MaplePrimes - answers and comments on Question, Replacing f(x) by f in an expression

By declare

Markiyan Hirnyk — Sun, 10 Mar 2013 14:23:01 Z

It can be done as follows.

>restart;with(PDEtools):
>declare(f(x), prime=x);
f(x) will now be displayed as f
derivatives with respect to x of functions of one variable will
now be displayed with '

> declare(g(x), prime = x);
                g(x) will now be displayed as g
derivatives with respect to x of functions of one variable will
   now be displayed with '
> q := f(x)^2+g(x)^3;

>q;

See ?PDEtools/declare for info.

Simpler: alias

Adri van der Meer — Tue, 12 Mar 2013 19:26:40 Z

restart;
p:=f(x)^2 + g(x)^3:
                             2       3
                         f(x)  + g(x) 
alias( f=f(x), g=g(x) );
                              f, g
p;
                             2    3
                            f  + g 
diff(p,x);
                       / d   \      2 / d   \
                   2 f |--- f| + 3 g  |--- g|
                       \ dx  /        \ dx  /

Using subs is not a good idea, because in that case you lose the information that f and g are functions of x.

Thanks for your answer

Willem Ottevanger — Sun, 10 Mar 2013 17:10:41 Z

Thanks for your answer

Don't

Markiyan Hirnyk — Sun, 10 Mar 2013 18:06:59 Z

@Willem Ottevanger mention it.

Thanks Adri

Willem Ottevanger — Wed, 13 Mar 2013 13:59:22 Z

In my case that doesnt work as I wanted to perform a Taylor expansion on q depending on f.

Or is there a neater way to do this?

> restart;
> q := cos(f(x)^2);
                              /    2\
                           cos\f(x) /
> p := subs(f(x) = f, q);
                               / 2\
                            cos\f /
> t := taylor(%, f = 0, 5);
                            1  4    / 8\
                        1 - - f  + O\f /
                            2           
> restart;


> q := cos(f(x)^2);
                              /    2\
                           cos\f(x) /
> alias(f = f(x));
                               f
> taylor(q, f = 0, 5);
%;
Error, invalid input: taylor received f(x) = 0, which is not valid for its 2nd argument, eqn

In that case...

Adri van der Meer — Wed, 13 Mar 2013 20:43:37 Z

@Willem Ottevanger I think that subs is the best possibility because you intend to lose the information that f is a function of x.