JuliaMatrix R

jobject.spad line 1628 [edit on github]

This domain provides a generic Julia matrix type stored in Julia with no bound checking on elt's. Minimum index is 1. Beware, for matrix with Nemo elements, contrary to Julia matrix, Nemo follows the convention of the C libraries, it wraps and uses row major representation. See https://nemocas.github.io/Nemo.jl/stable/developer/interfaces/#Column-major-vs-row-major-matrices for more information.

#: % -> NonNegativeInteger

from Aggregate

*: (%, %) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

*: (%, JuliaVector R) -> JuliaVector R

from MatrixCategory(R, JuliaVector R, JuliaVector R)

*: (%, R) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

*: (Integer, %) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

*: (JuliaVector R, %) -> JuliaVector R

from MatrixCategory(R, JuliaVector R, JuliaVector R)

*: (R, %) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

+: (%, %) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

-: % -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

-: (%, %) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

/: (%, R) -> % if R has Field

from MatrixCategory(R, JuliaVector R, JuliaVector R)

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> % if R has Field

from MatrixCategory(R, JuliaVector R, JuliaVector R)

^: (%, NonNegativeInteger) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

~=: (%, %) -> Boolean

from BasicType

antisymmetric?: % -> Boolean

from MatrixCategory(R, JuliaVector R, JuliaVector R)

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

from HomogeneousAggregate R

array2: List List R -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

blockConcat: List List % -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

blockSplit: (%, List NonNegativeInteger, List NonNegativeInteger) -> List List %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

blockSplit: (%, PositiveInteger, PositiveInteger) -> List List %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

coerce: % -> JuliaObject

from JuliaObjectType

coerce: % -> Matrix R

coerce(m) coerces a copy of m to a Matrix(R).

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: JuliaComplexF32Matrix -> JuliaMatrix JuliaObjComplexF32

coerce(x): convenience function.

coerce: JuliaComplexF64Matrix -> JuliaMatrix JuliaObjComplexF64

coerce(x): convenience function.

coerce: JuliaFloat32Matrix -> JuliaMatrix JuliaObjFloat32

coerce(x): convenience function.

coerce: JuliaFloat64Matrix -> JuliaMatrix JuliaObjFloat64

coerce(x): convenience function.

coerce: JuliaVector R -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

colSlice: % -> Segment Integer

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

column: (%, Integer) -> JuliaVector R

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

columnSpace: % -> List JuliaVector R if R has EuclideanDomain

from MatrixCategory(R, JuliaVector R, JuliaVector R)

convert: % -> String

from ConvertibleTo String

copy: % -> %

from Aggregate

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

from HomogeneousAggregate R

count: (R, %) -> NonNegativeInteger

from HomogeneousAggregate R

determinant: % -> R if R has CommutativeRing

from MatrixCategory(R, JuliaVector R, JuliaVector R)

diagonal?: % -> Boolean

from MatrixCategory(R, JuliaVector R, JuliaVector R)

diagonalMatrix: JuliaVector R -> %

diagonalMatrix(v) returns a diagonal matrix with elements of v.

diagonalMatrix: List % -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

diagonalMatrix: List R -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

eigenvalues: % -> JuliaVector R if R has ComplexCategory NemoRealField

eigenvalues(m) returns eigenvalues of m.

elt: (%, Integer) -> JuliaObject

from JuliaObjectAggregate

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, Integer, List Segment Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, JuliaSymbol) -> JuliaObject

from JuliaObjectAggregate

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, List Integer, Segment Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, List Segment Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, List Segment Integer, List Segment Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, List Segment Integer, Segment Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, Segment Integer, List Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

elt: (%, Segment Integer, List Segment Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

eq?: (%, %) -> Boolean

from Aggregate

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

from Evalable R

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

from Evalable R

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

from InnerEvalable(R, R)

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

from InnerEvalable(R, R)

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

from HomogeneousAggregate R

exquo: (%, R) -> Union(%, failed) if R has IntegralDomain

from MatrixCategory(R, JuliaVector R, JuliaVector R)

factorize: JuliaMatrix JuliaObjComplexF32 -> JuliaObject

factorize(m) factorizes m using a suited matrix factorization for m. For a symmetric matrix the Bunch-Kaufman factorization will be choosen whereas for generic matrices, a LU or a QR factorization will be used.

factorize: JuliaMatrix JuliaObjComplexF64 -> JuliaObject

factorize(m) factorizes m using a suited matrix factorization for m. For a symmetric matrix the Bunch-Kaufman factorization will be choosen whereas for generic matrices, a LU or a QR factorization will be used.

factorize: JuliaMatrix JuliaObjFloat32 -> JuliaObject

factorize(m) factorizes m using a suited matrix factorization for m. For a symmetric matrix the Bunch-Kaufman factorization will be choosen whereas for generic matrices, a LU or a QR factorization will be used.

factorize: JuliaMatrix JuliaObjFloat64 -> JuliaObject

factorize(m) factorizes m using a suited matrix factorization for m. For a symmetric matrix the Bunch-Kaufman factorization will be choosen whereas for generic matrices, a LU or a QR factorization will be used.

fill!: (%, R) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

hash: % -> SingleInteger if R has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if R has Hashable

from Hashable

horizConcat: (%, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

horizConcat: List % -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

horizSplit: (%, List NonNegativeInteger) -> List %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

horizSplit: (%, PositiveInteger) -> List %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

identity: NonNegativeInteger -> %

identity(n) returns a n by n identity matrix.

inverse: % -> %

inverse(m) returns inverse matrix. Throws a Julia error if m is no invertible.

inverse: % -> Union(%, failed) if R has Field

from MatrixCategory(R, JuliaVector R, JuliaVector R)

invertIfCan: % -> Union(%, failed) if R has IntegralDomain

invertIfCan(m) returns the inverse of the matrix m. If the matrix is not invertible, “failed” is returned. Error: if the matrix is not square.

jlAbout: % -> Void

from JuliaObjectType

jlApply: (String, %) -> %

from JuliaObjectType

jlApply: (String, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %, %) -> %

from JuliaObjectType

jlApprox?: (%, %) -> Boolean if R hasn’t NemoType

jlApprox?(A,B) computes component-wise inexact equality with default parameters. Two numbers compare equal if their relative distance or their absolute distance is within tolerance bounds.

jlDisplay: % -> Void

from JuliaObjectType

jlId: % -> JuliaInt64

from JuliaObjectType

jlObject: () -> String

from JuliaObjectType

jlRef: % -> SExpression

from JuliaObjectType

jlref: String -> %

from JuliaObjectType

jlType: % -> String

from JuliaObjectType

jmatrix: String -> %

jmatrix(str) evaluates the string str and returns the generated matrix. No checks are done at the FriCAS level.

kronecker_prod1: (%, Integer, List List NonNegativeInteger, List %, NonNegativeInteger, NonNegativeInteger, Union(R, one)) -> Void

from MatrixCategory(R, JuliaVector R, JuliaVector R)

kroneckerProduct: (%, %) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

kroneckerProduct: List % -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

kroneckerSum: (%, %) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

kroneckerSum: List % -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

latex: % -> String

from SetCategory

less?: (%, NonNegativeInteger) -> Boolean

from Aggregate

listOfLists: % -> List List R

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

map!: (R -> R, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

matrix: (NonNegativeInteger, NonNegativeInteger, (Integer, Integer) -> R) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

matrix: JuliaObject -> %

matrix: List List R -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

max: % -> R if R has OrderedSet

from HomogeneousAggregate R

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

from HomogeneousAggregate R

maxColIndex: % -> Integer

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

maxRowIndex: % -> Integer

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

member?: (R, %) -> Boolean

from HomogeneousAggregate R

members: % -> List R

from HomogeneousAggregate R

min: % -> R if R has OrderedSet

from HomogeneousAggregate R

minColIndex: % -> Integer

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

minordet: % -> R if R has CommutativeRing

from MatrixCategory(R, JuliaVector R, JuliaVector R)

minRowIndex: % -> Integer

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

mutable?: % -> Boolean

from JuliaObjectType

ncols: % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

new: (NonNegativeInteger, NonNegativeInteger, R) -> %

new(m, n, x) creates a matrix of size m by n with all elements x.

nothing?: % -> Boolean

from JuliaObjectType

nrand: (PositiveInteger, PositiveInteger) -> JuliaMatrix JuliaComplexFloat if R hasn’t NemoType and R has ComplexCategory JuliaFloat

nrand(m,n) returns a JuliaMatrix of size (m,n) with normally distributed random numbers. example{mat := nrand(4,4)$JuliaMatrix(JuliaComplexFloat)} example{qr := jlApply(“qr”, mat)} example{qr.Q * qr.R}

nrand: (PositiveInteger, PositiveInteger) -> JuliaMatrix JuliaFloat if R has FloatingPointSystem and R has arbitraryPrecision and R hasn’t NemoType

nrand(m,n) returns a JuliaMatrix of size (m,n) with normally distributed random numbers. For example: example{mat := nrand(4,4)$JuliaMatrix(JuliaFloat)} example{chol := jlApply(“cholesky”, mat * transpose(mat))} example{chol.L * chol.U}

nrows: % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

nullity: % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, JuliaVector R, JuliaVector R)

nullSpace: % -> List JuliaVector R if R has IntegralDomain

from MatrixCategory(R, JuliaVector R, JuliaVector R)

parts: % -> List R

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

Pfaffian: % -> R if R has CommutativeRing

from MatrixCategory(R, JuliaVector R, JuliaVector R)

positivePower: (%, Integer) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

qelt: (%, Integer) -> JuliaObject

from JuliaObjectAggregate

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

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

qelt: (%, JuliaSymbol) -> JuliaObject

from JuliaObjectAggregate

qnew: (NonNegativeInteger, NonNegativeInteger) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

qsetelt!: (%, Integer, Integer, R) -> R

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

radicalEigenvalues: % -> JuliaVector NemoAlgebraicNumber if R has NemoRing and R has QuotientFieldCategory NemoInteger or R has NemoRing and R has IntegerNumberSystem

radicalEigenvalues(mat) returns a Julia vector containing the eigenvalues of mat.

radicalEigenvaluesWithMultiplicities: % -> JuliaVector JuliaObjTuple if R has NemoRing and R has QuotientFieldCategory NemoInteger or R has NemoRing and R has IntegerNumberSystem

radicalEigenvaluesWithMultiplicities(mat) returns a Julia vector containing Julia tuples of the eigenvalues and their multiplicities. The tuples are of internal type (NemoAlgebraicNumber, JuliaObjInt64).

rank: % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, JuliaVector R, JuliaVector R)

row: (%, Integer) -> JuliaVector R

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

rowEchelon: % -> % if R has EuclideanDomain

from MatrixCategory(R, JuliaVector R, JuliaVector R)

rowSlice: % -> Segment Integer

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

sample: %

from Aggregate

scalarMatrix: (NonNegativeInteger, R) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

setColumn!: (%, Integer, JuliaVector R) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, Integer, Integer, R) -> R

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, Integer, List Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, Integer, List Segment Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, List Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, List Integer, List Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, List Integer, Segment Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, List Segment Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, List Segment Integer, List Segment Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, List Segment Integer, Segment Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, Segment Integer, List Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, Segment Integer, List Segment Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setelt!: (%, Segment Integer, Segment Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setRow!: (%, Integer, JuliaVector R) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

setsubMatrix!: (%, Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

smaller?: (%, %) -> Boolean if R has Comparable

from Comparable

square?: % -> Boolean

from MatrixCategory(R, JuliaVector R, JuliaVector R)

squareTop: % -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

string: % -> String

from JuliaType

subMatrix: (%, Integer, Integer, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

swapColumns!: (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

swapRows!: (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

symmetric?: % -> Boolean

from MatrixCategory(R, JuliaVector R, JuliaVector R)

transpose: % -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

transpose: JuliaVector R -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

urand01: (PositiveInteger, PositiveInteger) -> JuliaMatrix JuliaComplexFloat if R hasn’t NemoType and R has ComplexCategory JuliaFloat

urand01(m,n) returns a JuliaMatrix of size (m,n) with uniformly distributed random number contained in [0,1]. example{mat := urand01(4,4)$JuliaMatrix(JuliaComplexFloat)} example{qr := jlApply(“qr”, mat)} example{qr.Q * qr.R}

urand01: (PositiveInteger, PositiveInteger) -> JuliaMatrix JuliaFloat if R has FloatingPointSystem and R has arbitraryPrecision and R hasn’t NemoType

urand01(m,n) returns a JuliaMatrix of size (m,n) with uniformly distributed random number contained in [0,1]. example{mat := urand01(4,4)$JuliaMatrix(JuliaFloat)} example{qr := jlApply(“qr”, mat)} example{qr.Q * qr.R}

vertConcat: (%, %) -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

vertConcat: List % -> %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

vertSplit: (%, List NonNegativeInteger) -> List %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

vertSplit: (%, PositiveInteger) -> List %

from TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)

zero?: % -> Boolean

from MatrixCategory(R, JuliaVector R, JuliaVector R)

zero: (NonNegativeInteger, NonNegativeInteger) -> %

from MatrixCategory(R, JuliaVector R, JuliaVector R)

Aggregate

BasicType

CoercibleTo OutputForm

Comparable if R has Comparable

ConvertibleTo String

Evalable R if R has Evalable R

finiteAggregate

Hashable if R has Hashable

HomogeneousAggregate R

InnerEvalable(R, R) if R has Evalable R

JuliaMatrixCategory(R, JuliaVector R, JuliaVector R)

JuliaObjectAggregate

JuliaObjectType

JuliaType

MatrixCategory(R, JuliaVector R, JuliaVector R)

SetCategory

shallowlyMutable

TwoDimensionalArrayCategory(R, JuliaVector R, JuliaVector R)