FramedModule RΒΆ

algcat.spad line 1

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
from CoercibleTo OutputForm
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.
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
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup if R has AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid if R has AbelianGroup

CoercibleTo OutputForm

Comparable if R has Finite

ConvertibleTo InputForm if R has Finite

Finite if R has Finite

LeftModule R

SetCategory