IndexedDirectProductCategory(A, S)

indexedp.spad line 81 [edit on github]

• A : SetCategory
• S : SetCategory

This category represents the direct product of some set with respect to an ordered indexing set. The ordered set S is considered as the ``basis elements'' and the elements from A as ``coefficients''.

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

from AbelianGroup

* : (NonNegativeInteger, %) -> % if A has AbelianMonoid

from AbelianMonoid

* : (PositiveInteger, %) -> % if A has AbelianMonoid

from AbelianSemiGroup

+ : (%, %) -> % if A has AbelianMonoid

from AbelianSemiGroup

- : % -> % if A has AbelianGroup

from AbelianGroup

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

from AbelianGroup

0 : () -> % if A has AbelianMonoid

from AbelianMonoid

= : (%, %) -> Boolean if A has AbelianMonoid or A has Comparable and S has Comparable

from BasicType

coerce : % -> OutputForm if A has AbelianMonoid or A has Comparable and S has Comparable

from CoercibleTo(OutputForm)

construct : List(Record(k : S, c : A)) -> %

from IndexedProductCategory(A, S)

constructOrdered : List(Record(k : S, c : A)) -> % if S has Comparable

from IndexedProductCategory(A, S)

latex : % -> String if A has AbelianMonoid or A has Comparable and S has Comparable

from SetCategory

leadingCoefficient : % -> A if S has Comparable

from IndexedProductCategory(A, S)

leadingMonomial : % -> % if S has Comparable

from IndexedProductCategory(A, S)

leadingSupport : % -> S if S has Comparable

from IndexedProductCategory(A, S)

leadingTerm : % -> Record(k : S, c : A) if S has Comparable

from IndexedProductCategory(A, S)

listOfTerms : % -> List(Record(k : S, c : A))

listOfTerms(x) returns a list lt of terms with type Record(k: S, c: R) such that x equals construct(lt). If S has Comparable than x equals constructOrdered(lt).

map : (Mapping(A, A), %) -> %

from IndexedProductCategory(A, S)

monomial : (A, S) -> %

from IndexedProductCategory(A, S)

monomial? : % -> Boolean

from IndexedProductCategory(A, S)

numberOfMonomials : % -> NonNegativeInteger

numberOfMonomials(x) returns the number of monomials of x.

opposite? : (%, %) -> Boolean if A has AbelianMonoid

from AbelianMonoid

reductum : % -> % if S has Comparable

from IndexedProductCategory(A, S)

sample : () -> % if A has AbelianMonoid

from AbelianMonoid

smaller? : (%, %) -> Boolean if A has Comparable and S has Comparable

from Comparable

subtractIfCan : (%, %) -> Union(%, "failed") if A has CancellationAbelianMonoid

from CancellationAbelianMonoid

zero? : % -> Boolean if A has AbelianMonoid

from AbelianMonoid

~= : (%, %) -> Boolean if A has AbelianMonoid or A has Comparable and S has Comparable

from BasicType

BasicType

CoercibleTo(OutputForm)

AbelianMonoid

IndexedProductCategory(A, S)

Comparable

AbelianProductCategory(A)

SetCategory

CancellationAbelianMonoid

AbelianGroup

AbelianSemiGroup