IndexedExponents VarsetΒΆ

multpoly.spad line 834 [edit on github]

IndexedExponents of an ordered set of variables gives a representation for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables

0: %

from AbelianMonoid

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

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> % if NonNegativeInteger has AbelianGroup

from AbelianGroup

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

from AbelianGroup

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

construct: List Record(k: Varset, c: NonNegativeInteger) -> %

from IndexedProductCategory(NonNegativeInteger, Varset)

constructOrdered: List Record(k: Varset, c: NonNegativeInteger) -> %

from IndexedProductCategory(NonNegativeInteger, Varset)

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

leadingCoefficient: % -> NonNegativeInteger

from IndexedProductCategory(NonNegativeInteger, Varset)

leadingMonomial: % -> %

from IndexedProductCategory(NonNegativeInteger, Varset)

leadingSupport: % -> Varset

from IndexedProductCategory(NonNegativeInteger, Varset)

leadingTerm: % -> Record(k: Varset, c: NonNegativeInteger)

from IndexedProductCategory(NonNegativeInteger, Varset)

listOfTerms: % -> List Record(k: Varset, c: NonNegativeInteger)

from IndexedDirectProductCategory(NonNegativeInteger, Varset)

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

from IndexedProductCategory(NonNegativeInteger, Varset)

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

monomial?: % -> Boolean

from IndexedProductCategory(NonNegativeInteger, Varset)

monomial: (NonNegativeInteger, Varset) -> %

from IndexedProductCategory(NonNegativeInteger, Varset)

numberOfMonomials: % -> NonNegativeInteger

from IndexedDirectProductCategory(NonNegativeInteger, Varset)

opposite?: (%, %) -> Boolean

from AbelianMonoid

reductum: % -> %

from IndexedProductCategory(NonNegativeInteger, Varset)

sample: %

from AbelianMonoid

smaller?: (%, %) -> Boolean

from Comparable

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

sup: (%, %) -> %

from OrderedAbelianMonoidSup

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup if NonNegativeInteger has AbelianGroup

AbelianMonoid

AbelianProductCategory NonNegativeInteger

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Comparable

IndexedDirectProductCategory(NonNegativeInteger, Varset)

IndexedProductCategory(NonNegativeInteger, Varset)

OrderedAbelianMonoid

OrderedAbelianMonoidSup

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedSet

PartialOrder

SetCategory