FramedAlgebra(R, UP)ΒΆ

algcat.spad line 143

A FramedAlgebra is a FiniteRankAlgebra together with a fixed R-module basis.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, R) -> %
from RightModule R
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
from LeftModule R
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associator: (%, %, %) -> %
from NonAssociativeRng
basis: () -> Vector %
from FramedModule R
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
characteristicPolynomial: % -> UP
from FiniteRankAlgebra(R, UP)
charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero
from CharacteristicNonZero
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
from Algebra R
commutator: (%, %) -> %
from NonAssociativeRng
convert: % -> InputForm if R has Finite
from ConvertibleTo InputForm
convert: % -> Vector R
from FramedModule R
convert: Vector R -> %
from FramedModule R
coordinates: % -> Vector R
from FramedModule R
coordinates: (%, Vector %) -> Vector R
from FiniteRankAlgebra(R, UP)
coordinates: (Vector %, Vector %) -> Matrix R
from FiniteRankAlgebra(R, UP)
coordinates: Vector % -> Matrix R
from FramedModule R
discriminant: () -> R
discriminant() = determinant(traceMatrix()).
discriminant: Vector % -> R
from FiniteRankAlgebra(R, UP)
enumerate: () -> List % if R has Finite
from Finite
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
index: PositiveInteger -> % if R has Finite
from Finite
latex: % -> String
from SetCategory
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
lookup: % -> PositiveInteger if R has Finite
from Finite
minimalPolynomial: % -> UP if R has Field
from FiniteRankAlgebra(R, UP)
norm: % -> R
from FiniteRankAlgebra(R, UP)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
random: () -> % if R has Finite
from Finite
rank: () -> PositiveInteger
from FramedModule R
recip: % -> Union(%, failed)
from MagmaWithUnit
regularRepresentation: % -> Matrix R
regularRepresentation(a) returns the matrix m of the linear map defined by left multiplication by a with respect to the fixed basis. That is for all x we have coordinates(a*x) = m*coordinates(x).
regularRepresentation: (%, Vector %) -> Matrix R
from FiniteRankAlgebra(R, UP)
represents: (Vector R, Vector %) -> %
from FiniteRankAlgebra(R, UP)
represents: Vector R -> %
from FramedModule R
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
size: () -> NonNegativeInteger if R has Finite
from Finite
smaller?: (%, %) -> Boolean if R has Finite
from Comparable
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
trace: % -> R
from FiniteRankAlgebra(R, UP)
traceMatrix: () -> Matrix R
traceMatrix() is the n-by-n matrix ( Tr(vi * vj) ), where v1, ..., vn are the elements of the fixed basis.
traceMatrix: Vector % -> Matrix R
from FiniteRankAlgebra(R, UP)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

CharacteristicNonZero if R has CharacteristicNonZero

CharacteristicZero if R has CharacteristicZero

CoercibleTo OutputForm

Comparable if R has Finite

ConvertibleTo InputForm if R has Finite

Finite if R has Finite

FiniteRankAlgebra(R, UP)

FramedModule R

LeftModule %

LeftModule R

Magma

MagmaWithUnit

Module R

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule %

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown