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Run Example
(%i1)load(functs);
(%o1)      /usr/share/maxima/5.21.1/share/simplification/functs.mac
(%i2) polyfactor:true;
(%o2)                                true
(%i3) divide (expand(x^2-7*x+10),expand(x+3));
(%o3)                            [x - 10, 40]
(%i4) disp ((x^2-7*x-10)/(x+3));
                                  2
                                 x  - 7 x - 10
                                 -------------
                                     x + 3

(%o4)                                done
(%i5) gcdivide((x^2-7*x-10),(x+3));
                                  2
                                 x  - 7 x - 10
(%o5)                            -------------
                                     x + 3
(%i6) tellrat (ratsimp(%));
(%o6)            [(%i7) 
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 (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) 

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