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: Euler–Lagrange equations | Statement: [Noether's theorem, basedOn, Euler–Lagrange equations]

Target entity: Euler–Lagrange equations
Context triple: [Noether's theorem, basedOn, Euler–Lagrange equations]

• A. Euler–Lagrange equation chosen
  The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
• B. Lagrangian mechanics
  Lagrangian mechanics is a reformulation of classical mechanics that uses energy-based principles and the calculus of variations to derive the equations of motion for physical systems.
• C. principle of least action
  The principle of least action is a fundamental concept in physics stating that the path taken by a physical system between two states is the one for which a specific quantity called the action is minimized (or made stationary), forming the basis of Lagrangian and Hamiltonian mechanics.
• D. Euler equations
  The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
• E. Lagrange multipliers
  Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.