JuliaComplexF32SquareMatrix n

jarray32.spad line 918 [edit on github]

• n: NonNegativeInteger

This domain provides a fast Julia Float32 square matrix type with no bound checking on elt's. Minimum index is 1.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

#: % -> NonNegativeInteger

from Aggregate

*: (%, %) -> %

from Magma

*: (%, Integer) -> % if JuliaComplexF32 has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, JuliaComplexF32) -> %

from RightModule JuliaComplexF32

*: (%, JuliaComplexF32Vector) -> JuliaComplexF32Vector

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

*: (Integer, %) -> %

from AbelianGroup

*: (JuliaComplexF32, %) -> %

from LeftModule JuliaComplexF32

*: (JuliaComplexF32Vector, %) -> JuliaComplexF32Vector

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, JuliaComplexF32) -> %

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

antisymmetric?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

any?: (JuliaComplexF32 -> Boolean, %) -> Boolean

from HomogeneousAggregate JuliaComplexF32

associator: (%, %, %) -> %

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> JuliaComplexF32Matrix

coerce(m) coerces m to JuliaComplexF32Matrix

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

from CoercibleFrom Integer

coerce: JuliaComplexF32 -> %

from CoercibleFrom JuliaComplexF32

column: (%, Integer) -> JuliaComplexF32Vector

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

columnSpace: % -> List JuliaComplexF32Vector

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

commutator: (%, %) -> %

from NonAssociativeRng

convert: % -> InputForm if JuliaComplexF32 has Finite

from ConvertibleTo InputForm

convert: % -> String

from ConvertibleTo String

copy: % -> %

from Aggregate

count: (JuliaComplexF32 -> Boolean, %) -> NonNegativeInteger

from HomogeneousAggregate JuliaComplexF32

count: (JuliaComplexF32, %) -> NonNegativeInteger

from HomogeneousAggregate JuliaComplexF32

D: % -> %

from DifferentialRing

D: (%, JuliaComplexF32 -> JuliaComplexF32) -> %

from DifferentialExtension JuliaComplexF32

D: (%, JuliaComplexF32 -> JuliaComplexF32, NonNegativeInteger) -> %

from DifferentialExtension JuliaComplexF32

D: (%, List Symbol) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, Symbol) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

determinant: % -> JuliaComplexF32

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

diagonal?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

diagonal: % -> JuliaComplexF32Vector

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

diagonalMatrix: List JuliaComplexF32 -> %

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

diagonalProduct: % -> JuliaComplexF32

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

differentiate: % -> %

from DifferentialRing

differentiate: (%, JuliaComplexF32 -> JuliaComplexF32) -> %

from DifferentialExtension JuliaComplexF32

differentiate: (%, JuliaComplexF32 -> JuliaComplexF32, NonNegativeInteger) -> %

from DifferentialExtension JuliaComplexF32

differentiate: (%, List Symbol) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, Symbol) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if JuliaComplexF32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

elt: (%, Integer, Integer) -> JuliaComplexF32

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

elt: (%, Integer, Integer, JuliaComplexF32) -> JuliaComplexF32

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

enumerate: () -> List % if JuliaComplexF32 has Finite

from Finite

eq?: (%, %) -> Boolean

from Aggregate

eval: (%, Equation JuliaComplexF32) -> % if JuliaComplexF32 has Evalable JuliaComplexF32

from Evalable JuliaComplexF32

eval: (%, JuliaComplexF32, JuliaComplexF32) -> % if JuliaComplexF32 has Evalable JuliaComplexF32

from InnerEvalable(JuliaComplexF32, JuliaComplexF32)

eval: (%, List Equation JuliaComplexF32) -> % if JuliaComplexF32 has Evalable JuliaComplexF32

from Evalable JuliaComplexF32

eval: (%, List JuliaComplexF32, List JuliaComplexF32) -> % if JuliaComplexF32 has Evalable JuliaComplexF32

from InnerEvalable(JuliaComplexF32, JuliaComplexF32)

every?: (JuliaComplexF32 -> Boolean, %) -> Boolean

from HomogeneousAggregate JuliaComplexF32

exquo: (%, JuliaComplexF32) -> Union(%, failed)

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

hash: % -> SingleInteger if JuliaComplexF32 has Finite

from Hashable

hashUpdate!: (HashState, %) -> HashState if JuliaComplexF32 has Finite

from Hashable

index: PositiveInteger -> % if JuliaComplexF32 has Finite

from Finite

inverse: % -> Union(%, failed)

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

less?: (%, NonNegativeInteger) -> Boolean

from Aggregate

listOfLists: % -> List List JuliaComplexF32

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

lookup: % -> PositiveInteger if JuliaComplexF32 has Finite

from Finite

map: ((JuliaComplexF32, JuliaComplexF32) -> JuliaComplexF32, %, %) -> %

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

map: (JuliaComplexF32 -> JuliaComplexF32, %) -> %

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

matrix: List List JuliaComplexF32 -> %

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

max: % -> JuliaComplexF32 if JuliaComplexF32 has OrderedSet

from HomogeneousAggregate JuliaComplexF32

max: ((JuliaComplexF32, JuliaComplexF32) -> Boolean, %) -> JuliaComplexF32

from HomogeneousAggregate JuliaComplexF32

maxColIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

maxRowIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

member?: (JuliaComplexF32, %) -> Boolean

from HomogeneousAggregate JuliaComplexF32

members: % -> List JuliaComplexF32

from HomogeneousAggregate JuliaComplexF32

min: % -> JuliaComplexF32 if JuliaComplexF32 has OrderedSet

from HomogeneousAggregate JuliaComplexF32

minColIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

minordet: % -> JuliaComplexF32

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

minRowIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

ncols: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

nrows: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

nullity: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

nullSpace: % -> List JuliaComplexF32Vector

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

parts: % -> List JuliaComplexF32

from HomogeneousAggregate JuliaComplexF32

Pfaffian: % -> JuliaComplexF32

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra JuliaComplexF32

qcoerce: JuliaComplexF32Matrix -> %

qcoerce(m) coerces m to JuliaComplexF32SquareMatrix trusting that m is square.

qelt: (%, Integer, Integer) -> JuliaComplexF32

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

random: () -> % if JuliaComplexF32 has Finite

from Finite

rank: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

recip: % -> Union(%, failed)

from MagmaWithUnit

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if JuliaComplexF32 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix JuliaComplexF32, vec: Vector JuliaComplexF32)

from LinearlyExplicitOver JuliaComplexF32

reducedSystem: Matrix % -> Matrix Integer if JuliaComplexF32 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JuliaComplexF32

from LinearlyExplicitOver JuliaComplexF32

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JuliaComplexF32

from RetractableTo JuliaComplexF32

retractIfCan: % -> Union(Fraction Integer, failed)

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JuliaComplexF32, failed)

from RetractableTo JuliaComplexF32

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

row: (%, Integer) -> JuliaComplexF32Vector

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

rowEchelon: % -> %

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

sample: %

from AbelianMonoid

scalarMatrix: JuliaComplexF32 -> %

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

size: () -> NonNegativeInteger if JuliaComplexF32 has Finite

from Finite

smaller?: (%, %) -> Boolean if JuliaComplexF32 has Finite

from Comparable

square?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

squareMatrix: JuliaComplexF32Matrix -> %

squareMatrix(m) returns a copy of m as a JuliaComplexF32SquareMatrix.

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

symmetric?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

trace: % -> JuliaComplexF32

from SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Aggregate

Algebra JuliaComplexF32

BasicType

BiModule(%, %)

BiModule(JuliaComplexF32, JuliaComplexF32)

CancellationAbelianMonoid

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JuliaComplexF32

CoercibleTo JuliaComplexF32Matrix

CoercibleTo OutputForm

Comparable if JuliaComplexF32 has Finite

ConvertibleTo InputForm if JuliaComplexF32 has Finite

ConvertibleTo String

DifferentialExtension JuliaComplexF32

DifferentialRing

Evalable JuliaComplexF32 if JuliaComplexF32 has Evalable JuliaComplexF32

Finite if JuliaComplexF32 has Finite

finiteAggregate

FullyLinearlyExplicitOver JuliaComplexF32

FullyRetractableTo JuliaComplexF32

Hashable if JuliaComplexF32 has Finite

HomogeneousAggregate JuliaComplexF32

InnerEvalable(JuliaComplexF32, JuliaComplexF32) if JuliaComplexF32 has Evalable JuliaComplexF32

JuliaType

LeftModule %

LeftModule JuliaComplexF32

LinearlyExplicitOver Integer if JuliaComplexF32 has LinearlyExplicitOver Integer

LinearlyExplicitOver JuliaComplexF32

Magma

MagmaWithUnit

Module JuliaComplexF32

Monoid

NonAssociativeAlgebra JuliaComplexF32

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

PartialDifferentialRing Symbol if JuliaComplexF32 has PartialDifferentialRing Symbol

RectangularMatrixCategory(n, n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JuliaComplexF32

RightModule %

RightModule Integer if JuliaComplexF32 has LinearlyExplicitOver Integer

RightModule JuliaComplexF32

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

SquareMatrixCategory(n, JuliaComplexF32, JuliaComplexF32Vector, JuliaComplexF32Vector)

TwoSidedRecip

unitsKnown