QEtaLazyAlgebra(C, B)

qetaalg.spad line 502 [edit on github]

• C: CommutativeRing

• B: Join(Monoid, AbelianGroup) with

  *: (C, %) -> %

The domain QEtaLazyAlgebra(C, B) behaves like the C-algebra B, but all arithmetic operations are stored as a tree and only performed when the element is coerced back into an element of B.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (C, %) -> %

c*x create a new data structure for the multiplication of c with x.

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> B

coerc(x) turns the lazy data structure back into an element of B.

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: B -> %

coerce(b) embeds element b into this domain.

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

show: % -> OutputForm

size: % -> Integer

size(x) returns a concept of the size of the object.

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

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory