algebra-3.1: Constructive abstract algebra

Index

$* | Numeric.Covector
$@ | Numeric.Map
* | Numeric.Algebra.Class, Numeric.Algebra
*. | Numeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
+ | Numeric.Additive.Class, Numeric.Algebra
- | Numeric.Additive.Group, Numeric.Algebra
.* | Numeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
/ | Numeric.Algebra.Division, Numeric.Algebra
/~ | Numeric.Order.Class, Numeric.Algebra
< | Numeric.Order.Class, Numeric.Algebra
<~ | Numeric.Order.Class, Numeric.Algebra
> | Numeric.Order.Class, Numeric.Algebra
>~ | Numeric.Order.Class, Numeric.Algebra
Abelian | Numeric.Additive.Class, Numeric.Algebra
Additive | Numeric.Additive.Class, Numeric.Algebra
AdditiveOrder | Numeric.Order.Additive, Numeric.Algebra
addRep | Numeric.Module.Representable, Numeric.Algebra
adjoint | Numeric.Algebra.Involutive, Numeric.Algebra
Algebra | Numeric.Algebra.Class, Numeric.Algebra
antiEuclidean | Numeric.Coalgebra.Geometric
antipode | Numeric.Algebra.Hopf, Numeric.Algebra
antipodeM | Numeric.Covector, Numeric.Algebra
antipodeMap | Numeric.Map
appEnd | Numeric.Ring.Endomorphism
Band | Numeric.Algebra.Idempotent, Numeric.Band.Class, Numeric.Algebra
BasisCoblade |
1 (Type/Class) | Numeric.Coalgebra.Geometric
2 (Data Constructor) | Numeric.Coalgebra.Geometric
Bialgebra | Numeric.Algebra.Unital, Numeric.Algebra
char | Numeric.Rig.Characteristic, Numeric.Algebra
Characteristic | Numeric.Rig.Characteristic, Numeric.Algebra
charInt | Numeric.Rig.Characteristic, Numeric.Algebra
charWord | Numeric.Rig.Characteristic, Numeric.Algebra
cliffordConjugate | Numeric.Coalgebra.Geometric
Coalgebra | Numeric.Algebra.Class, Numeric.Algebra
CocommutativeCoalgebra | Numeric.Algebra.Commutative, Numeric.Algebra
coinv | Numeric.Algebra.Involutive, Numeric.Algebra
coinvM | Numeric.Covector, Numeric.Algebra
coinvMap | Numeric.Map
Commutative | Numeric.Algebra.Commutative, Numeric.Algebra
CommutativeAlgebra | Numeric.Algebra.Commutative, Numeric.Algebra
CommutativeBialgebra | Numeric.Algebra.Commutative, Numeric.Algebra
comparable | Numeric.Order.Class, Numeric.Algebra
Complex |
1 (Type/Class) | Numeric.Algebra.Complex
2 (Data Constructor) | Numeric.Algebra.Complex
ComplexBasis | Numeric.Algebra.Complex
complicate | Numeric.Algebra.Quaternion
complicate' | Numeric.Coalgebra.Quaternion
Complicated | Numeric.Algebra.Complex.Class, Numeric.Algebra.Complex, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
comult | Numeric.Algebra.Class, Numeric.Algebra
Comultivector | Numeric.Coalgebra.Geometric
comultM | Numeric.Covector, Numeric.Algebra
comultMap | Numeric.Map
contractL | Numeric.Coalgebra.Geometric
contractR | Numeric.Coalgebra.Geometric
convolveM | Numeric.Covector, Numeric.Algebra
convolveMap | Numeric.Map
Cos | Numeric.Coalgebra.Trigonometric
cos | Numeric.Coalgebra.Trigonometric.Class, Numeric.Coalgebra.Trigonometric
Cosh | Numeric.Coalgebra.Hyperbolic
cosh | Numeric.Coalgebra.Hyperbolic.Class, Numeric.Algebra.Hyperbolic, Numeric.Coalgebra.Hyperbolic
Cosh' | Numeric.Algebra.Hyperbolic
counit | Numeric.Algebra.Unital, Numeric.Algebra
CounitalCoalgebra | Numeric.Algebra.Unital, Numeric.Algebra
counitM | Numeric.Covector, Numeric.Algebra
counitMap | Numeric.Map
Covector |
1 (Type/Class) | Numeric.Covector, Numeric.Algebra
2 (Data Constructor) | Numeric.Covector, Numeric.Algebra
D |
1 (Data Constructor) | Numeric.Algebra.Dual
2 (Data Constructor) | Numeric.Coalgebra.Dual
d | Numeric.Algebra.Dual.Class, Numeric.Algebra.Dual, Numeric.Coalgebra.Dual
DecidableAssociates | Numeric.Decidable.Associates, Numeric.Algebra
DecidableUnits | Numeric.Decidable.Units, Numeric.Algebra
DecidableZero | Numeric.Decidable.Zero, Numeric.Algebra
Dioid | Numeric.Dioid.Class, Numeric.Algebra
Distinguished | Numeric.Algebra.Distinguished.Class, Numeric.Algebra.Complex, Numeric.Algebra.Quaternion, Numeric.Algebra.Dual, Numeric.Coalgebra.Dual, Numeric.Coalgebra.Quaternion
Division | Numeric.Algebra.Division, Numeric.Algebra
DivisionAlgebra | Numeric.Algebra.Division, Numeric.Algebra
DivisionRing | Numeric.Ring.Division, Numeric.Algebra
dot | Numeric.Coalgebra.Geometric
Dual |
1 (Type/Class) | Numeric.Algebra.Dual
2 (Data Constructor) | Numeric.Algebra.Dual
Dual' |
1 (Type/Class) | Numeric.Coalgebra.Dual
2 (Data Constructor) | Numeric.Coalgebra.Dual
DualBasis | Numeric.Algebra.Dual
DualBasis' | Numeric.Coalgebra.Dual
E |
1 (Data Constructor) | Numeric.Algebra.Complex
2 (Data Constructor) | Numeric.Algebra.Quaternion
3 (Data Constructor) | Numeric.Algebra.Dual
4 (Data Constructor) | Numeric.Coalgebra.Dual
e |
1 (Function) | Numeric.Algebra.Distinguished.Class, Numeric.Algebra.Complex, Numeric.Algebra.Quaternion, Numeric.Algebra.Dual, Numeric.Coalgebra.Dual, Numeric.Coalgebra.Quaternion
2 (Function) | Numeric.Coalgebra.Geometric
E' | Numeric.Coalgebra.Quaternion
Eigenbasis | Numeric.Coalgebra.Geometric
Eigenmetric | Numeric.Coalgebra.Geometric
End |
1 (Type/Class) | Numeric.Ring.Endomorphism
2 (Data Constructor) | Numeric.Ring.Endomorphism
Euclidean |
1 (Type/Class) | Numeric.Coalgebra.Geometric
2 (Data Constructor) | Numeric.Coalgebra.Geometric
euclidean | Numeric.Coalgebra.Geometric
Exp |
1 (Type/Class) | Numeric.Exp
2 (Data Constructor) | Numeric.Exp
Factorable | Numeric.Algebra.Factorable, Numeric.Algebra
factorWith | Numeric.Algebra.Factorable, Numeric.Algebra
Field | Numeric.Field.Class, Numeric.Algebra
filterGrade | Numeric.Coalgebra.Geometric
frobenius | Numeric.Ring.Endomorphism
fromEnd | Numeric.Ring.Endomorphism
fromInteger | Numeric.Ring.Class, Numeric.Algebra
fromIntegerRep | Numeric.Module.Representable, Numeric.Algebra
fromIntegral | Numeric.Ring.Class
fromNatural | Numeric.Rig.Class, Numeric.Algebra
fromNaturalNum | Numeric.Rig.Class
fromNaturalRep | Numeric.Module.Representable, Numeric.Algebra
fromWhole | Numeric.Rig.Class
geometric | Numeric.Coalgebra.Geometric
grade | Numeric.Coalgebra.Geometric
gradeInversion | Numeric.Coalgebra.Geometric
Group | Numeric.Additive.Group, Numeric.Algebra
Hamiltonian | Numeric.Algebra.Quaternion.Class, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
hestenes | Numeric.Coalgebra.Geometric
HopfAlgebra | Numeric.Algebra.Hopf, Numeric.Algebra
Hyper |
1 (Type/Class) | Numeric.Coalgebra.Hyperbolic
2 (Data Constructor) | Numeric.Coalgebra.Hyperbolic
Hyper' |
1 (Type/Class) | Numeric.Algebra.Hyperbolic
2 (Data Constructor) | Numeric.Algebra.Hyperbolic
HyperBasis | Numeric.Coalgebra.Hyperbolic
HyperBasis' | Numeric.Algebra.Hyperbolic
Hyperbolic | Numeric.Coalgebra.Hyperbolic.Class, Numeric.Algebra.Hyperbolic, Numeric.Coalgebra.Hyperbolic
I |
1 (Data Constructor) | Numeric.Algebra.Complex
2 (Data Constructor) | Numeric.Algebra.Quaternion
i | Numeric.Algebra.Complex.Class, Numeric.Algebra.Complex, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
I' | Numeric.Coalgebra.Quaternion
Idempotent | Numeric.Additive.Class, Numeric.Algebra
IdempotentAlgebra | Numeric.Algebra.Idempotent, Numeric.Algebra
IdempotentBialgebra | Numeric.Algebra.Idempotent, Numeric.Algebra
IdempotentCoalgebra | Numeric.Algebra.Idempotent
imagPart | Numeric.Algebra.Complex
Infinitesimal | Numeric.Algebra.Dual.Class, Numeric.Algebra.Dual, Numeric.Coalgebra.Dual
IntegralSemiring | Numeric.Semiring.Integral
Interval |
1 (Type/Class) | Numeric.Algebra.Incidence
2 (Data Constructor) | Numeric.Algebra.Incidence
Interval' |
1 (Type/Class) | Numeric.Coalgebra.Incidence
2 (Data Constructor) | Numeric.Coalgebra.Incidence
inv | Numeric.Algebra.Involutive, Numeric.Algebra
invM | Numeric.Covector, Numeric.Algebra
invMap | Numeric.Map
InvolutiveAlgebra | Numeric.Algebra.Involutive, Numeric.Algebra
InvolutiveBialgebra | Numeric.Algebra.Involutive, Numeric.Algebra
InvolutiveCoalgebra | Numeric.Algebra.Involutive, Numeric.Algebra
InvolutiveMultiplication | Numeric.Algebra.Involutive, Numeric.Algebra
InvolutiveSemiring | Numeric.Algebra.Involutive, Numeric.Semiring.Involutive, Numeric.Algebra
isAssociate | Numeric.Decidable.Associates
isAssociateIntegral | Numeric.Decidable.Associates
isAssociateWhole | Numeric.Decidable.Associates
isUnit | Numeric.Decidable.Units
isZero | Numeric.Decidable.Zero
J | Numeric.Algebra.Quaternion
j | Numeric.Algebra.Quaternion.Class, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
J' | Numeric.Coalgebra.Quaternion
K | Numeric.Algebra.Quaternion
k | Numeric.Algebra.Quaternion.Class, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
K' | Numeric.Coalgebra.Quaternion
LeftModule | Numeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
liftProduct | Numeric.Coalgebra.Geometric
liftRngHom | Numeric.Ring.Rng
LocallyFiniteOrder | Numeric.Order.LocallyFinite, Numeric.Algebra
LocalRing | Numeric.Ring.Local, Numeric.Algebra
Log |
1 (Type/Class) | Numeric.Log
2 (Data Constructor) | Numeric.Log
Map |
1 (Type/Class) | Numeric.Map
2 (Data Constructor) | Numeric.Map
memoM | Numeric.Covector, Numeric.Algebra
memoMap | Numeric.Map
metric | Numeric.Coalgebra.Geometric
minusRep | Numeric.Module.Representable, Numeric.Algebra
Module | Numeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
moebius | Numeric.Algebra.Incidence
moebius' | Numeric.Coalgebra.Incidence
moebiusInversion | Numeric.Order.LocallyFinite
Monoidal | Numeric.Algebra.Class, Numeric.Algebra
Morphism |
1 (Type/Class) | Numeric.Coalgebra.Categorical
2 (Data Constructor) | Numeric.Coalgebra.Categorical
mulRep | Numeric.Module.Representable, Numeric.Algebra
mult | Numeric.Algebra.Class, Numeric.Algebra
Multiplicative | Numeric.Algebra.Class, Numeric.Algebra
multM | Numeric.Covector, Numeric.Algebra
multMap | Numeric.Map
Natural | Numeric.Algebra
negate | Numeric.Additive.Group, Numeric.Algebra
negateRep | Numeric.Module.Representable, Numeric.Algebra
one | Numeric.Algebra.Unital, Numeric.Algebra
oneRep | Numeric.Module.Representable, Numeric.Algebra
Opposite |
1 (Type/Class) | Numeric.Ring.Opposite
2 (Data Constructor) | Numeric.Ring.Opposite
Order | Numeric.Order.Class, Numeric.Algebra
order | Numeric.Order.Class, Numeric.Algebra
OrderedRig | Numeric.Rig.Ordered, Numeric.Algebra
orderOrd | Numeric.Order.Class
outer | Numeric.Coalgebra.Geometric
padd | Numeric.Partial.Semigroup
PartialGroup | Numeric.Partial.Group
PartialMonoid | Numeric.Partial.Monoid
PartialSemigroup | Numeric.Partial.Semigroup
Partitionable | Numeric.Additive.Class, Numeric.Algebra
partitionWith | Numeric.Additive.Class, Numeric.Algebra
pminus | Numeric.Partial.Group
pnegate | Numeric.Partial.Group
pow | Numeric.Algebra.Unital, Numeric.Algebra
pow1p | Numeric.Algebra.Class, Numeric.Algebra
pow1pBand | Numeric.Algebra.Idempotent, Numeric.Band.Class, Numeric.Algebra
pow1pIntegral | Numeric.Algebra.Class
powBand | Numeric.Algebra.Idempotent, Numeric.Band.Class, Numeric.Algebra
product | Numeric.Algebra.Unital, Numeric.Algebra
product1 | Numeric.Algebra.Class, Numeric.Algebra
productWith | Numeric.Algebra.Unital, Numeric.Algebra
productWith1 | Numeric.Algebra.Class, Numeric.Algebra
psubtract | Numeric.Partial.Group
pzero | Numeric.Partial.Monoid
Quadrance | Numeric.Quadrance.Class, Numeric.Algebra
quadrance | Numeric.Quadrance.Class, Numeric.Algebra
Quaternion |
1 (Type/Class) | Numeric.Algebra.Quaternion
2 (Data Constructor) | Numeric.Algebra.Quaternion
Quaternion' |
1 (Type/Class) | Numeric.Coalgebra.Quaternion
2 (Data Constructor) | Numeric.Coalgebra.Quaternion
QuaternionBasis | Numeric.Algebra.Quaternion
QuaternionBasis' | Numeric.Coalgebra.Quaternion
range | Numeric.Order.LocallyFinite
rangeSize | Numeric.Order.LocallyFinite
realPart | Numeric.Algebra.Complex
recip | Numeric.Algebra.Division, Numeric.Algebra
recipriocal | Numeric.Algebra.Division, Numeric.Algebra
recipUnit | Numeric.Decidable.Units
recipUnitIntegral | Numeric.Decidable.Units
recipUnitWhole | Numeric.Decidable.Units
Rect |
1 (Type/Class) | Numeric.Band.Rectangular
2 (Data Constructor) | Numeric.Band.Rectangular
reverse | Numeric.Coalgebra.Geometric
Rig | Numeric.Rig.Class, Numeric.Algebra
RightModule | Numeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
Ring | Numeric.Ring.Class, Numeric.Algebra
Rng | Numeric.Rng.Class, Numeric.Algebra
RngRing |
1 (Type/Class) | Numeric.Ring.Rng
2 (Data Constructor) | Numeric.Ring.Rng
rngRingHom | Numeric.Ring.Rng
runBasisCoblade | Numeric.Coalgebra.Geometric
runExp | Numeric.Exp
runLog | Numeric.Log
runOpposite | Numeric.Ring.Opposite
runZeroRng | Numeric.Rng.Zero
scalarPart | Numeric.Algebra.Quaternion
scalarPart' | Numeric.Coalgebra.Quaternion
Semiring | Numeric.Algebra.Class, Numeric.Algebra
Sin | Numeric.Coalgebra.Trigonometric
sin | Numeric.Coalgebra.Trigonometric.Class, Numeric.Coalgebra.Trigonometric
Sinh | Numeric.Coalgebra.Hyperbolic
sinh | Numeric.Coalgebra.Hyperbolic.Class, Numeric.Algebra.Hyperbolic, Numeric.Coalgebra.Hyperbolic
Sinh' | Numeric.Algebra.Hyperbolic
sinnum | Numeric.Algebra.Class, Numeric.Algebra
sinnum1p | Numeric.Additive.Class, Numeric.Algebra
sinnum1pIdempotent | Numeric.Additive.Class, Numeric.Algebra
sinnum1pRep | Numeric.Module.Representable, Numeric.Algebra
sinnumIdempotent | Numeric.Algebra.Class, Numeric.Algebra
sinnumRep | Numeric.Module.Representable, Numeric.Algebra
subtract | Numeric.Additive.Group, Numeric.Algebra
subtractRep | Numeric.Module.Representable, Numeric.Algebra
sum | Numeric.Algebra.Class, Numeric.Algebra
sum1 | Numeric.Additive.Class, Numeric.Algebra
sumWith | Numeric.Algebra.Class, Numeric.Algebra
sumWith1 | Numeric.Additive.Class, Numeric.Algebra
times | Numeric.Additive.Group, Numeric.Algebra
timesRep | Numeric.Module.Representable, Numeric.Algebra
toEnd | Numeric.Ring.Endomorphism
toNatural | Numeric.Algebra
Trig |
1 (Type/Class) | Numeric.Coalgebra.Trigonometric
2 (Data Constructor) | Numeric.Coalgebra.Trigonometric
TrigBasis | Numeric.Coalgebra.Trigonometric
Trigonometric | Numeric.Coalgebra.Trigonometric.Class, Numeric.Coalgebra.Trigonometric
TriviallyInvolutive | Numeric.Algebra.Involutive, Numeric.Algebra
TriviallyInvolutiveAlgebra | Numeric.Algebra.Involutive, Numeric.Algebra
TriviallyInvolutiveBialgebra | Numeric.Algebra.Involutive, Numeric.Algebra
TriviallyInvolutiveCoalgebra | Numeric.Algebra.Involutive, Numeric.Algebra
uncomplicate | Numeric.Algebra.Complex
unit | Numeric.Algebra.Unital, Numeric.Algebra
Unital | Numeric.Algebra.Unital, Numeric.Algebra
UnitalAlgebra | Numeric.Algebra.Unital, Numeric.Algebra
unitM | Numeric.Covector, Numeric.Algebra
unitMap | Numeric.Map
v | Numeric.Coalgebra.Geometric
vectorPart | Numeric.Algebra.Quaternion
vectorPart' | Numeric.Coalgebra.Quaternion
Whole | Numeric.Algebra
zero | Numeric.Algebra.Class, Numeric.Algebra
zeroRep | Numeric.Module.Representable, Numeric.Algebra
ZeroRng |
1 (Type/Class) | Numeric.Rng.Zero
2 (Data Constructor) | Numeric.Rng.Zero
zeta | Numeric.Algebra.Incidence
zeta' | Numeric.Coalgebra.Incidence
\\ | Numeric.Algebra.Division, Numeric.Algebra
^ | Numeric.Algebra.Division, Numeric.Algebra
^? | Numeric.Decidable.Units
~~ | Numeric.Order.Class, Numeric.Algebra