B [ @sRdZddlmZddlmZmZmZmZmZm Z m Z ddl m Z m Z d ddZdS) zX This module implements a method to find Euler-Lagrange Equations for given Lagrangian. )combinations_with_replacement)FunctionsympifydiffEqSSymbol Derivative)iterablerangec sntrtnfs*t|tn$x"D]}t|ts0td|q0Wt|r^t|n|f}|stdj}ntdd|D}tdd|Dstd|x&D]}||jkstd||fqWt fdd|t D}g}x|D]t}t ||}xVt d |d D]D}x>> from sympy import Symbol, Function >>> from sympy.calculus.euler import euler_equations >>> x = Function('x') >>> t = Symbol('t') >>> L = (x(t).diff(t))**2/2 - x(t)**2/2 >>> euler_equations(L, x(t), t) [Eq(-x(t) - Derivative(x(t), (t, 2)), 0)] >>> u = Function('u') >>> x = Symbol('x') >>> L = (u(t, x).diff(t))**2/2 - (u(t, x).diff(x))**2/2 >>> euler_equations(L, u(t, x), [t, x]) [Eq(-Derivative(u(t, x), (t, 2)) + Derivative(u(t, x), (x, 2)), 0)] References ========== .. [1] http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation zFunction expected, got: %srcss|]}t|VqdS)N)r).0varr r 3lib/python3.7/site-packages/sympy/calculus/euler.py Ssz"euler_equations..css|]}t|tVqdS)N) isinstancer)r vr r rrUsz!Variables are not symbols, got %sz!Variables %s don't match args: %sc3s"|]}|jkrt|jVqdS)N)exprlenZ variables)r d)funcsr rr\s)r tupleZatomsrr TypeErrorargsall ValueErrormaxr rr rrZ NegativeOneappendr) LrvarsforderZeqnseqipr )rreuler_equations s0;        4r&N)r r )__doc__ itertoolsrZsympyrrrrrrr Zsympy.core.compatibilityr r r&r r r rs $