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\ ``''.

0: % if A has AbelianMonoid

from AbelianMonoid

*: (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

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

from BasicType

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

from BasicType

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

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 Comparable and S has Comparable or A has AbelianMonoid

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

from IndexedProductCategory(A, S)

monomial?: % -> Boolean

from IndexedProductCategory(A, S)

monomial: (A, S) -> %

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

AbelianGroup if A has AbelianGroup

AbelianMonoid if A has AbelianMonoid

AbelianProductCategory A

AbelianSemiGroup if A has AbelianMonoid

BasicType if A has Comparable and S has Comparable or A has AbelianMonoid

CancellationAbelianMonoid if A has CancellationAbelianMonoid

CoercibleTo OutputForm if A has Comparable and S has Comparable or A has AbelianMonoid

Comparable if A has Comparable and S has Comparable

IndexedProductCategory(A, S)

SetCategory if A has Comparable and S has Comparable or A has AbelianMonoid