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: O(n) ⋉ R^n | Statement: [ISO(n), isomorphicTo, O(n) ⋉ R^n]

Target entity: O(n) ⋉ R^n
Context triple: [ISO(n), isomorphicTo, O(n) ⋉ R^n]

• A. Grassmann
  Grassmann is a German surname most notably associated with mathematician Hermann Grassmann, a pioneer of vector spaces and linear algebra.
• B. Hilbert’s Nullstellensatz
  Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
• C. Polytopes
  Polytopes are large-scale multimedia architectural and musical installations created by Iannis Xenakis that combine sound, light, and spatial design into immersive, mathematically structured environments.
• D. The Hessian
  "The Hessian" is a historical novel by American writer Howard Fast that explores the moral and human complexities surrounding a captured German mercenary during the American Revolutionary War.
• E. Banach–Mazur compactum
  The Banach–Mazur compactum is a compact topological space whose points represent isometry classes of finite-dimensional normed spaces, serving as a fundamental object in the geometry of Banach spaces.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: O(n) ⋉ R^n
Target entity description: O(n) ⋉ R^n is the Euclidean group in n dimensions, consisting of all distance-preserving transformations formed by combining orthogonal rotations/reflections with translations in R^n.

• A. Grassmann
  Grassmann is a German surname most notably associated with mathematician Hermann Grassmann, a pioneer of vector spaces and linear algebra.
• B. Hilbert’s Nullstellensatz
  Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
• C. Polytopes
  Polytopes are large-scale multimedia architectural and musical installations created by Iannis Xenakis that combine sound, light, and spatial design into immersive, mathematically structured environments.
• D. The Hessian
  "The Hessian" is a historical novel by American writer Howard Fast that explores the moral and human complexities surrounding a captured German mercenary during the American Revolutionary War.
• E. Banach–Mazur compactum
  The Banach–Mazur compactum is a compact topological space whose points represent isometry classes of finite-dimensional normed spaces, serving as a fundamental object in the geometry of Banach spaces.
• F. None of above. chosen