mathematicallyUses
P4746
predicate
Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
All labels observed (36)
| Label | Occurrences |
|---|---|
| hasMathematicalForm | 56 |
| appearsInEquation | 37 |
| usesMathematics | 20 |
| mathematicallyExpressedAs | 19 |
| hasMathematicalTool | 16 |
| usesMathematicalConcept | 16 |
| usesMathematicalTool | 16 |
| mathematicalDescription | 10 |
| mathematicalFoundation | 9 |
| usesMathematicalObject | 9 |
| usesMathematicalStructure | 9 |
| roleInMathematics | 8 |
| usesMathematicalTools | 7 |
| mathematicalConceptUsed | 6 |
| computedUsing | 5 |
| hasMathematicalFramework | 5 |
| mathematicalFormalism | 5 |
| containsMathematics | 4 |
| mathematicalFormulationUses | 4 |
| mathematicalOperation | 4 |
| usedMathematicalConcept | 4 |
| usedMathematicalTool | 4 |
| calculationUses | 3 |
| mathematicalToolUsed | 3 |
| mathematicallyInvolves | 3 |
| usesNumberTheoryConcept | 3 |
| mathematicalDescriptionUses | 2 |
| mathematicallyUses canonical | 2 |
| singularityAnalysisUses | 2 |
| usesMathematicalConcepts | 2 |
| usesMathematicsOf | 2 |
| forComplexExponent | 1 |
| forRealExponent | 1 |
| mathematicalOperator | 1 |
| usesMathematicalForm | 1 |
| usesMathematicsLevel | 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: mathematicallyUses
Generated description
Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
Sample triples (300)
| Subject | Object |
|---|---|
| Berlekamp’s algorithm for factoring polynomials over finite fields | Frobenius endomorphism via predicate surface "mathematicalFoundation" ⓘ |
| Berlekamp’s algorithm for factoring polynomials over finite fields | structure of finite fields via predicate surface "mathematicalFoundation" ⓘ |
| Berlekamp’s algorithm for factoring polynomials over finite fields | linear algebra over GF(p) via predicate surface "mathematicalFoundation" ⓘ |
| Bloch waves | ψ_k(r) = e^{i k·r} u_k(r) via predicate surface "hasMathematicalForm" ⓘ |
| Kubo formula | response function equals integral of commutator of observables with perturbation operator via predicate surface "hasMathematicalForm" ⓘ |
| Minkowski interval | s^2 = -c^2 \,\Delta t^2 + \Delta x^2 + \Delta y^2 + \Delta z^2 (mostly plus signature) via predicate surface "hasMathematicalForm" ⓘ |
| Minkowski interval | s^2 = c^2 \,\Delta t^2 - \Delta x^2 - \Delta y^2 - \Delta z^2 (mostly minus signature) via predicate surface "hasMathematicalForm" ⓘ |
| spin Casimir operator | negative square of the Pauli–Lubanski vector via predicate surface "mathematicallyExpressedAs" ⓘ |
| coulomb | Q = I·t via predicate surface "appearsInEquation" ⓘ |
| AddRoundKey | state = state XOR roundKey via predicate surface "mathematicalDescription" ⓘ |
| Rayleigh scattering | classical electromagnetic theory via predicate surface "mathematicalDescriptionUses" ⓘ |
| Rayleigh scattering | dipole approximation via predicate surface "mathematicalDescriptionUses" ⓘ |
| Lyapunov time | T_L = 1 / λ_max via predicate surface "mathematicallyExpressedAs" ⓘ |
| Communication Nets: Stochastic Message Flow and Delay | Markov processes via predicate surface "hasMathematicalTool" ⓘ |
| Communication Nets: Stochastic Message Flow and Delay | Poisson processes via predicate surface "hasMathematicalTool" ⓘ |
| Communication Nets: Stochastic Message Flow and Delay | birth-death processes via predicate surface "hasMathematicalTool" ⓘ |
| Communication Nets: Stochastic Message Flow and Delay | queueing models via predicate surface "hasMathematicalTool" ⓘ |
| Communication Nets: Stochastic Message Flow and Delay | probability theory via predicate surface "hasMathematicalTool" ⓘ |
| Communication Nets: Stochastic Message Flow and Delay | stochastic modeling via predicate surface "hasMathematicalTool" ⓘ |
| Layer Normalization | elementwise affine transform after normalization via predicate surface "mathematicalOperation" ⓘ |
| Bayesian Occam factor | ratio of effective parameter volume supported by data to prior parameter volume via predicate surface "mathematicallyExpressedAs" ⓘ |
|
“A New Approach to Linear Filtering and Prediction Problems”
surface form:
A New Approach to Linear Filtering and Prediction Problems
|
state-space representation via predicate surface "usesMathematicalTool" ⓘ |
|
“A New Approach to Linear Filtering and Prediction Problems”
surface form:
A New Approach to Linear Filtering and Prediction Problems
|
linear dynamic systems via predicate surface "usesMathematicalTool" ⓘ |
|
“A New Approach to Linear Filtering and Prediction Problems”
surface form:
A New Approach to Linear Filtering and Prediction Problems
|
Gaussian noise models via predicate surface "usesMathematicalTool" ⓘ |
|
“A New Approach to Linear Filtering and Prediction Problems”
surface form:
A New Approach to Linear Filtering and Prediction Problems
|
stochastic differential equations via predicate surface "usesMathematicalTool" ⓘ |
| Fisher's fundamental theorem of natural selection | dW/dt = VA / W (in one common formulation) via predicate surface "hasMathematicalForm" ⓘ |
| Sommerfeld quantization rules | ∮ p_i dq_i = n_i h via predicate surface "usesMathematicalForm" ⓘ |
|
textbook "A First Course in General Relativity"
surface form:
A First Course in General Relativity
|
differential geometry via predicate surface "usesMathematics" ⓘ |
|
textbook "A First Course in General Relativity"
surface form:
A First Course in General Relativity
|
linear algebra via predicate surface "usesMathematics" ⓘ |
|
textbook "A First Course in General Relativity"
surface form:
A First Course in General Relativity
|
calculus via predicate surface "usesMathematics" ⓘ |
| Cauchy stress tensor | σ_ij = traction_i on face with normal in j-direction via predicate surface "mathematicallyExpressedAs" ⓘ |
| ECC | elliptic curves via predicate surface "usesMathematicsOf" ⓘ |
| Elliptic Curve Digital Signature Algorithm | elliptic curves via predicate surface "usesMathematicsOf" ⓘ |
| Faber–Jackson relation | L ∝ σ^γ via predicate surface "hasMathematicalForm" ⓘ |
| Umklapp scattering | addition of a reciprocal lattice vector to conserve quasi-momentum via predicate surface "mathematicallyInvolves" ⓘ |
| Euclidean quantum gravity | functional integration via predicate surface "usesMathematics" ⓘ |
| Euclidean quantum gravity | differential geometry via predicate surface "usesMathematics" ⓘ |
| Euclidean quantum gravity | Riemannian geometry via predicate surface "usesMathematics" ⓘ |
| Euclidean quantum gravity | topology of manifolds via predicate surface "usesMathematics" ⓘ |
| Euclidean quantum gravity | quantum field theory in curved spacetime via predicate surface "usesMathematics" ⓘ |
| Wasserstein GAN | optimal transport theory via predicate surface "mathematicalFoundation" ⓘ |
| Ohm's law for AC | complex numbers via predicate surface "usesMathematicalTool" ⓘ |
| Ohm's law for AC | phasors via predicate surface "usesMathematicalTool" ⓘ |
| Hamiltonian mechanics | differential equations via predicate surface "usesMathematics" ⓘ |
| Hamiltonian mechanics | symplectic geometry via predicate surface "usesMathematics" ⓘ |
| Hamiltonian mechanics | differential geometry via predicate surface "usesMathematics" ⓘ |
| Hamiltonian mechanics | canonical transformations theory via predicate surface "usesMathematics" ⓘ |
|
textbook "Quantum Electronics"
surface form:
Quantum Electronics
|
Maxwell's equations
via predicate surface "containsMathematics"
ⓘ
surface form:
Maxwell equations
|
|
textbook "Quantum Electronics"
surface form:
Quantum Electronics
|
wave equations via predicate surface "containsMathematics" ⓘ |
|
textbook "Quantum Electronics"
surface form:
Quantum Electronics
|
density matrix equations via predicate surface "containsMathematics" ⓘ |