ModuleOperator(R, M)

opalg.spad line 1 [edit on github]

• R: Ring

• M: LeftModule R

Algebra of ADDITIVE operators on a module.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, 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: (%, %) -> %

from NonAssociativeSemiRng

associator: (%, %, %) -> %

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero

from CharacteristicNonZero

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: BasicOperator -> %

from CoercibleFrom BasicOperator

coerce: Integer -> %

from NonAssociativeRing

coerce: R -> %

from Algebra R

commutator: (%, %) -> %

from NonAssociativeRng

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

from NonAssociativeAlgebra R

recip: % -> Union(%, failed)

from MagmaWithUnit

retract: % -> BasicOperator

from RetractableTo BasicOperator

retract: % -> R

from RetractableTo R

retractIfCan: % -> Union(BasicOperator, failed)

from RetractableTo BasicOperator

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)

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %)

BiModule(R, R) if R has CommutativeRing

CancellationAbelianMonoid

CharacteristicNonZero if R has CharacteristicNonZero

CharacteristicZero if R has CharacteristicZero

CoercibleFrom BasicOperator

CoercibleFrom R

CoercibleTo OutputForm

Eltable(M, M)

LeftModule %

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

RetractableTo BasicOperator

RetractableTo R

RightModule %

RightModule R if R has CommutativeRing

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown