LinearlyExplicitOver R

catdef.spad line 851 [edit on github]

• R: Ring

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

from CoercibleTo 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)

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

RightModule R

SetCategory