ModuleOperator(R, M)ΒΆ

opalg.spad line 1

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 RetractableTo 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
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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
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

CoercibleTo OutputForm

Eltable(M, M)

LeftModule %

LeftModule R if R has CommutativeRing

Magma

MagmaWithUnit

Module R if R has CommutativeRing

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RetractableTo BasicOperator

RetractableTo R

RightModule %

RightModule R if R has CommutativeRing

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown