isCommutative

P19409
predicate

Indicates that the result of applying an operation to two entities does not depend on their order (i.e., a ∘ b = b ∘ a).

All labels observed (8)

Label Occurrences
commutesWith 14
isCommutative canonical 6
additionIsCommutative 1

Description generation (PDg)

The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.

Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning.  
# Instructions
Focus on describing the relationship, not the entities themselves. 
# Response Format
Begin the description with \' Indicates...\'
Input
Predicate: isCommutative
Generated description
Indicates that the result of applying an operation to two entities does not depend on their order (i.e., a ∘ b = b ∘ a).

Sample triples (26)

Subject Object
Minkowski sum true
Gaussian integers true via predicate surface "isCommutativeRingWithIdentity"
Lie ring true via predicate surface "additionIsCommutative"
Lie derivative exterior derivative on differential forms via predicate surface "commutesWith"
Hamiltonian (time translation generator) spatial momentum operators in time-independent systems via predicate surface "commutesWith"
AddRoundKey other XOR-based key additions on same state via predicate surface "commutesWith"
Whitney sum true via predicate surface "isCommutativeUpToIsomorphism"
Hadamard product (of power series) true
Dirichlet convolution true
dAlembert operator Poincaré transformations in Minkowski spacetime via predicate surface "commutesWith"
Dirac Hamiltonian total angular momentum operator via predicate surface "commutesWith"
U(1) true via predicate surface "isCommutativeLieGroup"
Hodge Laplacian pullback by isometries via predicate surface "commutesWith"
residual maker matrix hat matrix H via predicate surface "commutesWith"
GF(p) true via predicate surface "isCommutativeUnderAddition"
GF(p) true via predicate surface "isCommutativeUnderMultiplication"
GF(p^m) true
four-momentum operator itself at different components up to structure constants via predicate surface "commutesWith"
Pauli–Lubanski pseudovector four-momentum operator in an irreducible representation via predicate surface "commutesWith"
T:z ↦ z+1
surface form: T : z ↦ z + 1
all integer translations z ↦ z + n via predicate surface "commutesWith"
Riesz transforms translations on R^n via predicate surface "commutesWith"
Riesz transforms dilations on R^n via predicate surface "commutesWith"
Riesz projection the operator T via predicate surface "commutesWith" NERFINISHED
Frobenius endomorphism base change to algebraic closures in characteristic p via predicate surface "commutesWith"
Jacobian varieties
surface form: Jacobian variety
true
Bose–Mesner algebra true