Noether.Algebra.Linear.Module

Documentation

data LeftModuleE

Constructors

LeftModule_Ring_AbelianGroup_Linear_Compatible

Fields

• leftModule_ring :: RingE
• leftModule_abelianGroup :: AbelianGroupE
• leftModule_actorLinearity :: ActorLinearE
• leftModule_acteeLinearity :: ActeeLinearE
• leftModule_compatibility :: CompatibleE

LeftModule_Named Symbol LeftModuleE

Instances

(RingK k3 k4 k5 p m r zr, AbelianGroupK k1 k2 a v zag, ActorLinearK k1 k2 k3 k5 k4 Side L m p r a v zor, ActeeLinearK k1 k2 k3 k4 Side L m r a v zee, CompatibleK k1 k3 k4 k L op m r v zlc) => LeftModuleK LeftModuleE k1 k2 k3 k4 k5 k op p m r a v (LeftModule_Ring_AbelianGroup_Linear_Compatible zr zag zor zee zlc)

class LeftModuleK op p m r a v s

A left module (v, a) over the ring (r, p, m).

Instances

(RingK k3 k4 k5 p m r zr, AbelianGroupK k1 k2 a v zag, ActorLinearK k1 k2 k3 k5 k4 Side L m p r a v zor, ActeeLinearK k1 k2 k3 k4 Side L m r a v zee, CompatibleK k1 k3 k4 k L op m r v zlc) => LeftModuleK LeftModuleE k1 k2 k3 k4 k5 k op p m r a v (LeftModule_Ring_AbelianGroup_Linear_Compatible zr zag zor zee zlc)

type family LeftModuleS (op :: k0) (p :: k1) (m :: k2) r (a :: k3) v :: LeftModuleE

Instances

type LeftModuleS BinaryNumeric BinaryNumeric BinaryNumeric BinaryNumeric Mul Add Mul Double Add Double

type LeftModuleS BinaryNumeric BinaryNumeric BinaryNumeric BinaryNumeric Mul Add Mul Double Add Double = DeriveLeftModule_Self BinaryNumeric BinaryNumeric Add Mul Double

type LeftModuleC op p m r a v = LeftModuleK op p m r a v (LeftModuleS op p m r a v)

type LeftModule op p m r a v = (LeftModuleC op p m r a v, Ring p m r, AbelianGroup a v, LinearActsOn L m p r a v, LeftCompatible op m r v)

data RightModuleE

Constructors

RightModule_Ring_AbelianGroup_Linear_Compatible

Fields

• rightModule_ring :: RingE
• rightModule_abelianGroup :: AbelianGroupE
• rightModule_actorLinearity :: ActorLinearE
• rightModule_acteeLinearity :: ActeeLinearE
• rightModule_compatibility :: CompatibleE

RightModule_Named Symbol RightModuleE

Instances

(RingK k3 k4 k5 p m r zr, AbelianGroupK k1 k2 a v zag, ActorLinearK k1 k2 k3 k5 k4 Side R m p r a v zor, ActeeLinearK k1 k2 k3 k4 Side R m r a v zee, CompatibleK k1 k3 k4 k R op m r v zrc) => RightModuleK RightModuleE k1 k2 k3 k4 k5 k op p m r a v (RightModule_Ring_AbelianGroup_Linear_Compatible zr zag zor zee zrc)

class RightModuleK op p m r a v s

A right module (v, a) over the ring (r, p, m).

Instances

(RingK k3 k4 k5 p m r zr, AbelianGroupK k1 k2 a v zag, ActorLinearK k1 k2 k3 k5 k4 Side R m p r a v zor, ActeeLinearK k1 k2 k3 k4 Side R m r a v zee, CompatibleK k1 k3 k4 k R op m r v zrc) => RightModuleK RightModuleE k1 k2 k3 k4 k5 k op p m r a v (RightModule_Ring_AbelianGroup_Linear_Compatible zr zag zor zee zrc)

type family RightModuleS (op :: k0) (p :: k1) (m :: k2) r (a :: k3) v :: RightModuleE

Instances

type RightModuleS BinaryNumeric BinaryNumeric BinaryNumeric BinaryNumeric Mul Add Mul Double Add Double

type RightModuleS BinaryNumeric BinaryNumeric BinaryNumeric BinaryNumeric Mul Add Mul Double Add Double = DeriveRightModule_Self BinaryNumeric BinaryNumeric Add Mul Double

type RightModuleC op p m r a v = RightModuleK op p m r a v (RightModuleS op p m r a v)

type RightModule op p m r a v = (RightModuleC op p m r a v, Ring p m r, AbelianGroup a v, LinearActsOn R m p r a v, RightCompatible op m r v)