oalg-base-1.1.4.0: Algebraic structures on oriented entities and limits as a tool kit to solve algebraic problems.

Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Limes.MinimaAndMaxima

Contents

Minima
Maxima
Duality

Description

minima and maxima within a Multiplicative structure, i.e. limits of Diagram (Chain t).

Synopsis

type Minima t n = Limits Mlt Projective (Chain t) (n + 1) n
type Minimum t n = Limes Mlt Projective (Chain t) (n + 1) n
type MinimumCone t n = Cone Mlt Projective (Chain t) (n + 1) n
type MinimumDiagram t n = Diagram (Chain t) (n + 1) n
minimaTo :: Multiplicative a => Minima To n a
minimaFrom :: Multiplicative a => Minima From n a
type Maxima t n = Limits Mlt Injective (Chain t) (n + 1) n
type Maximum t n = Limes Mlt Injective (Chain t) (n + 1) n
type MaximumCone t n = Cone Mlt Injective (Chain t) (n + 1) n
type MaximumDiagram t n = Diagram (Chain t) (n + 1) n
maximaTo :: Multiplicative a => Maxima To n a
maximaTo' :: Multiplicative a => p n -> f a -> Maxima To n a
maximaFrom :: Multiplicative a => Maxima From n a
maximaFrom' :: Multiplicative a => p n -> f a -> Maxima From n a
maxLimitsDualityTo :: Multiplicative a => LimitsDuality Mlt (Maxima To n) (Minima From n) a
maxLimitsDualityFrom :: Multiplicative a => LimitsDuality Mlt (Maxima From n) (Minima To n) a

Minima

type Minima t n = Limits Mlt Projective (Chain t) (n + 1) n Source #

minima for a Multiplicative structure.

type Minimum t n = Limes Mlt Projective (Chain t) (n + 1) n Source #

minimum as Limes.

type MinimumCone t n = Cone Mlt Projective (Chain t) (n + 1) n Source #

Cone for a minimum.

type MinimumDiagram t n = Diagram (Chain t) (n + 1) n Source #

Diagram for a minimum.

minimaTo :: Multiplicative a => Minima To n a Source #

minima according to Chain To.

minimaFrom :: Multiplicative a => Minima From n a Source #

minima according to Chain From.

Maxima

type Maxima t n = Limits Mlt Injective (Chain t) (n + 1) n Source #

maxima for a Multiplicative structure.

type Maximum t n = Limes Mlt Injective (Chain t) (n + 1) n Source #

maximum as a Limes.

type MaximumCone t n = Cone Mlt Injective (Chain t) (n + 1) n Source #

Cone for a maximum.

type MaximumDiagram t n = Diagram (Chain t) (n + 1) n Source #

Diagram for a maximum.

maximaTo :: Multiplicative a => Maxima To n a Source #

maxima according to Chain To.

maximaTo' :: Multiplicative a => p n -> f a -> Maxima To n a Source #

maxima according to Chain To given by two proxy types.

maximaFrom :: Multiplicative a => Maxima From n a Source #

maxima according to Chain From.

maximaFrom' :: Multiplicative a => p n -> f a -> Maxima From n a Source #

maxima according to Chain From given by two proxy types.

Duality

maxLimitsDualityTo :: Multiplicative a => LimitsDuality Mlt (Maxima To n) (Minima From n) a Source #

duality between Maxima To and Minima From.

maxLimitsDualityFrom :: Multiplicative a => LimitsDuality Mlt (Maxima From n) (Minima To n) a Source #

duality between Maxima From and Minima To.