Module algebra

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algebra

Modules§

AddMulOperation: $+,\times$
AdditiveOperation: $+$
ArrayOperation
BitAndOperation: &
BitOrOperation: |
BitXorOperation: ^
Bits
BottomkOperation
ConcatenateOperation
CountingOperation
EmptyAct
EmptyActLazy
EmptyAggActLazy
FindMajorityOperation: Find majority(strict) of a sequence.
FirstOperation: retain the first element
FlattenAct
FlattenLazy
LastOperation: retain the last element
LinearAct
LinearOperation: $(a, b) \circ (c, d) = \lambda x. c \times (a \times x + b) + d$
LogicalLinearOperation: $(a, b) \circ (c, d) = \lambda x. c \wedge (a \wedge x \oplus b) \oplus d$
MaxOperation: binary operation to select larger element
MinOperation: binary operation to select smaller element
MinimumIntervalMovement
MinimumIntervalMovementOperation
MultiplicativeOperation: $\times$
RangeChminChmaxAdd
RangeMaxRangeAdd
RangeMaxRangeUpdate
RangeMinRangeAdd
RangeMinRangeUpdate
RangeSumRangeAdd
RangeSumRangeChminChmaxAdd
RangeSumRangeLinear
RangeSumRangeUpdate
ReverseOperation
SortedConcatenateOperation
TopkOperation
UpdateAct

AbelianGroup: commutative group
AbelianMonoid: commutative monoid
Associative: $\forall a,\forall b,\forall c \in T, (a \circ b) \circ c = a \circ (b \circ c)$
BitAndIdentity
BitOrIdentity
BitXorIdentity
Commutative: $\forall a,\forall b \in T, a \circ b = b \circ a$
ExpBits
Field
Group: associative binary operation and an identity element and inverse elements
Idempotent: $\forall a \in T, a \circ a = a$
IdempotentMonoid: idempotent monoid
Invertible: $\exists e \in T, \forall a \in T, \exists b,c \in T, b \circ a = a \circ c = e$
LazyMapMonoid
Magma: binary operaion: $T \circ T \to T$
Monoid: associative binary operation and an identity element
MonoidAct
Ring
SemiGroup: associative binary operation
SemiRing
SignedExpBits
Unital: $\exists e \in T, \forall a \in T, e \circ a = a \circ e = e$