# Composite function

 0 If I define: var('x,y,z,t') g(t) = (t, t^2, t^3) f(x,y,z) = (2x,y+x+z,yx) Is there a way for me to define the composite f(g(t)) without going through: f(g(t)[0],g(t)[1],g(t)[2]) or something equally ugly? asked Apr 09 '11 BobB 1 ● 1 ● 3

 2 If you let g be a tuple of expressions involving t you can use the Python * operator to use the tuple entries as your inputs x, y, and z: sage: g = (t, t^2, t^3) sage: f = lambda x,y,z: (2*x, y+x+z, y*x) sage: f(*g) (2*t, t^3 + t^2 + t, t^3)  If you want to define both g and f as lambda functions you could do: sage: g = lambda t: (t, t^2, t^3) sage: f = lambda x,y,z: (2*x, y+x+z, y*x) sage: f(*g(t)) (2*t, t^3 + t^2 + t, t^3)  posted Apr 09 '11 benjaminfjones 2470 ● 3 ● 33 ● 66 http://bfj7.com/ You don't need f to be a lambda function for this; using "f(x,y,z) = (2*x,y+x+z,y*x)" works just fine. John Palmieri (Apr 09 '11) Thank you for the alternative. For the moment it looks like non-lambda functions work well. I'm not well versed in python and I'd like to make things look as much like mathematical notation as possible. Also, it seems using other properties (methods, functions?) like jacobian and derivative is more straight forward if lambda functions are avoided. BobB (Apr 10 '11)
 1 h(t) = f(*g(t)) posted Apr 09 '11 Ben Reynwar 45 ● 1 ● 5 Great! And very quick, thank you. I suppose I would have known that if I knew something about python? Or is * a sage operator of some sort? BobB (Apr 09 '11) It's a python thing -- see benjaminfjones' answer. John Palmieri (Apr 09 '11) But it might be nice to have this work without that. See http://trac.sagemath.org/sage_trac/ticket/11180; if someone can come up with a better title for that ticket, be my guest. kcrisman (Apr 11 '11)

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