algebra-4.3: Constructive abstract algebra

Index

$*Numeric.Covector, Numeric.Algebra
$@Numeric.Map
%Numeric.Field.Fraction
*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
AbelianNumeric.Additive.Class, Numeric.Algebra
AdditiveNumeric.Additive.Class, Numeric.Algebra
AdditiveOrderNumeric.Order.Additive, Numeric.Algebra
addRepNumeric.Module.Representable, Numeric.Algebra
adjointNumeric.Algebra.Involutive, Numeric.Algebra
AlgebraNumeric.Algebra.Class, Numeric.Algebra
antiEuclideanNumeric.Coalgebra.Geometric
antipodeNumeric.Algebra.Hopf, Numeric.Algebra
antipodeMNumeric.Covector, Numeric.Algebra
antipodeMapNumeric.Map
appEndNumeric.Ring.Endomorphism
BandNumeric.Algebra.Idempotent, Numeric.Band.Class, Numeric.Algebra
BasisCoblade 
1 (Type/Class)Numeric.Coalgebra.Geometric
2 (Data Constructor)Numeric.Coalgebra.Geometric
BialgebraNumeric.Algebra.Unital, Numeric.Algebra
charNumeric.Rig.Characteristic, Numeric.Algebra
CharacteristicNumeric.Rig.Characteristic, Numeric.Algebra
charIntNumeric.Rig.Characteristic, Numeric.Algebra
charWordNumeric.Rig.Characteristic, Numeric.Algebra
chineseRemainderNumeric.Domain.Euclidean
cliffordConjugateNumeric.Coalgebra.Geometric
CoalgebraNumeric.Algebra.Class, Numeric.Algebra
CocommutativeCoalgebraNumeric.Algebra.Commutative, Numeric.Algebra
coinvNumeric.Algebra.Involutive, Numeric.Algebra
coinvMNumeric.Covector, Numeric.Algebra
coinvMapNumeric.Map
CommutativeNumeric.Algebra.Commutative, Numeric.Algebra
CommutativeAlgebraNumeric.Algebra.Commutative, Numeric.Algebra
CommutativeBialgebraNumeric.Algebra.Commutative, Numeric.Algebra
comparableNumeric.Order.Class, Numeric.Algebra
Complex 
1 (Type/Class)Numeric.Algebra.Complex
2 (Data Constructor)Numeric.Algebra.Complex
ComplexBasisNumeric.Algebra.Complex
complicateNumeric.Algebra.Quaternion
complicate'Numeric.Coalgebra.Quaternion
ComplicatedNumeric.Algebra.Complex.Class, Numeric.Algebra.Complex, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
comultNumeric.Algebra.Class, Numeric.Algebra
ComultivectorNumeric.Coalgebra.Geometric
comultMNumeric.Covector, Numeric.Algebra
comultMapNumeric.Map
contractLNumeric.Coalgebra.Geometric
contractRNumeric.Coalgebra.Geometric
convolveMNumeric.Covector, Numeric.Algebra
convolveMapNumeric.Map
CosNumeric.Coalgebra.Trigonometric
cosNumeric.Coalgebra.Trigonometric.Class, Numeric.Coalgebra.Trigonometric
CoshNumeric.Coalgebra.Hyperbolic
coshNumeric.Coalgebra.Hyperbolic.Class, Numeric.Algebra.Hyperbolic, Numeric.Coalgebra.Hyperbolic
Cosh'Numeric.Algebra.Hyperbolic
counitNumeric.Algebra.Unital, Numeric.Algebra
CounitalCoalgebraNumeric.Algebra.Unital, Numeric.Algebra
counitMNumeric.Covector, Numeric.Algebra
counitMapNumeric.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
dNumeric.Algebra.Dual.Class, Numeric.Algebra.Dual, Numeric.Coalgebra.Dual
DecidableAssociatesNumeric.Decidable.Associates, Numeric.Algebra
DecidableNilpotentNumeric.Decidable.Nilpotent
DecidableUnitsNumeric.Decidable.Units, Numeric.Algebra
DecidableZeroNumeric.Decidable.Zero, Numeric.Algebra
degreeNumeric.Domain.Euclidean
denominatorNumeric.Field.Fraction
DioidNumeric.Dioid.Class, Numeric.Algebra
DistinguishedNumeric.Algebra.Distinguished.Class, Numeric.Algebra.Complex, Numeric.Algebra.Dual, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Dual, Numeric.Coalgebra.Quaternion
divideNumeric.Domain.Euclidean
dividesNumeric.Domain.Integral
DivisionNumeric.Algebra.Division, Numeric.Algebra
DivisionAlgebraNumeric.Algebra.Division, Numeric.Algebra
DivisionRingNumeric.Ring.Division, Numeric.Algebra
DomainNumeric.Domain.Class
dotNumeric.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
DualBasisNumeric.Algebra.Dual
DualBasis'Numeric.Coalgebra.Dual
E 
1 (Data Constructor)Numeric.Algebra.Complex
2 (Data Constructor)Numeric.Algebra.Dual
3 (Data Constructor)Numeric.Algebra.Quaternion
4 (Data Constructor)Numeric.Coalgebra.Dual
e 
1 (Function)Numeric.Algebra.Distinguished.Class, Numeric.Algebra.Complex, Numeric.Algebra.Dual, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Dual, Numeric.Coalgebra.Quaternion
2 (Function)Numeric.Coalgebra.Geometric
E'Numeric.Coalgebra.Quaternion
egcdNumeric.Domain.PID
EigenbasisNumeric.Coalgebra.Geometric
EigenmetricNumeric.Coalgebra.Geometric
End 
1 (Type/Class)Numeric.Ring.Endomorphism
2 (Data Constructor)Numeric.Ring.Endomorphism
euclidNumeric.Domain.Euclidean
Euclidean 
1 (Type/Class)Numeric.Domain.Euclidean
2 (Type/Class)Numeric.Coalgebra.Geometric
3 (Data Constructor)Numeric.Coalgebra.Geometric
euclideanNumeric.Coalgebra.Geometric
Exp 
1 (Type/Class)Numeric.Exp
2 (Data Constructor)Numeric.Exp
FactorableNumeric.Algebra.Factorable, Numeric.Algebra
factorWithNumeric.Algebra.Factorable, Numeric.Algebra
FieldNumeric.Field.Class, Numeric.Algebra
filterGradeNumeric.Coalgebra.Geometric
FractionNumeric.Field.Fraction
frobeniusNumeric.Ring.Endomorphism
fromEndNumeric.Ring.Endomorphism
fromIntegerNumeric.Ring.Class, Numeric.Algebra
fromIntegerRepNumeric.Module.Representable, Numeric.Algebra
fromIntegralNumeric.Ring.Class
fromNaturalNumeric.Rig.Class, Numeric.Algebra
fromNaturalRepNumeric.Module.Representable, Numeric.Algebra
gcdNumeric.Domain.GCD
gcd'Numeric.Domain.GCD
GCDDomainNumeric.Domain.GCD
geometricNumeric.Coalgebra.Geometric
gradeNumeric.Coalgebra.Geometric
gradeInversionNumeric.Coalgebra.Geometric
GroupNumeric.Additive.Group, Numeric.Algebra
HamiltonianNumeric.Algebra.Quaternion.Class, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
hestenesNumeric.Coalgebra.Geometric
HopfAlgebraNumeric.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
HyperBasisNumeric.Coalgebra.Hyperbolic
HyperBasis'Numeric.Algebra.Hyperbolic
HyperbolicNumeric.Coalgebra.Hyperbolic.Class, Numeric.Algebra.Hyperbolic, Numeric.Coalgebra.Hyperbolic
I 
1 (Data Constructor)Numeric.Algebra.Complex
2 (Data Constructor)Numeric.Algebra.Quaternion
iNumeric.Algebra.Complex.Class, Numeric.Algebra.Complex, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
I'Numeric.Coalgebra.Quaternion
IdempotentNumeric.Additive.Class, Numeric.Algebra
IdempotentAlgebraNumeric.Algebra.Idempotent, Numeric.Algebra
IdempotentBialgebraNumeric.Algebra.Idempotent, Numeric.Algebra
IdempotentCoalgebraNumeric.Algebra.Idempotent
imagPartNumeric.Algebra.Complex
InfinitesimalNumeric.Algebra.Dual.Class, Numeric.Algebra.Dual, Numeric.Coalgebra.Dual
IntegralDomainNumeric.Domain.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
invNumeric.Algebra.Involutive, Numeric.Algebra
invMNumeric.Covector, Numeric.Algebra
invMapNumeric.Map
InvolutiveAlgebraNumeric.Algebra.Involutive, Numeric.Algebra
InvolutiveBialgebraNumeric.Algebra.Involutive, Numeric.Algebra
InvolutiveCoalgebraNumeric.Algebra.Involutive, Numeric.Algebra
InvolutiveMultiplicationNumeric.Algebra.Involutive, Numeric.Algebra
InvolutiveSemiringNumeric.Algebra.Involutive, Numeric.Semiring.Involutive, Numeric.Algebra
isAssociateNumeric.Decidable.Associates
isAssociateIntegralNumeric.Decidable.Associates
isAssociateWholeNumeric.Decidable.Associates
isNilpotentNumeric.Decidable.Nilpotent
isUnitNumeric.Decidable.Units
isZeroNumeric.Decidable.Zero
JNumeric.Algebra.Quaternion
jNumeric.Algebra.Quaternion.Class, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
J'Numeric.Coalgebra.Quaternion
KNumeric.Algebra.Quaternion
kNumeric.Algebra.Quaternion.Class, Numeric.Algebra.Quaternion, Numeric.Coalgebra.Quaternion
K'Numeric.Coalgebra.Quaternion
lcmNumeric.Domain.GCD
leadingUnitNumeric.Algebra.Unital.UnitNormalForm
LeftModuleNumeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
liftProductNumeric.Coalgebra.Geometric
liftRngHomNumeric.Ring.Rng
LocallyFiniteOrderNumeric.Order.LocallyFinite, Numeric.Algebra
LocalRingNumeric.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
maybeQuotNumeric.Domain.Integral
metricNumeric.Coalgebra.Geometric
minusRepNumeric.Module.Representable, Numeric.Algebra
ModuleNumeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
moebiusNumeric.Algebra.Incidence
moebius'Numeric.Coalgebra.Incidence
moebiusInversionNumeric.Order.LocallyFinite
MonoidalNumeric.Algebra.Class, Numeric.Algebra
Morphism 
1 (Type/Class)Numeric.Coalgebra.Categorical
2 (Data Constructor)Numeric.Coalgebra.Categorical
mulRepNumeric.Module.Representable, Numeric.Algebra
multNumeric.Algebra.Class, Numeric.Algebra
MultiplicativeNumeric.Algebra.Class, Numeric.Algebra
multMNumeric.Covector, Numeric.Algebra
multMapNumeric.Map
NaturalNumeric.Algebra
negateNumeric.Additive.Group, Numeric.Algebra
negateRepNumeric.Module.Representable, Numeric.Algebra
normalizeNumeric.Algebra.Unital.UnitNormalForm
numeratorNumeric.Field.Fraction
oneNumeric.Algebra.Unital, Numeric.Algebra
oneRepNumeric.Module.Representable, Numeric.Algebra
Opposite 
1 (Type/Class)Numeric.Ring.Opposite
2 (Data Constructor)Numeric.Ring.Opposite
OrderNumeric.Order.Class, Numeric.Algebra
orderNumeric.Order.Class, Numeric.Algebra
OrderedRigNumeric.Rig.Ordered, Numeric.Algebra
orderOrdNumeric.Order.Class
outerNumeric.Coalgebra.Geometric
paddNumeric.Partial.Semigroup
PartialGroupNumeric.Partial.Group
PartialMonoidNumeric.Partial.Monoid
PartialSemigroupNumeric.Partial.Semigroup
PartitionableNumeric.Additive.Class, Numeric.Algebra
partitionWithNumeric.Additive.Class, Numeric.Algebra
PIDNumeric.Domain.PID
pminusNumeric.Partial.Group
pnegateNumeric.Partial.Group
powNumeric.Algebra.Unital, Numeric.Algebra
pow1pNumeric.Algebra.Class, Numeric.Algebra
pow1pBandNumeric.Algebra.Idempotent, Numeric.Band.Class, Numeric.Algebra
pow1pIntegralNumeric.Algebra.Class
powBandNumeric.Algebra.Idempotent, Numeric.Band.Class, Numeric.Algebra
productNumeric.Algebra.Unital, Numeric.Algebra
product1Numeric.Algebra.Class, Numeric.Algebra
productWithNumeric.Algebra.Unital, Numeric.Algebra
productWith1Numeric.Algebra.Class, Numeric.Algebra
prsNumeric.Domain.Euclidean
psubtractNumeric.Partial.Group
pzeroNumeric.Partial.Monoid
QuadranceNumeric.Quadrance.Class, Numeric.Algebra
quadranceNumeric.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
QuaternionBasisNumeric.Algebra.Quaternion
QuaternionBasis'Numeric.Coalgebra.Quaternion
quotNumeric.Domain.Euclidean
rangeNumeric.Order.LocallyFinite
rangeSizeNumeric.Order.LocallyFinite
RatioNumeric.Field.Fraction
realPartNumeric.Algebra.Complex
recipNumeric.Algebra.Division, Numeric.Algebra
recipriocalNumeric.Algebra.Division, Numeric.Algebra
recipUnitNumeric.Decidable.Units
recipUnitIntegralNumeric.Decidable.Units
recipUnitWholeNumeric.Decidable.Units
Rect 
1 (Type/Class)Numeric.Band.Rectangular
2 (Data Constructor)Numeric.Band.Rectangular
reduceFractionNumeric.Domain.GCD
remNumeric.Domain.Euclidean
reverseNumeric.Coalgebra.Geometric
RigNumeric.Rig.Class, Numeric.Algebra
RightModuleNumeric.Algebra.Class, Numeric.Module.Class, Numeric.Algebra
RingNumeric.Ring.Class, Numeric.Algebra
RngNumeric.Rng.Class, Numeric.Algebra
RngRing 
1 (Type/Class)Numeric.Ring.Rng
2 (Data Constructor)Numeric.Ring.Rng
rngRingHomNumeric.Ring.Rng
runBasisCobladeNumeric.Coalgebra.Geometric
runExpNumeric.Exp
runLogNumeric.Log
runOppositeNumeric.Ring.Opposite
runZeroRngNumeric.Rng.Zero
scalarPartNumeric.Algebra.Quaternion
scalarPart'Numeric.Coalgebra.Quaternion
SemiringNumeric.Algebra.Class, Numeric.Algebra
SinNumeric.Coalgebra.Trigonometric
sinNumeric.Coalgebra.Trigonometric.Class, Numeric.Coalgebra.Trigonometric
SinhNumeric.Coalgebra.Hyperbolic
sinhNumeric.Coalgebra.Hyperbolic.Class, Numeric.Algebra.Hyperbolic, Numeric.Coalgebra.Hyperbolic
Sinh'Numeric.Algebra.Hyperbolic
sinnumNumeric.Algebra.Class, Numeric.Algebra
sinnum1pNumeric.Additive.Class, Numeric.Algebra
sinnum1pIdempotentNumeric.Additive.Class, Numeric.Algebra
sinnum1pRepNumeric.Module.Representable, Numeric.Algebra
sinnumIdempotentNumeric.Algebra.Class, Numeric.Algebra
sinnumRepNumeric.Module.Representable, Numeric.Algebra
splitUnitNumeric.Algebra.Unital.UnitNormalForm
subtractNumeric.Additive.Group, Numeric.Algebra
subtractRepNumeric.Module.Representable, Numeric.Algebra
sumNumeric.Algebra.Class, Numeric.Algebra
sum1Numeric.Additive.Class, Numeric.Algebra
sumWithNumeric.Algebra.Class, Numeric.Algebra
sumWith1Numeric.Additive.Class, Numeric.Algebra
timesNumeric.Additive.Group, Numeric.Algebra
timesRepNumeric.Module.Representable, Numeric.Algebra
toEndNumeric.Ring.Endomorphism
Trig 
1 (Type/Class)Numeric.Coalgebra.Trigonometric
2 (Data Constructor)Numeric.Coalgebra.Trigonometric
TrigBasisNumeric.Coalgebra.Trigonometric
TrigonometricNumeric.Coalgebra.Trigonometric.Class, Numeric.Coalgebra.Trigonometric
TriviallyInvolutiveNumeric.Algebra.Involutive, Numeric.Algebra
TriviallyInvolutiveAlgebraNumeric.Algebra.Involutive, Numeric.Algebra
TriviallyInvolutiveBialgebraNumeric.Algebra.Involutive, Numeric.Algebra
TriviallyInvolutiveCoalgebraNumeric.Algebra.Involutive, Numeric.Algebra
UFDNumeric.Domain.UFD
uncomplicateNumeric.Algebra.Complex
unitNumeric.Algebra.Unital, Numeric.Algebra
UnitalNumeric.Algebra.Unital, Numeric.Algebra
UnitalAlgebraNumeric.Algebra.Unital, Numeric.Algebra
unitMNumeric.Covector, Numeric.Algebra
unitMapNumeric.Map
UnitNormalFormNumeric.Algebra.Unital.UnitNormalForm
vNumeric.Coalgebra.Geometric
vectorPartNumeric.Algebra.Quaternion
vectorPart'Numeric.Coalgebra.Quaternion
zeroNumeric.Algebra.Class, Numeric.Algebra
ZeroProductSemiringNumeric.Semiring.ZeroProduct
zeroRepNumeric.Module.Representable, Numeric.Algebra
ZeroRng 
1 (Type/Class)Numeric.Rng.Zero
2 (Data Constructor)Numeric.Rng.Zero
zetaNumeric.Algebra.Incidence
zeta'Numeric.Coalgebra.Incidence
\\Numeric.Algebra.Division, Numeric.Algebra
^Numeric.Algebra.Division, Numeric.Algebra
^?Numeric.Decidable.Units
~~Numeric.Order.Class, Numeric.Algebra