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: A Treatise on the Theory of Determinants | Statement: [Thomas Muir, notableWork, A Treatise on the Theory of Determinants]

Target entity: A Treatise on the Theory of Determinants
Context triple: [Thomas Muir, notableWork, A Treatise on the Theory of Determinants]

• A. 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.
• B. Treatise on Demonstration of Problems of Algebra
  Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
• C. Theorie der binären algebraischen Formen
  "Theorie der binären algebraischen Formen" is a foundational 19th-century mathematical treatise by Alfred Clebsch on the theory of binary algebraic forms and invariants.
• D. Traité des substitutions et des équations algébriques
  Traité des substitutions et des équations algébriques is Camille Jordan’s foundational 1870 treatise that systematically developed group theory and the theory of algebraic equations.
• E. Treatise of Algebra
  Treatise of Algebra is an 18th-century mathematical work by Scottish mathematician Colin Maclaurin that systematically develops algebraic theory and its applications.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: A Treatise on the Theory of Determinants
Target entity description: A Treatise on the Theory of Determinants is a foundational mathematical work by Thomas Muir that systematically develops and surveys the theory and applications of determinants.

• A. 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.
• B. Treatise on Demonstration of Problems of Algebra
  Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
• C. Theorie der binären algebraischen Formen
  "Theorie der binären algebraischen Formen" is a foundational 19th-century mathematical treatise by Alfred Clebsch on the theory of binary algebraic forms and invariants.
• D. Traité des substitutions et des équations algébriques
  Traité des substitutions et des équations algébriques is Camille Jordan’s foundational 1870 treatise that systematically developed group theory and the theory of algebraic equations.
• E. Treatise of Algebra
  Treatise of Algebra is an 18th-century mathematical work by Scottish mathematician Colin Maclaurin that systematically develops algebraic theory and its applications.
• F. None of above. chosen