of equations from a set of solution after solve ?

what are these ways?

[a = s/RootOf(_Z^2-s^2+s), b = -RootOf(_Z^2-s^2+s)/s, c = RootOf(_Z^2-s^2+s)]

diff(F(x,F(x)), x);

how to differentiate this?

(D[1](F))(x, F(x))+(D[2](F))(x, F(x))*(diff(F(x), x))

how to find (D[1](F))(x, F(x)) and (D[2](F))(x, F(x)) ?

i guess need define new calculus for two variables

Limit((F(x+h,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x)) - F(x,F(x)))/h, h = 0);
Limit((F(x,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x,y)) - F(x,F(x,y)))/h, h = 0);
Limit((F(x,F(x+h,y)) - F(x,F(x,y)))/h, h = 0);

if inside F(x) is F(x,y)

it seems need to find the basic definition of F(x,y) first

if i define F(x,y) as

F := (x,y) -> min(x,y)/max(x,y);

i may be wrong, how to differentiate correctly?

abc
bca

if starting position is at first position,

i have to write a very long substitution, and need a temporary variable t and t2

subs(t2=c,subs(t=a,subs(a=b,subs(b=t2,subs(c=t,a*b*c+a*b)))));

if starting position is at second position, it will be

abc
acb

is there any simple method to do this circular shift of variables for a polynomial

 a new function from an existing function and how?

http://www.mapleprimes.com/posts/38019-Calling-Out-To-C-From-Maple#

if i can use maple to call c# function such as AForge.QLearning

how to set some tasks for it to guess some system of polynomials to fit hibert series criteria?

how to set a game for it to run itself to discover itself?