JuliaMatrixCategory(R, Row, Col)

jarray64.spad line 1 [edit on github]

• R: AbelianMonoid

• Row: FiniteLinearAggregate R

• Col: FiniteLinearAggregate R

This category provides Julia matrices.

#: % -> NonNegativeInteger

from Aggregate

*: (%, %) -> % if R has SemiRng

from MatrixCategory(R, Row, Col)

*: (%, Col) -> Col if R has SemiRng

from MatrixCategory(R, Row, Col)

*: (%, R) -> % if R has SemiRng

from MatrixCategory(R, Row, Col)

*: (Integer, %) -> % if R has AbelianGroup

from MatrixCategory(R, Row, Col)

*: (R, %) -> % if R has SemiRng

from MatrixCategory(R, Row, Col)

*: (Row, %) -> Row if R has SemiRng

from MatrixCategory(R, Row, Col)

+: (%, %) -> %

from MatrixCategory(R, Row, Col)

-: % -> % if R has AbelianGroup

from MatrixCategory(R, Row, Col)

-: (%, %) -> % if R has AbelianGroup

from MatrixCategory(R, Row, Col)

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

from MatrixCategory(R, Row, Col)

=: (%, %) -> Boolean

from BasicType

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

from MatrixCategory(R, Row, Col)

^: (%, NonNegativeInteger) -> % if R has Monoid and R has SemiRng

from MatrixCategory(R, Row, Col)

~=: (%, %) -> Boolean

from BasicType

antisymmetric?: % -> Boolean if R has AbelianGroup

from MatrixCategory(R, Row, Col)

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

from HomogeneousAggregate R

array2: List List R -> %

from TwoDimensionalArrayCategory(R, Row, Col)

blockConcat: List List % -> %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Col -> %

from MatrixCategory(R, Row, Col)

colSlice: % -> Segment Integer

from TwoDimensionalArrayCategory(R, Row, Col)

column: (%, Integer) -> Col

from TwoDimensionalArrayCategory(R, Row, Col)

columnSpace: % -> List Col if R has EuclideanDomain

from MatrixCategory(R, Row, Col)

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, Row, Col)

diagonal?: % -> Boolean

from MatrixCategory(R, Row, Col)

diagonalMatrix: List % -> %

from MatrixCategory(R, Row, Col)

diagonalMatrix: List R -> %

from MatrixCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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, Row, Col)

fill!: (%, R) -> %

from TwoDimensionalArrayCategory(R, Row, Col)

hash: % -> SingleInteger if R has Hashable

from Hashable

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

from Hashable

horizConcat: (%, %) -> %

from TwoDimensionalArrayCategory(R, Row, Col)

horizConcat: List % -> %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

horizSplit: (%, PositiveInteger) -> List %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from MatrixCategory(R, Row, Col)

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

from MatrixCategory(R, Row, Col)

kroneckerProduct: (%, %) -> % if R has SemiRng

from MatrixCategory(R, Row, Col)

kroneckerProduct: List % -> % if R has SemiRng

from MatrixCategory(R, Row, Col)

kroneckerSum: (%, %) -> %

from MatrixCategory(R, Row, Col)

kroneckerSum: List % -> %

from MatrixCategory(R, Row, Col)

latex: % -> String

from SetCategory

less?: (%, NonNegativeInteger) -> Boolean

from Aggregate

listOfLists: % -> List List R

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from MatrixCategory(R, Row, Col)

matrix: List List R -> %

from MatrixCategory(R, Row, Col)

max: % -> R if R has OrderedSet

from HomogeneousAggregate R

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

from HomogeneousAggregate R

maxColIndex: % -> Integer

from TwoDimensionalArrayCategory(R, Row, Col)

maxRowIndex: % -> Integer

from TwoDimensionalArrayCategory(R, Row, Col)

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, Row, Col)

minordet: % -> R if R has CommutativeRing

from MatrixCategory(R, Row, Col)

minRowIndex: % -> Integer

from TwoDimensionalArrayCategory(R, Row, Col)

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

ncols: % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

nrows: % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, Row, Col)

nullity: % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, Row, Col)

nullSpace: % -> List Col if R has IntegralDomain

from MatrixCategory(R, Row, Col)

parts: % -> List R

from TwoDimensionalArrayCategory(R, Row, Col)

Pfaffian: % -> R if R has CommutativeRing

from MatrixCategory(R, Row, Col)

positivePower: (%, Integer) -> % if R has SemiRng

from MatrixCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

qnew: (NonNegativeInteger, NonNegativeInteger) -> %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

rank: % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, Row, Col)

row: (%, Integer) -> Row

from TwoDimensionalArrayCategory(R, Row, Col)

rowEchelon: % -> % if R has EuclideanDomain

from MatrixCategory(R, Row, Col)

rowSlice: % -> Segment Integer

from TwoDimensionalArrayCategory(R, Row, Col)

sample: %

from Aggregate

scalarMatrix: (NonNegativeInteger, R) -> %

from MatrixCategory(R, Row, Col)

setColumn!: (%, Integer, Col) -> %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

setRow!: (%, Integer, Row) -> %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

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

from Comparable

square?: % -> Boolean

from MatrixCategory(R, Row, Col)

squareTop: % -> %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

symmetric?: % -> Boolean

from MatrixCategory(R, Row, Col)

transpose: % -> %

from TwoDimensionalArrayCategory(R, Row, Col)

transpose: Row -> %

from MatrixCategory(R, Row, Col)

vertConcat: (%, %) -> %

from TwoDimensionalArrayCategory(R, Row, Col)

vertConcat: List % -> %

from TwoDimensionalArrayCategory(R, Row, Col)

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

from TwoDimensionalArrayCategory(R, Row, Col)

vertSplit: (%, PositiveInteger) -> List %

from TwoDimensionalArrayCategory(R, Row, Col)

zero?: % -> Boolean

from MatrixCategory(R, Row, Col)

zero: (NonNegativeInteger, NonNegativeInteger) -> %

from MatrixCategory(R, Row, Col)

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

JuliaType

MatrixCategory(R, Row, Col)

SetCategory

shallowlyMutable

TwoDimensionalArrayCategory(R, Row, Col)