JLF32SquareMatrix n

jarray32.spad line 463 [edit on github]

• n: NonNegativeInteger

This domain provides a fast JL 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

*: (%, DirectProduct(n, JLFloat32)) -> DirectProduct(n, JLFloat32)

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

*: (%, Integer) -> % if JLFloat32 has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, JLFloat32) -> %

from RightModule JLFloat32

*: (DirectProduct(n, JLFloat32), %) -> DirectProduct(n, JLFloat32)

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

*: (Integer, %) -> %

from AbelianGroup

*: (JLFloat32, %) -> %

from LeftModule JLFloat32

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, JLFloat32) -> %

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

antisymmetric?: % -> Boolean

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

any?: (JLFloat32 -> Boolean, %) -> Boolean

from HomogeneousAggregate JLFloat32

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

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> JLFloat32Matrix

from CoercibleTo JLFloat32Matrix

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JLFloat32 -> %

from Algebra JLFloat32

column: (%, Integer) -> DirectProduct(n, JLFloat32)

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

columnSpace: % -> List DirectProduct(n, JLFloat32)

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

commutator: (%, %) -> %

from NonAssociativeRng

convert: % -> InputForm if JLFloat32 has Finite

from ConvertibleTo InputForm

convert: % -> String

from ConvertibleTo String

copy: % -> %

from Aggregate

count: (JLFloat32 -> Boolean, %) -> NonNegativeInteger

from HomogeneousAggregate JLFloat32

count: (JLFloat32, %) -> NonNegativeInteger

from HomogeneousAggregate JLFloat32

D: % -> %

from DifferentialRing

D: (%, JLFloat32 -> JLFloat32) -> %

from DifferentialExtension JLFloat32

D: (%, JLFloat32 -> JLFloat32, NonNegativeInteger) -> %

from DifferentialExtension JLFloat32

D: (%, List Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

determinant: % -> JLFloat32

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

diagonal?: % -> Boolean

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

diagonal: % -> DirectProduct(n, JLFloat32)

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

diagonalMatrix: List JLFloat32 -> %

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

diagonalProduct: % -> JLFloat32

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

differentiate: % -> %

from DifferentialRing

differentiate: (%, JLFloat32 -> JLFloat32) -> %

from DifferentialExtension JLFloat32

differentiate: (%, JLFloat32 -> JLFloat32, NonNegativeInteger) -> %

from DifferentialExtension JLFloat32

differentiate: (%, List Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

elt: (%, Integer, Integer) -> JLFloat32

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

elt: (%, Integer, Integer, JLFloat32) -> JLFloat32

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

enumerate: () -> List % if JLFloat32 has Finite

from Finite

eq?: (%, %) -> Boolean

from Aggregate

eval: (%, Equation JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from Evalable JLFloat32

eval: (%, JLFloat32, JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from InnerEvalable(JLFloat32, JLFloat32)

eval: (%, List Equation JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from Evalable JLFloat32

eval: (%, List JLFloat32, List JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from InnerEvalable(JLFloat32, JLFloat32)

every?: (JLFloat32 -> Boolean, %) -> Boolean

from HomogeneousAggregate JLFloat32

exquo: (%, JLFloat32) -> Union(%, failed)

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

hash: % -> SingleInteger if JLFloat32 has Finite

from Hashable

hashUpdate!: (HashState, %) -> HashState if JLFloat32 has Finite

from Hashable

index: PositiveInteger -> % if JLFloat32 has Finite

from Finite

inverse: % -> Union(%, failed)

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

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 JLFloat32

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

lookup: % -> PositiveInteger if JLFloat32 has Finite

from Finite

map: ((JLFloat32, JLFloat32) -> JLFloat32, %, %) -> %

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

map: (JLFloat32 -> JLFloat32, %) -> %

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

matrix: List List JLFloat32 -> %

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

max: % -> JLFloat32

from HomogeneousAggregate JLFloat32

max: ((JLFloat32, JLFloat32) -> Boolean, %) -> JLFloat32

from HomogeneousAggregate JLFloat32

maxColIndex: % -> Integer

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

maxRowIndex: % -> Integer

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

member?: (JLFloat32, %) -> Boolean

from HomogeneousAggregate JLFloat32

members: % -> List JLFloat32

from HomogeneousAggregate JLFloat32

min: % -> JLFloat32

from HomogeneousAggregate JLFloat32

minColIndex: % -> Integer

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

minordet: % -> JLFloat32

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

minRowIndex: % -> Integer

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

ncols: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

nrows: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

nullity: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

nullSpace: % -> List DirectProduct(n, JLFloat32)

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

parts: % -> List JLFloat32

from HomogeneousAggregate JLFloat32

Pfaffian: % -> JLFloat32

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra JLFloat32

qcoerce: JLFloat32Matrix -> %

qcoerce(m) coerces m to JLF32SquareMatrix trusting that m is square.

qelt: (%, Integer, Integer) -> JLFloat32

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

random: () -> % if JLFloat32 has Finite

from Finite

rank: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

recip: % -> Union(%, failed)

from MagmaWithUnit

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if JLFloat32 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix JLFloat32, vec: Vector JLFloat32)

from LinearlyExplicitOver JLFloat32

reducedSystem: Matrix % -> Matrix Integer if JLFloat32 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JLFloat32

from LinearlyExplicitOver JLFloat32

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JLFloat32

from RetractableTo JLFloat32

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JLFloat32, failed)

from RetractableTo JLFloat32

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

row: (%, Integer) -> DirectProduct(n, JLFloat32)

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

rowEchelon: % -> %

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

sample: %

from AbelianMonoid

scalarMatrix: JLFloat32 -> %

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

size: () -> NonNegativeInteger if JLFloat32 has Finite

from Finite

smaller?: (%, %) -> Boolean if JLFloat32 has Finite

from Comparable

square?: % -> Boolean

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

squareMatrix: JLFloat32Matrix -> %

squareMatrix(m) returns a copy of m as a JLF32SquareMatrix.

string: % -> String

from JLType

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

from CancellationAbelianMonoid

symmetric?: % -> Boolean

from RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

trace: % -> JLFloat32

from SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Aggregate

Algebra JLFloat32

BasicType

BiModule(%, %)

BiModule(JLFloat32, JLFloat32)

CancellationAbelianMonoid

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JLFloat32

CoercibleTo JLFloat32Matrix

CoercibleTo OutputForm

Comparable if JLFloat32 has Finite

ConvertibleTo InputForm if JLFloat32 has Finite

ConvertibleTo String

DifferentialExtension JLFloat32

DifferentialRing

Evalable JLFloat32 if JLFloat32 has Evalable JLFloat32

Finite if JLFloat32 has Finite

finiteAggregate

FullyLinearlyExplicitOver JLFloat32

FullyRetractableTo JLFloat32

Hashable if JLFloat32 has Finite

HomogeneousAggregate JLFloat32

InnerEvalable(JLFloat32, JLFloat32) if JLFloat32 has Evalable JLFloat32

JLType

LeftModule %

LeftModule JLFloat32

LinearlyExplicitOver Integer if JLFloat32 has LinearlyExplicitOver Integer

LinearlyExplicitOver JLFloat32

Magma

MagmaWithUnit

Module JLFloat32

Monoid

NonAssociativeAlgebra JLFloat32

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

PartialDifferentialRing Symbol if JLFloat32 has PartialDifferentialRing Symbol

RectangularMatrixCategory(n, n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JLFloat32

RightModule %

RightModule Integer if JLFloat32 has LinearlyExplicitOver Integer

RightModule JLFloat32

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

SquareMatrixCategory(n, JLFloat32, DirectProduct(n, JLFloat32), DirectProduct(n, JLFloat32))

TwoSidedRecip

unitsKnown