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fullratsimp

(((b*y)*(b+2*y))/((b-...

fullratsimp(%);

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fullratsimp-remfunction-remvalue-solve

remvalue(all);

remfunction(all);

e1: T(s) = B1*W1(s) +...

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fullratsimp-integrate-solve

eq1(x):=(R*x-M)*x/(EI);

int1(x):=integrate(eq...

int1(x);

Calculate

fullratsimp

fullratsimp(%pi*(((30...

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fullratsimp-linsolve

eqs:[2 *x1+x2+x3=1, 3...

linsolve(eqs, [x1,x2,...

a[2]:fullratsimp(eqs[...

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fullratsimp-imagpart-numer-realpart

/* Umwandlung stern d...

Z20:R20+X20;

Z30:R30+X30;

Calculate

fullratsimp

fullratsimp( (x^(A/2)...

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fullratsimp

p:(x^3+1)/(x+1) ;

fullratsimp (p) ;

Calculate

fullratsimp

fullratsimp((1+x+x^2+...

Calculate

fullratsimp-load-sqrt

load(vect);

n: [x,y,z];

nn: n / sqrt(n.n);

Calculate

fullratsimp

Run Example
(%i1)num1: 2*a*x;
(%o1)                                2 a x
(%i2) num2: 2*y*sqrt(a*b*(a*x*x+b*y*y-1));
                                         2      2
(%o2)                   2 y sqrt(a b (b y  + a x  - 1))
(%i3) den: 2*a*(a*x*x+b*y*y);
                                       2      2
(%o3)                          2 a (b y  + a x )
(%i4) x1: (num1+num2)/den;
                                     2      2
                    2 y sqrt(a b (b y  + a x  - 1)) + 2 a x
(%o4)               ---------------------------------------
                                       2      2
                               2 a (b y  + a x )
(%i5) x2: (num1-num2)/den;
                                             2      2
                    2 a x - 2 y sqrt(a b (b y  + a x  - 1))
(%o5)               ---------------------------------------
                                       2      2
                               2 a (b y  + a x )
(%i6) y1: (1-a*x*x1)/(b*y);
                                        2      2
                    x (2 y sqrt(a b (b y  + a x  - 1)) + 2 a x)
                1 - -------------------------------------------
                                        2      2
                                  2 (b y  + a x )
(%o6)           -----------------------------------------------
                                      b y
(%i7) y2: (1-a*x*x2)/(b*y);
                                                2      2
                    x (2 a x - 2 y sqrt(a b (b y  + a x  - 1)))
                1 - -------------------------------------------
                                        2      2
                                  2 (b y  + a x )
(%o7)           -----------------------------------------------
                                      b y
(%i8) d1_2: fullratsimp(ratexpand((x-x1)^2+(y-y1)^2));
              3  6          3      2  2   2    3        2   4
(%o8) - (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y
                2      2            2             3
 + sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y
                2   3
 + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
          2  2    3     4       2    2     2    2         2    3    6
 + ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x
       2      3   4     2         2      3  4      2  2  2  2    3    4
 + (2 a  b - a ) x  + (a  - a b) x )/(a b  y  + 2 a  b  x  y  + a  b x )
(%i9) d2_2: fullratsimp((x-x2)^2+(y-y2)^2);
          3  6        3      2  2   2    3        2   4
(%o9) (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y
           2  2    2    2             2             3
 + sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y
                2   3
 + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
        2  2    3     4         2    2     2    2         2    3    6
 + ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x
     3      2     4           2   2      3  4      2  2  2  2    3    4
 + (a  - 2 a  b) x  + (a b - a ) x )/(a b  y  + 2 a  b  x  y  + a  b x )
(%i10) d12_2: fullratsimp((x2-x1)^2+(y2-y1)^2);
           3  4          2      2     2      2   2      3  4      2  2
        4 b  y  + ((4 a b  + 4 a  b) x  - 4 b ) y  + 4 a  x  - 4 a  x
(%o10)  --------------------------------------------------------------
                         3  4      2  2  2  2    3    4
                      a b  y  + 2 a  b  x  y  + a  b x
(%i11) cosT: (d1_2+d2_2-d12_2)/(2*sqrt(d1_2*d2_2));
              3  4          2      2     2      2   2      3  4      2  2
           4 b  y  + ((4 a b  + 4 a  b) x  - 4 b ) y  + 4 a  x  - 4 a  x
(%o11) ((- --------------------------------------------------------------
                            3  4      2  2  2  2    3    4
                         a b  y  + 2 a  b  x  y  + a  b x
       3  6        3      2  2   2    3        2   4
 + (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y
           2  2    2    2             2             3
 + sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y
                2   3
 + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
        2  2    3     4         2    2     2    2         2    3    6
 + ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x
     3      2     4           2   2      3  4      2  2  2  2    3    4
 + (a  - 2 a  b) x  + (a b - a ) x )/(a b  y  + 2 a  b  x  y  + a  b x )
         3  6          3      2  2   2    3        2   4
 - (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y
                2      2            2             3
 + sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y
                2   3
 + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
          2  2    3     4       2    2     2    2         2    3    6
 + ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x
       2      3   4     2         2      3  4      2  2  2  2    3    4
 + (2 a  b - a ) x  + (a  - a b) x )/(a b  y  + 2 a  b  x  y  + a  b x ))
 !   3  4      2  2  2  2    3    4!                  3  6          3      2  2   2    3        2   4                2      2            2             3                2   3                              2  2    3     4       2    2     2    2         2    3    6       2      3   4     2         2      3  6        3      2  2   2    3        2   4           2  2    2    2             2             3                2   3                            2  2    3     4         2    2     2    2         2    3    6     3      2     4           2
 !a b  y  + 2 a  b  x  y  + a  b x !)/(2 sqrt(- (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y  + sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y) + ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x  + (2 a  b - a ) x  + (a  - a b) x ) (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y  + sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y) + ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x  + (a  - 2 a  b) x  + (a b - a )
  2
 x )))
(%i12) fullratsimp(ratexpand(cosT));
            3  6        3      2  2   2    3        2   4
(%o12) ((a b  y  + ((a b  + 2 a  b ) x  - b  - 2 a b ) y
           2  2    2    2           2           3
 + sqrt(a b  y  + a  b x  - a b) ((b  - a b) x y
            2   3                                2      2
 + ((a b - a ) x  + (a - b) x) y) + sqrt(a b (b y  + a x  - 1))
          2     3      2         3
 ((a b - b ) x y  + ((a  - a b) x  + (b - a) x) y)
        2  2    3     4           2      2     2    2         2    3    6
 + ((2 a  b  + a  b) x  + (- 3 a b  - 3 a  b) x  + b  + a b) y  + a  b x
         2      3   4           2   2  !   3  4      2  2  2  2    3    4!
 + (- 2 a  b - a ) x  + (a b + a ) x ) !a b  y  + 2 a  b  x  y  + a  b x !)
      3  4      2  2  2  2    3    4               3  6          3      2  2   2    3        2   4                2      2            2             3                2   3                              2  2    3     4       2    2     2    2         2    3    6       2      3   4     2         2      3  6        3      2  2   2    3        2   4           2  2    2    2             2             3                2   3
/((a b  y  + 2 a  b  x  y  + a  b x ) sqrt(- (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y  + sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y) + ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x  + (2 a  b - a ) x  + (a  - a b) x ) (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y  + sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
        2  2    3     4         2    2     2    2         2    3    6
 + ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x
     3      2     4           2
 + (a  - 2 a  b) x  + (a b - a )
  2
 x )))
(%i13) 
Run Example
m: 4;
(%o1)                                  4
(%i2) e0: ((m+1)*x+(m-1)*y)/(2*m);
                                   3 y + 5 x
(%o2)                              ---------
                                       8
(%i3) e1: ((m-1)*x+(m+1)*y)/(2*m);
                                   5 y + 3 x
(%o3)                              ---------
                                       8
(%i4) fullratsimp(subst(e0, y, e1));
                                  15 y + 49 x
(%o4)                             -----------
                                      64
(%i5)  solve((a-r)*(d-r)-b*c,r);
                   2                    2
             sqrt(d  - 2 a d + 4 b c + a ) - d - a
(%o5) [r = - -------------------------------------, 
                               2
                                               2                    2
                                         sqrt(d  - 2 a d + 4 b c + a ) + d + a
                                     r = -------------------------------------]
                                                           2
(%i6) a0: 0;
(%o6)                                  0
(%i7) a1: 1;
(%o7)                                  1
(%i8) a: 49/64;
                                      49
(%o8)                                 --
                                      64
(%i9) b: 15/64;
                                      15
(%o9)                                 --
                                      64
(%i10) c: 3/8;
                                       3
(%o10)                                 -
                                       8
(%i11) d: 5/8;
                                       5
(%o11)                                 -
                                       8
(%i12) sqrt(a^2+d^2-2*a*d+4*b*c);
                                      39
(%o12)                                --
                                      64
(%i13) a1*b/sqrt(a^2+d^2-2*a*d+4*b*c);
                                      5
(%o13)                                --
                                      13
(%i14) 
Run Example
f: x/(1-x/a) = b/(1-b/a)*exp(r*t);
                                            r t
                                  x     b %e
(%o1)                           ----- = -------
                                    x        b
                                1 - -    1 - -
                                    a        a
(%i2) solve(f,x);
                                           r t
                                     a b %e
(%o2)                        [x = ---------------]
                                      r t
                                  b %e    - b + a
(%i3) fullratsimp(%o2);
(%o3)             fullratsimp(x/(1-x/a));
[assume,exp,fortran,fullratsimp,integrate] [assume,exp,fullratsimp,integrate] [block,denom,equal,ev,fullratsimp,lhs,maplist,return,rhs,trigexpand] [cos,diff,fullratsimp,integrate,sin,solve] [cos,diff,fullratsimp,sin] [cos,factor,fullratsimp,log,matrix,plot2d,ratexpand] [cos,fullratsimp,integrate,plot2d,sin,sqrt] [cos,fullratsimp,log,matrix,plot2d,ratexpand] [cos,fullratsimp,sin] [diff,display,do,ev,exp,fullratsimp] [diff,ev,float,fullratsimp,integrate,rhs,solve] [diff,exp,fullratsimp] [diff,factor,fullratsimp,plot2d,solve] [diff,fullratsimp,ic1,ode2] [diff,fullratsimp,plot2d,solve,sqrt] [diff,fullratsimp,plot2d] [diff,fullratsimp,sin] [diff,fullratsimp] [ev,expand,float,fullratsimp,kill,multthru,numer] [ev,float,fullratsimp,integrate,rhs,solve] [ev,float,fullratsimp,kill,multthru,numer] [ev,float,fullratsimp,solve,subst] [ev,fullratsimp,integrate,rhs,solve] [ev,fullratsimp,rhs,var] [exp,fortran,fullratsimp,jacobian,log,sum] [exp,fullratsimp,jacobian,log,sum] [exp,fullratsimp,pade,taylor] [exp,fullratsimp] [expand,fullratsimp,ratsimp] [expand,fullratsimp] [factor,fullratsimp,linsolve,rhs] [factor,fullratsimp,sqrt] [first,fullratsimp,solve] [fullratsimp,inf,integrate,limit,simpsum,true] [fullratsimp,integrate,rhs,solve] [fullratsimp,integrate,solve] [fullratsimp,integrate] [fullratsimp,linsolve,subst] [fullratsimp,linsolve] [fullratsimp,pade,tan,taylor] [fullratsimp,ratsimp,solve] [fullratsimp,ratsimp,sum] [fullratsimp,ratsimp] [fullratsimp,solve,sqrt,subst] [fullratsimp,solve,sqrt] [fullratsimp,solve] [fullratsimp,sqrt,subst] [fullratsimp,sqrt] [fullratsimp,subst] [fullratsimp]

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