On Dec 19, 2009, at 11:14 AM, Christopher Olah wrote: > Greetings! > > I can't seem to figure out how (elegantly) to make a function that is > the repeated composite of another. eg. Suppose I have a function f, > how do I get f*f*f*f... > > In math, I could just f^n,
One difficulty with supporting that would be that it's bit ambiguous as powering is also often used for powering after application, not only repeated application (e.g. sin^2(x) is usually interpreted as (sin(x))^2) and it would make the gulf between functions and expressions even bigger. sage: f(x) = sin(x) sage: f^2 x |--> sin(x)^2 sage: f = sin(x) sage: f^2 sin(x)^2 > in normal lambda calculus, I'd just use n.f > (church numeral), but in sage the only way I could come up with was > using a loop to generate "f(f(...(x)))" and then printing it and copy > pasting it to the end of "g=lambda x: " and using that (and even then, > when I used ~100 iterations, sage crashed). There's got to be a more > elegant way... Though it's not perfect, you could do sage: def compose(f, n, x): return x if n == 0 else compose(f, n-1, f(x)) ....: sage: compose(sin, 3, x) sin(sin(sin(x))) sage: compose(sin, 100, x) sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(sin(x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) sage: foo = compose(sin, 500, x) sage: foo(x=1.5) 0.0770617846688116 > > Thanks, > > Christopher > > PS. If your wondering why I'm doing this, have a look at > http://christopherolah.wordpress.com/2009/12/19/formation-of-escape-time-fractals/ > , I'm making some really neat pictures of the formation of escape time > fractals! Neat. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
