ModuleOperator(R, M)

opalg.spad line 1 [edit on github]

• R : Ring
• M : LeftModule(R)

Algebra of ADDITIVE operators on a module.

* : (%, %) -> %

from Magma

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

from RightModule(R)

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

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, Integer) -> %

op^n is undocumented

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

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 : R -> %

from Algebra(R)

coerce : BasicOperator -> %

from CoercibleFrom(BasicOperator)

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

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

evaluateInverse(x, f) is 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 : % -> R

from RetractableTo(R)

retract : % -> BasicOperator

from RetractableTo(BasicOperator)

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

from RetractableTo(R)

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

from RetractableTo(BasicOperator)

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

~= : (%, %) -> Boolean

from BasicType

CharacteristicNonZero

CoercibleFrom(R)

Algebra(R)

RightModule(%)

Monoid

AbelianMonoid

BiModule(R, R)

NonAssociativeAlgebra(R)

CancellationAbelianMonoid

MagmaWithUnit

NonAssociativeRing

AbelianGroup

CoercibleFrom(BasicOperator)

RetractableTo(R)

LeftModule(%)

LeftModule(R)

SetCategory

Rng

Magma

Eltable(M, M)

SemiGroup

BiModule(%, %)

unitsKnown

CoercibleTo(OutputForm)

AbelianSemiGroup

RetractableTo(BasicOperator)

NonAssociativeSemiRing

Module(R)

NonAssociativeRng

Ring

RightModule(R)

SemiRng

NonAssociativeSemiRng

CharacteristicZero

BasicType

SemiRing