mathematicallyExpressedBy

P12675
predicate

Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.

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All labels observed (89)

Label Occurrences
expressedAs 57
mathematicalTool 57
symbolicForm 21

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: mathematicallyExpressedBy
Generated description
Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.

Sample triples (446)

Subject Object
London penetration depth B(x) = B(0) exp(-x / λ) via predicate surface "occursInEquation" ⓘ
Einstein synchronization convention t_B = (t_A1 + t_A2) / 2 via predicate surface "mathematicalCondition" ⓘ
Ricci flow ∂g_ij/∂t = -2 Ric_ij via predicate surface "governingEquation" ⓘ
Riemann–Roch theorem dimension of the space of global sections of a line bundle via predicate surface "givesFormulaFor" ⓘ
Riemann–Roch theorem dimension of the space of meromorphic functions with prescribed zeros and poles via predicate surface "givesFormulaFor" ⓘ
Riemann zeta function ζ(s) = Σ_{n=1}^{∞} 1/n^s via predicate surface "DirichletSeriesDefinition" ⓘ
Riemann zeta function ζ(s) = ∏_{p prime} (1 - p^{-s})^{-1} via predicate surface "EulerProduct" ⓘ
Riemann zeta function ζ(s) = 2^s π^{s-1} sin(πs/2) Γ(1-s) ζ(1-s) via predicate surface "functionalEquation" ⓘ
Riemann zeta function all nontrivial zeros lie on Re(s) = 1/2 via predicate surface "RiemannHypothesisStatement" ⓘ
Klein quartic x^3 y + y^3 z + z^3 x = 0 via predicate surface "equation" ⓘ
Christoffel symbols geodesic equation d^2x^μ/dτ^2 + Γ^μ_{νρ}(dx^ν/dτ)(dx^ρ/dτ) = 0 via predicate surface "enterEquation" ⓘ
Christoffel symbols covariant derivative ∇_μ V^ν = ∂_μ V^ν + Γ^ν_{μρ} V^ρ via predicate surface "enterEquation" ⓘ
Christoffel symbols covariant derivative ∇_μ ω_ν = ∂_μ ω_ν − Γ^ρ_{μν} ω_ρ via predicate surface "enterEquation" ⓘ
Christoffel symbols first derivatives of the metric via predicate surface "expressibleInTermsOf" ⓘ
Sackur–Tetrode equation molar form via predicate surface "expressibleIn" ⓘ
Sackur–Tetrode equation per-particle form via predicate surface "expressibleIn" ⓘ
Gibbons–Hawking temperature T = \frac{\hbar}{2\pi k_B} \sqrt{\frac{\Lambda}{3}} via predicate surface "relatedFormula" ⓘ
Karush–Kuhn–Tucker conditions system of equations and inequalities via predicate surface "expressedAs" ⓘ
Tomonaga–Schwinger equation functional differential equation via predicate surface "expressedAs" ⓘ
Lorentz force F = q(E + v × B) via predicate surface "expressedAs" ⓘ
ideal gas law PV = nRT via predicate surface "symbolicForm" ⓘ
ideal gas law pV = nRT via predicate surface "symbolicForm" ⓘ
Fourier's law of heat conduction q = -k ∇T via predicate surface "expressedAs" ⓘ
Fourier's law of heat conduction q_i = -k_{ij} ∂T/∂x_j via predicate surface "expressedAs" ⓘ
moment magnitude scale seismic moment tensor via predicate surface "hasMathematicalBasis" ⓘ
Einstein–Maxwell equations G_{μν} = 8π T_{μν}^{(EM)} + 8π T_{μν}^{(matter)} via predicate surface "expressedAs" ⓘ
Einstein–Maxwell equations ∇_{μ} F^{μν} = 4π J^{ν} via predicate surface "expressedAs" ⓘ
Einstein–Maxwell equations ∇_{[α} F_{βγ]} = 0 via predicate surface "expressedAs" ⓘ
axiom of choice every family of nonempty sets admits a choice function via predicate surface "expressedAs" ⓘ
On the Curvature of Space differential equations via predicate surface "mathematicalTool" ⓘ
On the Curvature of Space Riemannian geometry via predicate surface "mathematicalTool" ⓘ
axiom schema of separation ∀A ∀p1 … ∀pn ∃B ∀x (x ∈ B ↔ x ∈ A ∧ φ(x, p1, …, pn)) via predicate surface "expressedAs" ⓘ
axiom schema of separation first-order logic with equality and membership via predicate surface "expressibleIn" ⓘ
Lemaître–Hubble law v = H₀ d via predicate surface "expressedAs" ⓘ
Wigner surmise P(s) = (2^{18}/3^6 π^3) s^4 exp(-64 s^2 / 9π) via predicate surface "GSEFormula" ⓘ
matrix mechanics commutator of matrices via predicate surface "noncommutativityExpressedBy" ⓘ
Hardy–Weinberg principle p + q = 1 for two alleles via predicate surface "equationForm" ⓘ
Hardy–Weinberg principle p² + 2pq + q² = 1 for genotype frequencies with two alleles via predicate surface "equationForm" ⓘ
Heaviside step function 1/s for Re(s)>0 via predicate surface "LaplaceTransform" ⓘ
telegrapher's equations ∂V/∂x = -RI - L ∂I/∂t via predicate surface "equationForm" ⓘ
telegrapher's equations ∂I/∂x = -GV - C ∂V/∂t via predicate surface "equationForm" ⓘ
Jacobi ellipsoid ellipsoidal figure with constant density and uniform rotation via predicate surface "hasMathematicalDescription" ⓘ
hertz f = 1/T via predicate surface "inFormula" ⓘ
hertz f = N/Δt via predicate surface "inFormula" ⓘ
Weierstrass elliptic functions
surface form: Weierstrass σ-function
σ′(z)/σ(z) = ζ(z) via predicate surface "logarithmicDerivative" ⓘ
Federal electoral districts of Newfoundland and Labrador Constitution Act, 1867 via predicate surface "representationFormula" ⓘ
surface form: Constitution Act, 1867 and subsequent amendments
Hooke's law F = −k x via predicate surface "expressedAs" ⓘ
Hooke's law F = k x (magnitude only) via predicate surface "expressedAs" ⓘ
Heisenberg operator formulation of quantum mechanics Heisenberg operator formulation of quantum mechanics via predicate surface "governingEquation" self-linksurface differs ⓘ
surface form: Heisenberg equation of motion
Heisenberg operator formulation of quantum mechanics commutator form of dynamics via predicate surface "governingEquation" ⓘ