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