FramedModule(R)

algcat.spad line 1 [edit on github]

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

* : (R, %) -> %
from LeftModule(R)
* : (Integer, %) -> % if R has AbelianGroup
from AbelianGroup
* : (NonNegativeInteger, %) -> %
from AbelianMonoid
* : (PositiveInteger, %) -> %
from AbelianSemiGroup
+ : (%, %) -> %
from AbelianSemiGroup
- : % -> % if R has AbelianGroup
from AbelianGroup
- : (%, %) -> % if R has AbelianGroup
from AbelianGroup
0 : () -> %
from AbelianMonoid
= : (%, %) -> Boolean
from BasicType
basis : () -> Vector(%)

basis() returns the fixed R-module basis.

coerce : % -> OutputForm
from CoercibleTo(OutputForm)
convert : Vector(R) -> %

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

convert : % -> InputForm if R has Finite
from ConvertibleTo(InputForm)
convert : % -> Vector(R)

convert(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.

coordinates : % -> Vector(R)

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

enumerate : () -> List(%) if R has Finite
from Finite
hash : % -> SingleInteger if R has Hashable
from Hashable
hashUpdate! : (HashState, %) -> HashState if R has Hashable
from Hashable
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
from CancellationAbelianMonoid
zero? : % -> Boolean
from AbelianMonoid
~= : (%, %) -> Boolean
from BasicType

Finite

CancellationAbelianMonoid

BasicType

CoercibleTo(OutputForm)

Hashable

AbelianGroup

AbelianSemiGroup

SetCategory

Comparable

AbelianMonoid

LeftModule(R)

ConvertibleTo(InputForm)