# FramedModule R¶

A FramedModule is a finite rank free module with fixed R-module basis.

0: %

from AbelianMonoid

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

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> % if R has AbelianGroup

from AbelianGroup

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

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

basis: () -> Vector %

basis() returns the fixed R-module basis.

coerce: % -> OutputForm
convert: % -> InputForm if R has Finite
convert: % -> Vector R

convert(a) returns the coordinates of a with respect to the fixed R-module basis.

convert: Vector R -> %

convert([a1, .., an]) returns a1*v1 + ... + an*vn, where v1, …, vn are the elements of the fixed basis.

coordinates: % -> Vector R

coordinates(a) returns the coordinates of a with respect to the fixed R-module basis.

coordinates: Vector % -> Matrix R

coordinates([v1, ..., vm]) returns the coordinates of the vi's with to the fixed basis. The coordinates of vi are contained in the ith row of the matrix returned by this function.

enumerate: () -> List % if R has Finite

from Finite

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

index: PositiveInteger -> % if R has Finite

from Finite

latex: % -> String

from SetCategory

lookup: % -> PositiveInteger if R has Finite

from Finite

opposite?: (%, %) -> Boolean

from AbelianMonoid

random: () -> % if R has Finite

from Finite

rank: () -> PositiveInteger

rank() returns the rank of the module

represents: Vector R -> %

represents([a1, .., an]) returns a1*v1 + ... + an*vn, where v1, …, vn are the elements of the fixed basis.

sample: %

from AbelianMonoid

size: () -> NonNegativeInteger if R has Finite

from Finite

smaller?: (%, %) -> Boolean if R has Finite

from Comparable

subtractIfCan: (%, %) -> Union(%, failed) if R has AbelianGroup
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup if R has AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

Comparable if R has Finite

ConvertibleTo InputForm if R has Finite

Finite if R has Finite

SetCategory