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Composite function

asked 13 years ago

BobB gravatar image

updated 13 years ago

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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answered 13 years ago

benjaminfjones gravatar image

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.

John Palmieri gravatar imageJohn Palmieri ( 13 years ago )

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 gravatar imageBobB ( 13 years ago )
1

answered 13 years ago

Ben Reynwar gravatar image

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?

BobB gravatar imageBobB ( 13 years ago )

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

John Palmieri gravatar imageJohn Palmieri ( 13 years ago )

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 gravatar imagekcrisman ( 13 years ago )

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Asked: 13 years ago

Seen: 2,815 times

Last updated: Apr 09 '11