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: Jacobi determinant | Statement: [Carl Gustav Jacob Jacobi, notableWork, Jacobi determinant]

Target entity: Jacobi determinant
Context triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi determinant]

• A. Carathéodory–Jacobi–Lie theorem
  The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
• B. implicit function theorem
  The implicit function theorem is a fundamental result in calculus and differential geometry that guarantees, under suitable smoothness and nondegeneracy conditions, the local solvability of equations for some variables as differentiable functions of others.
• C. inverse function theorem chosen
  The inverse function theorem is a fundamental result in calculus and differential geometry that gives conditions under which a differentiable function has a locally defined differentiable inverse near a point where its derivative is invertible.
• D. Jacobi method
  The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
• E. Lie derivative
  The Lie derivative is a fundamental differential operator in differential geometry that measures how a tensor field changes along the flow generated by a vector field.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.