VectorCategory(R)

vector.spad line 35 [edit on github]

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.

# : % -> NonNegativeInteger
from Aggregate
* : (%, R) -> % if R has SemiGroup

y * r multiplies each component of the vector y by the element r.

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

r * y multiplies the element r times each component of the vector y.

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

n * y multiplies each component of the vector y by the integer n.

+ : (%, %) -> % 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
any? : (Mapping(Boolean, R), %) -> Boolean
from HomogeneousAggregate(R)
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
copyInto! : (%, %, Integer) -> %
from LinearAggregate(R)
count : (R, %) -> NonNegativeInteger if R has BasicType
from HomogeneousAggregate(R)
count : (Mapping(Boolean, R), %) -> NonNegativeInteger
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 AbelianMonoid and R has SemiRng

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 : (%, UniversalSegment(Integer)) -> %
from Eltable(UniversalSegment(Integer), %)
elt : (%, Integer) -> R
from Eltable(Integer, R)
elt : (%, Integer, R) -> R
from EltableAggregate(Integer, R)
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 : (%, R, R) -> % if R has Evalable(R) and R has SetCategory
from InnerEvalable(R, R)
eval : (%, Equation(R)) -> % if R has Evalable(R) and R has SetCategory
from Evalable(R)
eval : (%, List(R), List(R)) -> % if R has Evalable(R) and R has SetCategory
from InnerEvalable(R, R)
eval : (%, List(Equation(R))) -> % if R has Evalable(R) and R has SetCategory
from Evalable(R)
every? : (Mapping(Boolean, R), %) -> Boolean
from HomogeneousAggregate(R)
fill! : (%, R) -> %
from IndexedAggregate(Integer, R)
find : (Mapping(Boolean, R), %) -> Union(R, "failed")
from Collection(R)
first : (%, NonNegativeInteger) -> %
from LinearAggregate(R)
first : % -> R
from IndexedAggregate(Integer, R)
hash : % -> SingleInteger if R has Hashable
from Hashable
hashUpdate! : (HashState, %) -> HashState if R has Hashable
from Hashable
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 : (Mapping(R, R), %) -> %
from HomogeneousAggregate(R)
map : (Mapping(R, R, R), %, %) -> %
from LinearAggregate(R)
map! : (Mapping(R, R), %) -> %
from HomogeneousAggregate(R)
max : (%, %) -> % if R has OrderedSet
from OrderedSet
max : % -> R if R has OrderedSet
from HomogeneousAggregate(R)
max : (Mapping(Boolean, R, R), %) -> R
from HomogeneousAggregate(R)
maxIndex : % -> Integer
from IndexedAggregate(Integer, R)
member? : (R, %) -> Boolean if R has BasicType
from HomogeneousAggregate(R)
members : % -> List(R)
from HomogeneousAggregate(R)
merge : (%, %) -> % if R has OrderedSet
from LinearAggregate(R)
merge : (Mapping(Boolean, R, R), %, %) -> %
from LinearAggregate(R)
min : (%, %) -> % if R has OrderedSet
from OrderedSet
min : % -> R if R has OrderedSet
from HomogeneousAggregate(R)
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).

parts : % -> List(R)
from HomogeneousAggregate(R)
position : (R, %) -> Integer if R has BasicType
from LinearAggregate(R)
position : (R, %, Integer) -> Integer if R has BasicType
from LinearAggregate(R)
position : (Mapping(Boolean, R), %) -> Integer
from LinearAggregate(R)
qelt : (%, Integer) -> R
from EltableAggregate(Integer, R)
qsetelt! : (%, Integer, R) -> R
from EltableAggregate(Integer, R)
reduce : (Mapping(R, R, R), %) -> R
from Collection(R)
reduce : (Mapping(R, R, R), %, R) -> R
from Collection(R)
reduce : (Mapping(R, R, R), %, R, R) -> R if R has BasicType
from Collection(R)
remove : (R, %) -> % if R has BasicType
from Collection(R)
remove : (Mapping(Boolean, R), %) -> %
from Collection(R)
removeDuplicates : % -> % if R has BasicType
from Collection(R)
reverse : % -> %
from LinearAggregate(R)
reverse! : % -> %
from LinearAggregate(R)
rightTrim : (%, R) -> % if R has BasicType
from LinearAggregate(R)
sample : () -> %
from Aggregate
select : (Mapping(Boolean, R), %) -> %
from Collection(R)
setelt! : (%, Integer, R) -> R
from EltableAggregate(Integer, R)
setelt! : (%, UniversalSegment(Integer), R) -> R
from LinearAggregate(R)
size? : (%, NonNegativeInteger) -> Boolean
from Aggregate
smaller? : (%, %) -> Boolean if R has Comparable
from Comparable
sort : % -> % if R has OrderedSet
from LinearAggregate(R)
sort : (Mapping(Boolean, R, R), %) -> %
from LinearAggregate(R)
sort! : % -> % if R has OrderedSet
from LinearAggregate(R)
sort! : (Mapping(Boolean, R, R), %) -> %
from LinearAggregate(R)
sorted? : % -> Boolean if R has OrderedSet
from LinearAggregate(R)
sorted? : (Mapping(Boolean, R, R), %) -> Boolean
from LinearAggregate(R)
swap! : (%, Integer, Integer) -> Void
from IndexedAggregate(Integer, 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?(x) returns true if x is a zero vector, false otherwise.

~= : (%, %) -> Boolean if R has BasicType
from BasicType

Comparable

ConvertibleTo(InputForm)

shallowlyMutable

Aggregate

BasicType

LinearAggregate(R)

HomogeneousAggregate(R)

OrderedSet

SetCategory

EltableAggregate(Integer, R)

InnerEvalable(R, R)

OneDimensionalArrayAggregate(R)

PartialOrder

CoercibleTo(OutputForm)

FiniteLinearAggregate(R)

IndexedAggregate(Integer, R)

Hashable

finiteAggregate

Eltable(UniversalSegment(Integer), %)

Evalable(R)

Collection(R)

Eltable(Integer, R)