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mainvar

Run Example
(%i1)derivabbrev:true ;
(%o1)                                true
(%i2) mainvar: t;
(%o2)                                  t
(%i3) x(t):= r(t)*sin(theta(t));
(%o3)                     x(t) := r(t) sin(theta(t))
(%i4) y(t):=r(t)*cos(theta(t));
(%o4)                     y(t) := r(t) cos(theta(t))
(%i5) xdot(t):= diff(x(t), t, 1);
(%o5)                     xdot(t) := diff(x(t), t, 1)
(%i6) ydot(t):= diff(y(t), t, 1);
(%o6)                     ydot(t) := diff(y(t), t, 1)
(%i7) xdotdot(t):= diff(xdot(t), t, 1);
(%o7)                  xdotdot(t) := diff(xdot(t), t, 1)
(%i8) ydotdot(t):= diff(ydot(t), t, 1);
(%o8)                  ydotdot(t) := diff(ydot(t), t, 1)
(%i9) thetadot(t):= diff(theta(t), t, 1);
(%o9)                 thetadot(t) := diff(theta(t), t, 1)
(%i10) thetadotdot(t) := diff(thetadot(t), t, 1);
(%o10)             thetadotdot(t) := diff(thetadot(t), t, 1)
(%i11) Assumption1: xdotdot(t)=0;
                                                                      2
(%o11) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
                  + 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
                          t                       t       t t
(%i12) solve(Assumption1, r(t));
                 sin(theta(t)) r(t)    + 2 cos(theta(t)) theta(t)  r(t)
                                   t t                           t     t
(%o12) [r(t) = - -------------------------------------------------------]
                                                                      2
                 cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                                       t t                          t
(%i13) Assumption2: ydotdot(t)=0;
                                                                        2
(%o13) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
                                    t t                               t
                  - 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
                          t                       t       t t
(%i14) E1_1: subst(rdot(t), diff(r(t), t, 1), Assumption1);
                                                                      2
(%o14) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
                + 2 rdot(t) cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
                                                  t       t t
(%i15) E1_2: subst(rdotdot(t), diff(diff(r(t), t, 1),t,1), E1_1);
                                                                      2
(%o15) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
             + 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
                                               t
(%i16) E1_3: subst(rr(t), r(t), E1_2);
                                                                        2
(%o16) rr(t) cos(theta(t)) theta(t)    - rr(t) sin(theta(t)) (theta(t) )
                                   t t                                t
             + 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
                                               t
(%i17) E1_4: solve(E1_3, rr(t));
                  2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
                                                  t
(%o17) [rr(t) = - ------------------------------------------------------------]
                                                                          2
                     cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                                           t t                          t
(%i18) E1_5: subst(r(t), rr(t), E1_4[1]);
                2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
                                                t
(%o18) r(t) = - ------------------------------------------------------------
                                                                        2
                   cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                                         t t                          t
(%i19) 
Run Example
declare([s0,s1,s3,s4,in], mainvar);
(%o1)                                done
(%i2)    solve([y1 = (s1 + f * t1 * y0) * g1], [y1]);
(%o2)                      [y1 = g1 s1 + f g1 t1 y0]
(%i3) 
Run Example
a0 : 7^(1/3);
                                      1/3
(%o1)                                7
(%i2) a1: a0*%e^(2*%i*%pi/3);
                              1/3  sqrt(3) %i   1
(%o2)                        7    (---------- - -)
                                       2        2
(%i3) a2: a0*%e^(4*%i*%pi/3);
                             1/3    sqrt(3) %i   1
(%o3)                       7    (- ---------- - -)
                                        2        2
(%i4) rectform(a1*a1*a1);
(%o4)                                  7
(%i5) declare(x,mainvar);
(%o5)                                done
(%i6) rat(expand(((x-a0)^5-10)*((x-a1)^5-10)*((x-a2)^5-10)),x);
               15          12                     1/3 7
(%o6)/R/ (512 x   - 17920 x   + (- 6400 sqrt(3) (7   )
                3                    1/3 4      11
 + (6400 sqrt(3)  + 25600 sqrt(3)) (7   ) ) %i x
                   3   1/3 8               7             5               3
 + ((- 1520 sqrt(3)  (7   )  + (688 sqrt(3)  + 16 sqrt(3)  + 4400 sqrt(3) )
   1/3 5             1/3 11          1/3 8           10
 (7   ) ) %i - 256 (7   )   + 1792 (7   )  - 15360) x
                    7                 5                 3                9
 + ((- 35280 sqrt(3)  - 129360 sqrt(3)  + 705600 sqrt(3) ) %i + 250880) x
                      1/3 13                 7               3
 + ((- 1280 sqrt(3) (7   )   + (- 320 sqrt(3)  + 8800 sqrt(3)  + 600 sqrt(3))
   1/3 10                 9              5                  1/3 7
 (7   )   + (- 840 sqrt(3)  + 160 sqrt(3)  + 800 sqrt(3)) (7   )
                5                3    1/3 2              1/3 13
 + (6400 sqrt(3)  - 19200 sqrt(3) ) (7   ) ) %i + 1280 (7   )
          1/3 10   8                   5                   1/3 11
 - 8960 (7   )  ) x  + (((- 800 sqrt(3)  + 2000 sqrt(3)) (7   )
                  9                7               5              3
 + (- 2000 sqrt(3)  + 10160 sqrt(3)  - 8880 sqrt(3)  - 800 sqrt(3)
                   1/3 8              1/3 14           1/3 11             7
 + 6400 sqrt(3)) (7   ) ) %i - 1440 (7   )   + 10080 (7   )   - 3225600) x
                    9                  7                  5                  3
 + ((- 13720 sqrt(3)  - 1618960 sqrt(3)  + 2730280 sqrt(3)  + 6750240 sqrt(3) )
                6                 5             3                 1/3 16
 %i - 1756160) x  + (((- 8 sqrt(3)  + 80 sqrt(3)  - 40 sqrt(3)) (7   )
                  5               3    1/3 13
 + (- 1600 sqrt(3)  - 2000 sqrt(3) ) (7   )
                  7                5               3                    1/3 10
 + (- 2448 sqrt(3)  + 16496 sqrt(3)  + 7360 sqrt(3)  + 32080 sqrt(3)) (7   )
               3   1/3 8                   5                 3    1/3 5
 - 1600 sqrt(3)  (7   )  + (- 45600 sqrt(3)  + 148000 sqrt(3) ) (7   ) ) %i
          1/3 16           1/3 13            5
 + 2968 (7   )   - 20776 (7   )   + 153600) x
                   5              3                   1/3 14
 + (((- 200 sqrt(3)  + 400 sqrt(3)  - 2000 sqrt(3)) (7   )
              9              7             5               3
 + (80 sqrt(3)  + 200 sqrt(3)  + 40 sqrt(3)  + 2200 sqrt(3)  - 640 sqrt(3))
   1/3 11                7                5                3             1/3 17
 (7   )   + 19600 sqrt(3)  - 39200 sqrt(3)  - 58800 sqrt(3) ) %i + 675 (7   )
          1/3 14              4                 7               3
 - 4725 (7   )   - 33868800) x  + (((800 sqrt(3)  - 8800 sqrt(3)
                   1/3 10                 5                3
 - 8000 sqrt(3)) (7   )   + (- 800 sqrt(3)  + 28000 sqrt(3)  + 12800 sqrt(3))
   1/3 7                 9                 7                 5
 (7   )  + 192080 sqrt(3)  - 192080 sqrt(3)  - 384160 sqrt(3)
                  3                 3                  5              3
 - 2304960 sqrt(3) ) %i + 6146560) x  + (((- 40 sqrt(3)  + 400 sqrt(3)
                  1/3 16                9             7              5
 - 200 sqrt(3)) (7   )   + (- 40 sqrt(3)  + 80 sqrt(3)  - 200 sqrt(3)
               3                   1/3 13
 - 1600 sqrt(3)  + 3200 sqrt(3)) (7   )
                  7               5                3    1/3 8
 + (- 3200 sqrt(3)  + 1600 sqrt(3)  + 24000 sqrt(3) ) (7   ) ) %i - 10752000)
  2                7             5              3    1/3 14                 7
 x  + (((40 sqrt(3)  - 80 sqrt(3)  - 120 sqrt(3) ) (7   )   - 274400 sqrt(3)
                 5                  3                           1/3 16
 + 411600 sqrt(3)  + 1234800 sqrt(3) ) %i - 26342400) x - 135 (7   )
         1/3 13
 + 945 (7   )   - 9117184)/512
(%i7) 

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