# VectorCategory RΒΆ

- R: Type

VectorCategory represents the type of vector like objects, i.e. finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.

- *: (%, R) -> % if R has SemiGroup
`y * r`

multiplies each component of the vector`y`

by the element`r`

.

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

multiplies each component of the vector`y`

by the integer`n`

.

- *: (R, %) -> % if R has SemiGroup
`r * y`

multiplies the element`r`

times each component of the vector`y`

.

- +: (%, %) -> % if R has AbelianSemiGroup
`x + y`

returns the component-wise sum of the vectors`x`

and`y`

. Error: if`x`

and`y`

are not of the same length.

- -: % -> % if R has AbelianGroup
`-x`

negates all components of the vector`x`

.

- -: (%, %) -> % if R has AbelianGroup
`x - y`

returns the component-wise difference of the vectors`x`

and`y`

. Error: if`x`

and`y`

are not of the same length.- <: (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- <=: (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- =: (%, %) -> Boolean if R has BasicType
- from BasicType
- >: (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- >=: (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- ~=: (%, %) -> Boolean if R has BasicType
- from BasicType
- coerce: % -> OutputForm if R has CoercibleTo OutputForm
- from CoercibleTo OutputForm
- concat: (%, %) -> %
- from LinearAggregate R
- concat: (%, R) -> %
- from LinearAggregate R
- concat: (R, %) -> %
- from LinearAggregate R
- concat: List % -> %
- from LinearAggregate R
- construct: List R -> %
- from Collection R
- convert: % -> InputForm if R has ConvertibleTo InputForm
- from ConvertibleTo InputForm
- copy: % -> %
- from Aggregate
- count: (R, %) -> NonNegativeInteger if R has BasicType
- from HomogeneousAggregate R

- cross: (%, %) -> % if R has Ring
`cross(u, v)`

constructs the cross product of`u`

and`v`

. Error: if`u`

and`v`

are not of length 3.- delete: (%, Integer) -> %
- from LinearAggregate R
- delete: (%, UniversalSegment Integer) -> %
- from LinearAggregate R

- dot: (%, %) -> R if R has SemiRng and R has AbelianMonoid
`dot(x, y)`

computes the inner product of the two vectors`x`

and`y`

. Error: if`x`

and`y`

are not of the same length.- elt: (%, Integer) -> R
- from Eltable(Integer, R)
- elt: (%, Integer, R) -> R
- from EltableAggregate(Integer, R)
- elt: (%, UniversalSegment Integer) -> %
- from Eltable(UniversalSegment Integer, %)
- empty: () -> %
- from Aggregate
- empty?: % -> Boolean
- from Aggregate
- entries: % -> List R
- from IndexedAggregate(Integer, R)
- entry?: (R, %) -> Boolean if R has BasicType
- from IndexedAggregate(Integer, R)
- eq?: (%, %) -> Boolean
- from Aggregate
- eval: (%, Equation R) -> % if R has SetCategory and R has Evalable R
- from Evalable R
- eval: (%, List Equation R) -> % if R has SetCategory and R has Evalable R
- from Evalable R
- eval: (%, List R, List R) -> % if R has SetCategory and R has Evalable R
- from InnerEvalable(R, R)
- eval: (%, R, R) -> % if R has SetCategory and R has Evalable R
- from InnerEvalable(R, R)
- find: (R -> Boolean, %) -> Union(R, failed)
- from Collection R
- first: % -> R
- from IndexedAggregate(Integer, R)
- hash: % -> SingleInteger if R has SetCategory
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState if R has SetCategory
- from SetCategory
- index?: (Integer, %) -> Boolean
- from IndexedAggregate(Integer, R)
- indices: % -> List Integer
- from IndexedAggregate(Integer, R)
- insert: (%, %, Integer) -> %
- from LinearAggregate R
- insert: (R, %, Integer) -> %
- from LinearAggregate R
- latex: % -> String if R has SetCategory
- from SetCategory
- leftTrim: (%, R) -> % if R has BasicType
- from LinearAggregate R

- length: % -> R if R has RadicalCategory and R has Ring
`length(v)`

computes the sqrt(dot(`v`

,`v`

)), i.e. the euclidean length- less?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- map: ((R, R) -> R, %, %) -> %
- from LinearAggregate R
- map: (R -> R, %) -> %
- from HomogeneousAggregate R
- max: (%, %) -> % if R has OrderedSet
- from OrderedSet
- maxIndex: % -> Integer
- from IndexedAggregate(Integer, R)
- member?: (R, %) -> Boolean if R has BasicType
- from HomogeneousAggregate R
- merge: (%, %) -> % if R has OrderedSet
- from LinearAggregate R
- min: (%, %) -> % if R has OrderedSet
- from OrderedSet
- minIndex: % -> Integer
- from IndexedAggregate(Integer, R)
- more?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- new: (NonNegativeInteger, R) -> %
- from LinearAggregate R

- outerProduct: (%, %) -> Matrix R if R has Ring
`outerProduct(u, v)`

constructs the matrix whose (`i`

,`j`

)`'`

th element is`u`

(`i`

)`*v`

(`j`

).- position: (R, %) -> Integer if R has BasicType
- from LinearAggregate R
- position: (R, %, Integer) -> Integer if R has BasicType
- from LinearAggregate R
- qelt: (%, Integer) -> R
- from EltableAggregate(Integer, R)
- reduce: ((R, R) -> R, %, R, R) -> R if R has BasicType
- from Collection R
- remove: (R, %) -> % if R has BasicType
- from Collection R
- removeDuplicates: % -> % if R has BasicType
- from Collection R
- rightTrim: (%, R) -> % if R has BasicType
- from LinearAggregate R
- sample: %
- from Aggregate
- size?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- smaller?: (%, %) -> Boolean if R has Comparable
- from Comparable
- sort!: % -> % if R has OrderedSet
- from LinearAggregate R
- sort: % -> % if R has OrderedSet
- from LinearAggregate R
- sorted?: % -> Boolean if R has OrderedSet
- from LinearAggregate R
- trim: (%, R) -> % if R has BasicType
- from LinearAggregate R

- zero: NonNegativeInteger -> % if R has AbelianMonoid
`zero(n)`

creates a zero vector of length`n`

.

- zero?: % -> Boolean if R has AbelianMonoid
`zero?(y)`

returns`true`

if`y`

is a zero vector,`true`

otherwise

CoercibleTo OutputForm if R has CoercibleTo OutputForm

Comparable if R has Comparable

ConvertibleTo InputForm if R has ConvertibleTo InputForm

Eltable(UniversalSegment Integer, %)

Evalable R if R has SetCategory and R has Evalable R

InnerEvalable(R, R) if R has SetCategory and R has Evalable R

OneDimensionalArrayAggregate R

OrderedSet if R has OrderedSet

PartialOrder if R has OrderedSet

SetCategory if R has SetCategory