ModuleOperator(R, M)ΒΆ
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
- ^: (%, Integer) -> %
op^n
undocumented- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- adjoint: % -> % if R has CommutativeRing
adjoint(op)
returns the adjoint of the operatorop
.
- adjoint: (%, %) -> % if R has CommutativeRing
adjoint(op1, op2)
sets the adjoint ofop1
to beop2
.op1
must be a basic operator
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: BasicOperator -> %
- coerce: Integer -> %
from NonAssociativeRing
- coerce: R -> %
from CoercibleFrom R
- commutator: (%, %) -> %
from NonAssociativeRng
- conjug: R -> R if R has CommutativeRing
conjug(x)
should be local but conditional
- evaluate: (%, M -> M) -> %
evaluate(f, u +-> g u)
attaches the mapg
tof
.f
must be a basic operatorg
MUST be additive, i.e.g(a + b) = g(a) + g(b)
for anya
,b
inM
. This implies thatg(n a) = n g(a)
for anya
inM
and integern > 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
- 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
Algebra R if R has CommutativeRing
BiModule(%, %)
BiModule(R, R) if R has CommutativeRing
CharacteristicNonZero if R has CharacteristicNonZero
CharacteristicZero if R has CharacteristicZero
Eltable(M, M)
LeftModule R if R has CommutativeRing
Module R if R has CommutativeRing
NonAssociativeAlgebra R if R has CommutativeRing
RightModule R if R has CommutativeRing