# LinearlyExplicitOver RΒΆ

An extension ring with an explicit linear dependence test.

0: %

from AbelianMonoid

*: (%, R) -> %

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
latex: % -> String

from SetCategory

opposite?: (%, %) -> Boolean

from AbelianMonoid

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix R, vec: Vector R)

`reducedSystem(A, v)` returns a matrix `B` and a vector `w` such that `A x = v` and `B x = w` have the same solutions in `R`.

reducedSystem: Matrix % -> Matrix R

`reducedSystem(A)` returns a matrix `B` such that `A x = 0` and `B x = 0` have the same solutions in `R`.

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

SetCategory