mathematicallyDefinedAs

P114498
predicate

Indicates that one entity is precisely specified or characterized in terms of another using a formal mathematical definition or expression.

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All labels observed (9)

Label Occurrences
mathematicallyDefinedAs canonical 3
isDefinedByFormula 2
mathematicalOrigin 2

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: mathematicallyDefinedAs
Generated description
Indicates that one entity is precisely specified or characterized in terms of another using a formal mathematical definition or expression.

Sample triples (13)

Subject Object
Cauchy horizon boundary of the domain of dependence of a partial Cauchy surface ⓘ
Schmidt orthogonalization iterative orthogonalization procedure via predicate surface "mathematicallyDescribedAs" ⓘ
OneHotEncoder mapping from category set to standard basis vectors via predicate surface "isMathematically" ⓘ
Gaussian mixture models
surface form: Gaussian mixture model
weighted sum of Gaussian probability density functions ⓘ
Eliassen–Palm flux zonal-mean quasi-geostrophic equations via predicate surface "mathematicallyDefinedIn" ⓘ
Goldstone bosons
surface form: Goldstone boson
degenerate vacuum manifold via predicate surface "mathematicalOrigin" ⓘ
Goldstone bosons
surface form: Goldstone boson
coset space G/H of symmetry breaking via predicate surface "mathematicalOrigin" ⓘ
NFA 5-tuple (Q, Σ, δ, q0, F) ⓘ
Wythoff Nim P-positions are described using the golden ratio via predicate surface "hasMathematicalCharacterization" ⓘ
Chebyshev polynomials of the first kind T_n(\cos \theta) = \cos(n\theta) via predicate surface "hasTrigonometricDefinition" ⓘ
Arnold cat map (x',y') = (2x + y, x + y) mod 1 via predicate surface "isDefinedByFormula" ⓘ
Arnold cat map (x',y') = A(x,y) mod 1 with A = [[2,1],[1,1]] via predicate surface "isDefinedByFormula" ⓘ
product logarithm W(z) e^{W(z)} = z via predicate surface "definingEquation" ⓘ