solve( f(x)+g(x) = f(x)*g(x) , f(x) )
On Mar 25, 2013 1:41 AM, "Thomas D. Dean" <tomdean at speakeasy.org> wrote:
> If this is too far off topic, please tell me.
>
> I am attempting to demonstrate with maxima, "Show that there exists an
> infinite number of rational functions, f and g, such that
> f(x) + g(x) = f(x) * g(x);"
>
> I had to go back to Calculus from ODE to brush up. If I keep going this
> way, I will be in the first grade!
>
> I spent a lot of time on "Prove every function with domain R can be
> written as the sum of an even function and an odd function." Can not nail
> down the case where f is neither even or odd.
>
> declare(o,oddfun); declare(e,evenfun); kill(f);
> /* if f(x) is odd */ ratsimp((o(x)+e(-x))/2+(o(x)-**e(-x))/2);
> /* if f(x) is even */ ratsimp((e(x)+o(-x))/2+(e(x)-**o(-x))/2);
> /* if f(x) is neither */ ratsimp((f(x)+f(-x))/2+(f(x)-**f(-x))/2);
>
> But, this is not the sum of an odd and an even function. Any ideas?
>
> Tom Dean
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