LinearlyExplicitOver(R)

catdef.spad line 852 [edit on github]

• R : Ring

An extension ring with an explicit linear dependence test.

* : (%, R) -> %

from RightModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

latex : % -> String

from SetCategory

opposite? : (%, %) -> Boolean

from AbelianMonoid

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.

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.

sample : () -> %

from AbelianMonoid

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

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

CoercibleTo(OutputForm)

AbelianMonoid

RightModule(R)

AbelianSemiGroup

BasicType

SetCategory

AbelianGroup