Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Bernstein polynomials | Statement: [Weierstrass approximation theorem, alternativeProofMethod, Bernstein polynomials]

Target entity: Bernstein polynomials
Context triple: [Weierstrass approximation theorem, alternativeProofMethod, Bernstein polynomials]

• A. Bernstein polynomials chosen
  Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
• B. Bernstein inequalities
  Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
• C. Jacobi polynomials
  Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
• D. Bernoulli numbers
  Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
• E. Orthogonal Polynomials
  Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: alternativeProofMethod
Context triple: [Weierstrass approximation theorem, alternativeProofMethod, Bernstein polynomials]

• A. alternativeForm
  Indicates that one entity is an alternative version, variant, or representation of another entity.
• B. hasProofMethod chosen
  Indicates that there exists a specific method or technique used to establish or demonstrate the validity of something (such as a statement, claim, or theorem).
• C. proved
  Indicates that one entity has demonstrated the truth or validity of another entity (such as a statement, theorem, or claim) through logical or evidential means.
• D. alternativeLaunchMethod
  Indicates that there exists a different or non-standard method by which the launch of something can be carried out.
• E. secondaryMethod
  Indicates that an entity serves as an additional or backup method used alongside or after a primary method in performing an action or achieving a result.
• F. None of above.