# ModuleOperator(R, M)ΒΆ

Algebra of ADDITIVE operators on a module.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, R) -> % if R has CommutativeRing

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> % if R has CommutativeRing

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

`op^n` undocumented

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

adjoint: % -> % if R has CommutativeRing

`adjoint(op)` returns the adjoint of the operator `op`.

adjoint: (%, %) -> % if R has CommutativeRing

`adjoint(op1, op2)` sets the adjoint of `op1` to be `op2`. `op1` must be a basic operator

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
associator: (%, %, %) -> %
characteristic: () -> NonNegativeInteger
charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero
coerce: % -> OutputForm
coerce: BasicOperator -> %
coerce: Integer -> %
coerce: R -> %

from CoercibleFrom R

commutator: (%, %) -> %
conjug: R -> R if R has CommutativeRing

`conjug(x)`should be local but conditional

elt: (%, M) -> M

from Eltable(M, M)

evaluate: (%, M -> M) -> %

`evaluate(f, u +-> g u)` attaches the map `g` to `f`. `f` must be a basic operator `g` MUST be additive, i.e. `g(a + b) = g(a) + g(b)` for any `a`, `b` in `M`. This implies that `g(n a) = n g(a)` for any `a` in `M` and integer `n > 0`.

evaluateInverse: (%, M -> M) -> %

`evaluateInverse(x, f)` undocumented

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

makeop: (R, FreeGroup BasicOperator) -> %

`makeop should` be local but conditional

one?: % -> Boolean

from MagmaWithUnit

opeval: (BasicOperator, M) -> M

`opeval should` be local but conditional

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> % if R has CommutativeRing
recip: % -> Union(%, failed)

from MagmaWithUnit

retract: % -> BasicOperator
retract: % -> R

from RetractableTo R

retractIfCan: % -> Union(BasicOperator, failed)
retractIfCan: % -> Union(R, failed)

from RetractableTo R

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %)

BiModule(R, R) if R has CommutativeRing

CancellationAbelianMonoid

Eltable(M, M)

LeftModule R if R has CommutativeRing

Magma

MagmaWithUnit

Module R if R has CommutativeRing

Monoid

NonAssociativeAlgebra R if R has CommutativeRing

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule R if R has CommutativeRing

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown