2020-05-19 08:47:03 +0200 received badge ● Nice Question (source) 2020-05-18 19:00:23 +0200 received badge ● Student (source) 2020-05-18 18:48:05 +0200 asked a question Trig simplification of implicit functions fails I'd like to use Sage to verify my solutions to Lagrangian equations of motion for a double pendulum. However, Sage seems unable to handle some basic substitutions needed to make sense of this relatively simple problem. For example, this all works fine: var('z') r = cos(z)**2 + sin(z)**2 assert r.simplify_trig() == 1  However, when z is a function of time, things break down entirely: var('x,y,t,z') θ1 = function('θ1')(t) θ2 = function('θ2')(t) K = sin(θ1)**2 + cos(θ1)**2 assert K.simplify_trig() == 1  Specifically, K.simplify_trig() throws: TypeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined. I would also expect assert K.substitute_function(θ1, z) == cos(z)^2 + sin(z)^2  However K.substitute_function(θ1, z) just gives me K unchanged. Seems related, but I'm still stumped: ask.sagemath.org/question/7856/lagranian-mechanics/