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composition of functions - Alberto Candel - 07-22-2014 01:23 AM
Is there a command for the composition of two functions, f and g, in CAS? There is f@@g in xcas, but I do not seem to get it to work in the Prime.
RE: composition of functions - Mark Hardman - 07-22-2014 02:17 AM
(07-22-2014 01:23 AM)Alberto Candel Wrote: Is there a command for the composition of two functions, f and g, in CAS? There is f@@g in xcas, but I do not seem to get it to work in the Prime.
Try something along the lines of:
f(x):=√(x²-1)
g(x):=4*x
The composition of the two functions is simply:
f(g(x))
HTH
RE: composition of functions - Alberto Candel - 07-22-2014 03:54 AM
Thank you Mark. But I was looking for something like that on page 12 of this Xcas/giac tutorial
RE: composition of functions - parisse - 07-22-2014 09:51 AM
In Xcas, @ does function composition, not @@, @@ is for composition power.
RE: composition of functions - Alberto Candel - 07-22-2014 03:44 PM
(07-22-2014 09:51 AM)parisse Wrote: In Xcas, @ does function composition, not @@, @@ is for composition power.
Yes, thanks, I should have written f@g for the composition and f@@n for the composite of f with itself n times. The prime accepts f@g, but it seems to return a function like (x,y)->(f(x),g(y)) (if f and g are 1 variable functions).
RE: composition of functions - parisse - 07-22-2014 04:07 PM
Please give an example.
RE: composition of functions - Alberto Candel - 07-22-2014 09:14 PM
(07-22-2014 04:07 PM)parisse Wrote: Please give an example.
For instance
f(x):=x^2
g(x):=x+1
f@g returns ((x)->x^2)@((x)->x+1)
I do not know the meaning of @
RE: composition of functions - Mark Hardman - 07-22-2014 11:11 PM
(07-22-2014 09:14 PM)Alberto Candel Wrote:(07-22-2014 04:07 PM)parisse Wrote: Please give an example.
For instance
f(x):=x^2
g(x):=x+1
f@g returns ((x)->x^2)@((x)->x+1)
I do not know the meaning of @
The CAS is providing an intermediate solution to the composition.
If you execute:
simplify(f@g)
You get the expected result:
(_(x))->_(x)²+2*_(x)+1
RE: composition of functions - Alberto Candel - 07-23-2014 02:41 PM
That works, thanks.
But it would be better without the simplify part.
[edit] Actually, if you define k:=f@g, then k(x)=x^2+2*x+1, without the simplify.[/edit]
RE: composition of functions - parisse - 07-23-2014 06:23 PM
You can also type (f@g)(x). Note that f@g is a function, not an expression.
RE: composition of functions - Alberto Candel - 07-23-2014 09:21 PM
(07-23-2014 06:23 PM)parisse Wrote: You can also type (f@g)(x). Note that f@g is a function, not an expression.
Yes, thanks. I think my original mistake was to write f@g(x) instead of (f@g)(x).