I am trying to write the following function in maple:
f(P(x)) = (x-1)*P'(x)-x*P(1)
Where P(x) = 1 + x + x^2
My approach thus far has yielded limited results; i am able to get some, but not all, of the results expected.
This is my code,( the relevant bits ):
p := x-> 1+x+x^2
f:= P -> (x-1)*P'(x)-x*P(1);
if i then type f(1); in maple i get the expected result of -x
if however i type f(x) i get an equation that is unable to produce the expected result when simplified - seemingly, it doesn't parse for maple. The expected result would be -1
Using unapply make's no difference. Either i have made a mistake typing in my functions - in which case i would like an ëxplanation as to what i did wrong, or seemingly there is a different approach here? Perhaps solving this problem with maple is simply not doable? - anyway my line of reasoning leads me to finally ask how i write a function within a function in this nice program :)
Any help in this matter is greatly appreciated - i only just recently started using this program.