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fibtophi-numer-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z)),numer;

f(12,34,36);

Calculate

fibtophi-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z));

Calculate

fibtophi-ratsimp

fibtophi (fib (n));

fib (n-1) + fib (n) ...

fibtophi (%);

Calculate

fibtophi-numer-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z)),numer;

f(12,34,36);

Calculate

fibtophi-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z));

Calculate

fibtophi-ratsimp

fibtophi (fib (n));

fib (n-1) + fib (n) ...

fibtophi (%);

Calculate

fibtophi

Run Example
(%i1)fibtophi (fib (n));
                                  n             n
                              %phi  - (1 - %phi)
(%o1)                         -------------------
                                  2 %phi - 1
(%i2)  fib (n-1) + fib (n) - fib (n+1);
(%o2)                 - fib(n + 1) + fib(n) + fib(n - 1)
(%i3)  fibtophi (%);
(%o3)              ratsimp (%);
 e : expand ((%phi^2 - %phi - 1) * (a + 1));
(%o4)             (%i5)  ratsimp (e);
                        2                      2
(%o5)               %phi  a - %phi a - a + %phi  - %phi - 1
(%i6)  tellrat (%phi^2 - %phi - 1);
                         2                     2
(%o6)               (%phi  - %phi - 1) a + %phi  - %phi - 1
(%i7)  algebraic : true;
                                   2
(%o7)                         [%phi  - %phi - 1]
(%i8)  ratsimp (e);
(%o8)                                true
(%i9) 
Run Example
fibtophi (fib (n));
                                  n             n
                              %phi  - (1 - %phi)
(%o1)                         -------------------
                                  2 %phi - 1
(%i2)  fib (n-1) + fib (n) - fib (n+1);
(%o2)                 - fib(n + 1) + fib(n) + fib(n - 1)
(%i3)  fibtophi (%);
(%o3)              ratsimp (%);
 e : expand ((%phi^2 - %phi - 1) * (A + 1));
(%o4)             (%i5)  ratsimp (e);
                        2                      2
(%o5)               %phi  A - %phi A - A + %phi  - %phi - 1
(%i6)  tellrat (%phi^2 - %phi - 1);
                         2                     2
(%o6)               (%phi  - %phi - 1) A + %phi  - %phi - 1
(%i7)  algebraic : true;
                                   2
(%o7)                         [%phi  - %phi - 1]
(%i8)  ratsimp (e);
(%o8)                                true
(%i9) 
Run Example
? fibtophi;

 -- Function: fibtophi (<expr>)
     Expresses Fibonacci numbers in <expr> in terms of the constant
     `%phi', which is `(1 + sqrt(5))/2', approximately 1.61803399.

     Examples:

          (%i1) fibtophi (fib (n));
                                     n             n
                                 %phi  - (1 - %phi)
          (%o1)                  -------------------
                                     2 %phi - 1
          (%i2) fib (n-1) + fib (n) - fib (n+1);
          (%o2)          - fib(n + 1) + fib(n) + fib(n - 1)
          (%i3) fibtophi (%);
                      n + 1             n + 1       n             n
                  %phi      - (1 - %phi)        %phi  - (1 - %phi)
          (%o3) - --------------------------- + -------------------
                          2 %phi - 1                2 %phi - 1
                                                    n - 1             n - 1
                                                %phi      - (1 - %phi)
                                              + ---------------------------
                                                        2 %phi - 1
          (%i4) ratsimp (%);
          (%o4)                           0


(%o1)                                true
(%i2) 

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