B c‹dl ã@sndZddlmZddlmZmZmZddlmZddl m Z ddl m Z ddl mZddlmZd d d „Zd S)zX This module implements a method to find Euler-Lagrange Equations for given Lagrangian. é)Úcombinations_with_replacement)Ú DerivativeÚFunctionÚdiff)ÚEq)ÚS)ÚSymbol)Úsympify)Úiterable©c s„tˆƒrtˆƒnˆf‰ˆs*t| t¡ƒ‰n$x"ˆD]}t|tƒs0td|ƒ‚q0Wt|ƒr^t|ƒn|f}|stˆdj}ntdd„|Dƒƒ}tdd„|Dƒƒs¤td|ƒ‚x&ˆD]}||jksªtd||fƒ‚qªWt ‡fdd „| t ¡Dƒdgƒ}g}xŒˆD]„}t ||ƒ}xVt d |d ƒD]D}x>> from sympy import euler_equations, Symbol, Function >>> 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] https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation zFunction expected, got: %srcss|]}t|ƒVqdS)N)r )Ú.0Úvarr r úa/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/sympy/calculus/euler.pyú Vsz"euler_equations..css|]}t|tƒVqdS)N)Ú isinstancer)r Úvr r rrXsz!Variables are not symbols, got %sz"Variables %s do not match args: %scs g|]}|jˆkrt|jƒ‘qSr )ÚexprÚlenÚ variables)r Úd)Úfuncsr rú _sz#euler_equations..é)r ÚtupleZatomsrrÚ TypeErrorÚargsÚallÚ ValueErrorÚmaxrrÚrangerrZ NegativeOnerÚappend) ÚLrÚvarsÚfÚorderZeqnsÚeqÚiÚpZnew_eqr )rrÚeuler_equationss6:         4  r(N)r r )Ú__doc__Ú itertoolsrZsympy.core.functionrrrZsympy.core.relationalrZsympy.core.singletonrZsympy.core.symbolrZsympy.core.sympifyr Zsympy.utilities.iterablesr r(r r r rÚs