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 |
| isCommutativeLieGroup | 1 |
| isCommutativeRingWithIdentity | 1 |
| isCommutativeUnderAddition | 1 |
| isCommutativeUnderMultiplication | 1 |
| isCommutativeUpToIsomorphism | 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 ⓘ |