### The Maxima on-line user's manual

Algebra Calculator

#### 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) ```

### Related Examples

##### 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;

Calculate

##### fibtophi-inf-limit

limit(fibtophi(fib(n)...

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;

Calculate

##### fibtophi-inf-limit

limit(fibtophi(fib(n)...

Calculate