Int -> MultiLam -> ShowS

show :: MultiLam -> String

showList :: [MultiLam] -> ShowS

Pretty MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

pretty :: MultiLam -> String

prettyInParens :: MultiLam -> String

Theta MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

theta :: MultiLam -> MultiLam

Permute MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

permute :: Permutation -> MultiLam -> MultiLam

ExtendToCommonSize MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

extendToCommonSize :: (MultiLam, MultiLam) -> (MultiLam, MultiLam)

Pontrjagin MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

pontrjaginOne :: MultiLam

pontrjaginMul :: MultiLam -> MultiLam -> MultiLam

PsiEvenOdd MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

psiEvenOdd :: MultiLam -> MultiLam

Omega123 MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega123 :: MultiLam -> MultiLam

Omega MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> MultiLam -> MultiLam

Cross MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

cross :: MultiLam -> MultiLam -> MultiLam

crossMany :: [MultiLam] -> MultiLam

crossInterleave :: MultiLam -> MultiLam -> MultiLam

SuperNormalize MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

superNormalize :: MultiLam -> MultiLam

Normalize MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: MultiLam -> MultiLam

Empty MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

empty :: MultiLam

Degree MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Associated Types

type MultiDegree MultiLam

Methods

totalDegree :: MultiLam -> Int

multiDegree :: MultiLam -> MultiDegree MultiLam

Psi MultiLam SingleLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: MultiLam -> SingleLam

SingleToMulti SingleLam MultiLam

Defined in Math.RootLoci.Motivic.Abstract

Methods

singleToMulti :: SingleLam -> MultiLam

Theta (ZMod MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

theta :: ZMod MultiLam -> ZMod MultiLam

Permute (ZMod MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

permute :: Permutation -> ZMod MultiLam -> ZMod MultiLam

PsiEvenOdd (ZMod MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

psiEvenOdd :: ZMod MultiLam -> ZMod MultiLam

(Eq c, Num c) => Omega123 (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega123 :: FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Omega (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Cross (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

cross :: FreeMod c MultiLam -> FreeMod c MultiLam -> FreeMod c MultiLam

crossMany :: [FreeMod c MultiLam] -> FreeMod c MultiLam

crossInterleave :: FreeMod c MultiLam -> FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => SuperNormalize (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

superNormalize :: FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Normalize (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Psi (FreeMod c MultiLam) (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: FreeMod c MultiLam -> FreeMod c SingleLam

(Eq c, Num c) => SingleToMulti (FreeMod c SingleLam) (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

singleToMulti :: FreeMod c SingleLam -> FreeMod c MultiLam

type MultiDegree MultiLam

Defined in Math.RootLoci.Motivic.Abstract

type MultiDegree MultiLam = [Int]

class Shift a where

Shift de Bruijn levels

Methods

shift :: Int -> a -> a

Instances

Shift Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

shift :: Int -> Multi -> Multi

Shift Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

shift :: Int -> Single -> Single

Shift Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

shift :: Int -> Var -> Var

class Rename a where

Rename variables

Methods

rename :: (Var -> Var) -> a -> a

Instances

Rename Multi

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> Multi -> Multi

Rename Single

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> Single -> Single

Rename Var

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> Var -> Var

Rename (Var, Int)

Defined in Math.RootLoci.Motivic.Abstract

Methods

rename :: (Var -> Var) -> (Var, Int) -> (Var, Int)

exponentOf :: Var -> Single -> Int

Extract the exponent of a given variable

exponentVectorOf :: Var -> Multi -> [Int]

Extract the exponent vector of a given variable

normalizeWithExpo :: (Rename term, Normalize term, Ord expo) => (expo -> Bool) -> (Var -> term -> expo) -> (Bindings, term) -> (Bindings, term)