# Composite function

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?

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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)

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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.

( 2011-04-09 20:07:54 +0200 )edit

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.

( 2011-04-10 05:05:12 +0200 )edit

h(t) = f(*g(t))

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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?

( 2011-04-09 20:08:29 +0200 )edit

It's a python thing -- see benjaminfjones' answer.

( 2011-04-09 20:09:22 +0200 )edit

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.

( 2011-04-12 00:07:50 +0200 )edit