I am testing Sage with basic simbolic expressions appliying derivatives to some functions f(t). When I try to simplify the trigonometric final expressión Sage Notebook does not recognize the partial derivative symbol. I do not understand the new variable psi(t) that appears in the solution.
Here is the Notebook Sage code:
var('t,alpha,beta,gamma');
alpha(t)=function('alpha',t); beta(t)=function('beta',t); gamma(t)=function('gamma',t);
mi(t)=sin(beta)^2*diff(alpha(t), t) + (cos(beta)*diff(alpha(t), t) +diff(gamma(t), t))*cos(beta);
print(mi(t).expand());
print(mi(t).expand().trig_simplify());
Here is the result:
cos(beta(t))^2*diff(alpha(t), t) + sin(beta(t))^2*diff(alpha(t), t) +
cos(beta(t))*diff(gamma(t), t)
cos(beta(t))*gamma(t)*psi(t) + diff(alpha(t), t)
