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: determinant de Cauchy | Statement: [Cauchy determinant, namedInLanguage, determinant de Cauchy]

Target entity: determinant de Cauchy
Context triple: [Cauchy determinant, namedInLanguage, determinant de Cauchy]

• A. Cauchy determinant chosen
  The Cauchy determinant is a classical determinant formula in linear algebra that gives a closed-form expression for matrices with entries of the form 1/(x_i + y_j), named after the French mathematician Augustin-Louis Cauchy.
• B. Cauchy matrix
  A Cauchy matrix is a structured matrix whose entries are defined by the reciprocals of pairwise differences of two sequences, widely used in numerical analysis, interpolation, and algebra.
• C. Sylvester determinant
  The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
• D. Jacobian determinant
  The Jacobian determinant is a scalar value derived from the Jacobian matrix that measures how a multivariable function locally scales and distorts volume under a change of variables.
• E. Jacobi's theorem on determinants
  Jacobi's theorem on determinants is a fundamental result in linear algebra that relates the minors of a matrix to the minors of its adjugate (or inverse), providing key identities used in determinant and matrix theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.