Sponsored links: Algebra eBooks
 

Related

ratsimpexpons

? ratsimpexpons;

Calculate

ratsimpexpons

? ratsimpexpons ;

Calculate

ratsimpexpons

? ratsimpexpons;

Calculate

ratsimpexpons

? ratsimpexpons ;

Calculate

ratsimpexpons

Run Example
(%i1)eq:(x^2-17*x+1)^(x^2-34*x+1)=1;
                                       2
                         2            x  - 34 x + 1
(%o1)                  (x  - 17 x + 1)              = 1
(%i2) ratdisp:false;
(%o2)                                false
(%i3) ratsimpexpons:false;
(%o3)                                false
(%i4) rat(lhs(eq)), ratsimp;
                                         2
                           2            x  - 34 x + 1
(%o4)                    (x  - 17 x + 1)
(%i5) 
Run Example
x(t) := exp((3+sqrt(5))/4*t) + exp((3-sqrt(5))/4*t);
                            3 + sqrt(5)          3 - sqrt(5)
(%o1)           x(t) := exp(----------- t) + exp(----------- t)
                                 4                    4
(%i2) y(t) := (sqrt(5)-1)*exp((3+sqrt(5))/4*t) - (sqrt(5)+1)*exp((3-sqrt(5))/4*t);
                                3 + sqrt(5)
(%o2) y(t) := (sqrt(5) - 1) exp(----------- t)
                                     4
                                                                 3 - sqrt(5)
                                             - (sqrt(5) + 1) exp(----------- t)
                                                                      4
(%i3) diff(x(t),t);
                       (sqrt(5) + 3) t                   (3 - sqrt(5)) t
                       ---------------                   ---------------
                              4                                 4
       (sqrt(5) + 3) %e                  (3 - sqrt(5)) %e
(%o3)  ------------------------------- + -------------------------------
                      4                                 4
(%i4) diff(y(t),t), ratsimpexpons: true;
                                    (sqrt(5) + 3) t
                                    ---------------
                                           4
      (sqrt(5) - 1) (sqrt(5) + 3) %e
(%o4) ---------------------------------------------
                            4
                                                                (sqrt(5) - 3) t
                                                              - ---------------
                                                                       4
                                (sqrt(5) - 3) (sqrt(5) + 1) %e
                              + -----------------------------------------------
                                                       4
(%i5) ratsimp(%,t);
(%o5)             
Run Example
eq:(x^2-17*x+1)^(x^2-34*x+1)=1;
                                       2
                         2            x  - 34 x + 1
(%o1)                  (x  - 17 x + 1)              = 1
(%i2) ratdisp:false;
(%o2)                                false
(%i3) ratsimpexpons:true;
(%o3)                                true
(%i4) ratexpand(lhs(eq));
                         2                               2
       2   2            x  - 34 x          2            x  - 34 x
(%o4) x  (x  - 17 x + 1)          - 17 x (x  - 17 x + 1)
                                                                       2
                                                         2            x  - 34 x
                                                     + (x  - 17 x + 1)
(%i5) rat(lhs(eq));
                                                       2
                         2               2            x
                       (x  - 17 x + 1) (x  - 17 x + 1)
(%o5)/R/               ---------------------------------
                                2            x 34
                             ((x  - 17 x + 1) )
(%i6) polydecomp(lhs(eq), x);
                          2                        2                   2
        2   2            x           2            x      2            x
       x  (x  - 17 x + 1)   - 17 x (x  - 17 x + 1)   + (x  - 17 x + 1)
(%o6) [-----------------------------------------------------------------]
                                2            34 x
                              (x  - 17 x + 1)
(%i7) taylor(lhs(eq), x, 0, 3);
                                      2         3
(%o7)/T/              1 - 17 x + 579 x  - 4964 x  + . . .
(%i8) 

Related Help

Help for Ratsimpexpons