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ratsubst-solve

f1: N = A / l_p^2;

f2: E = (1/2) * N * k...

f3: E = M * c^2;

Calculate

ratsubst

ratsubst (a, x*y^2, x...

Calculate

ratsubst-solve

f1: N = A / l_p^2;

f2: E = (1/2) * N * k...

f3: E = M * c^2;

Calculate

ratsubst

eq: (yx+1)*(x^2-y)^2-...

ratsubst(x^2-y,x^2-y+...

Calculate

ratsubst-solve

?ratsubst;

G0: Uaus = Adc12/1638...

G1: Uteil = U48 * R2/...

Calculate

ratsubst-solve

f1: N = A / l_p^2;

f2: E = (1/2) * N * k...

f3: E = M * c^2;

Calculate

ratsubst-solve

f1: N = A / l_p^2;

f2: E = (1/2) * N * k...

f3: E = M * c^2;

Calculate

ratsubst-solve

f1: N = A / l_p^2;

f2: E = (1/2) * N * k...

f3: E = M * c^2;

Calculate

ratsubst-solve-sqrt

Z0: (p1 - p2)/SE;

Z1 : ratsubst(sqrt(p*...

Z2 : ratsubst((p1*n1+...

Calculate

ratsubst

Run Example
(%i1)Z0: (p1 - p2)/SE;
                                    p1 - p2
(%o1)                               -------
                                      SE
(%i2) Z1 : ratsubst(sqrt(p*(1-p)*((1/n1)+(1/n2))),SE,Z0);
                                     p2 - p1
(%o2)                     - -------------------------
                                  1    1
                            sqrt((-- + --) (1 - p) p)
                                  n2   n1
(%i3) Z2 : ratsubst((p1*n1+p2*n2)/(n1+n2),p,Z1);
                                      p2 - p1
(%o3) - --------------------------------------------------------------------
                 2    2                                        2    2
               n2  (p2  - p2) + n1 n2 ((2 p1 - 1) p2 - p1) + n1  (p1  - p1)
        sqrt(- ------------------------------------------------------------)
                                          2     2
                                     n1 n2  + n1  n2
(%i4) Z3 : ratsubst(x*p2,p1,Z2);
(%o4) 
                                    p2 x - p2
  -----------------------------------------------------------------------------
           2    2  2                 2            2                         2
         p2  (n1  x  + 2 n1 n2 x + n2 ) + p2 (- n1  x + n1 n2 (- x - 1) - n2 )
  sqrt(- ---------------------------------------------------------------------)
                                         2     2
                                    n1 n2  + n1  n2
(%i5) solve(Z3,x);
(%o5)                               [x = 1]
(%i6) 
Run Example
eq: ratsubst(sin(a)^2,1-cos(a)^2,trigexpand(cos(9*a)));
                    8                    6                    4
(%o1) 256 cos(a) sin (a) - 448 cos(a) sin (a) + 240 cos(a) sin (a)
                                                                  2
                                                   - 40 cos(a) sin (a) + cos(a)
(%i2) 
Run Example
k:0;
(%o1)                                  0
(%i2) deg:8;
(%o2)                                  8
(%i3) f(s,k,deg):=block([eq],eq:expand(sum(a[2*ii]*(s-s0)^(2*ii),ii,0,deg)),if k>
0 then ( eq: diff(eq,s,k) ),return(eq));
(%o3) f(s, k, deg) := block([eq], eq : 
                         2 ii
expand(sum(a     (s - s0)    , ii, 0, deg)), 
            2 ii
if k > 0 then eq : diff(eq, s, k), return(eq))
(%i4) g(s,k,deg):=block([eq],eq:expand(sum((-s)^ii*sum(a[2*jj]*binomial(2*jj,ii)*s0^(2*jj-ii),jj,ceiling(ii/2),deg),ii,0,deg)),if k>
0 then ( eq: diff(eq,s,k) ),return(eq));
(%o4) g(s, k, deg) := block([eq], eq : 
                ii                                2 jj - ii              ii
expand(sum((- s)   sum(a     binomial(2 jj, ii) s0         , jj, ceiling(--), 
                        2 jj                                             2
deg), ii, 0, deg)), if k > 0 then eq : diff(eq, s, k), return(eq))
(%i5) ff:ratsubst(0,s^(deg/2),f(s,k,deg));
            16              15             2          14
(%o5) a   s0   - 16 a   s s0   + (120 a   s  + a  ) s0
       16            16                16       14
               3               13            2          12
 + (- 560 a   s  - 14 a   s) s0   + (91 a   s  + a  ) s0
           16          14                14       12
               3               11            2          10
 + (- 364 a   s  - 12 a   s) s0   + (66 a   s  + a  ) s0
           14          12                12       10
               3               9            2         8
 + (- 220 a   s  - 10 a   s) s0  + (45 a   s  + a ) s0
           12          10               10       8
               3             7           2         6
 + (- 120 a   s  - 8 a  s) s0  + (28 a  s  + a ) s0
           10         8               8       6
             3             5           2         4             3             3
 + (- 56 a  s  - 6 a  s) s0  + (15 a  s  + a ) s0  + (- 20 a  s  - 4 a  s) s0
          8         6               6       4               6         4
          2         2            3                    2
 + (6 a  s  + a ) s0  + (- 4 a  s  - 2 a  s) s0 + a  s  + a
       4       2              4         2          2       0
(%i6) gg:ratsubst(0,s^(deg/2),g(s,k,deg));
            16              15             2          14
(%o6) a   s0   - 16 a   s s0   + (120 a   s  + a  ) s0
       16            16                16       14
               3               13            2          12
 + (- 560 a   s  - 14 a   s) s0   + (91 a   s  + a  ) s0
           16          14                14       12
               3               11            2          10
 + (- 364 a   s  - 12 a   s) s0   + (66 a   s  + a  ) s0
           14          12                12       10
               3               9            2         8
 + (- 220 a   s  - 10 a   s) s0  + (45 a   s  + a ) s0
           12          10               10       8
               3             7           2         6
 + (- 120 a   s  - 8 a  s) s0  + (28 a  s  + a ) s0
           10         8               8       6
             3             5           2         4             3             3
 + (- 56 a  s  - 6 a  s) s0  + (15 a  s  + a ) s0  + (- 20 a  s  - 4 a  s) s0
          8         6               6       4               6         4
          2         2            3                    2
 + (6 a  s  + a ) s0  + (- 4 a  s  - 2 a  s) s0 + a  s  + a
       4       2              4         2          2       0
(%i7) rat(ff-gg);
(%o7)/R/                               0
(%i8) 
[abs,del,depends,diff,pi,ratsubst,sqrt] [abs,depends,diff,pi,radsubstflag,ratsubst,sqrt,true] [abs,depends,diff,pi,ratsubst,sqrt] [append,coeff,cos,display2d,false,makelist,ratsubst,sin,solve,sqrt,sum,trigexpand] [assume,constant,cos,declare,diff,globalsolve,let,letsimp,lhs,posfun,ratsubst,realonly,sin,subst,trigsimp,true] [binomial,block,ceiling,diff,expand,ratsubst,return,sum] [coeff,cos,display2d,do,false,makelist,print,ratsubst,sin,sqrt,sum,trigexpand] [coeff,cos,display2d,false,makelist,ratsubst,sin,solve,sqrt,sum,trigexpand] [coeff,cos,display2d,false,makelist,ratsubst,sin,sqrt,sum,trigexpand] [coeff,cos,eliminate,makelist,rat,ratexpand,ratsubst,sin,trigexpand] [coeff,cos,eliminate,makelist,rat,ratsubst,sin,trigexpand] [coeff,cos,makelist,num,rat,ratexpand,ratsubst,sin,trigexpand] [coeff,cos,makelist,rat,ratsubst,sin,solve,trigexpand] [coeff,cos,makelist,rat,ratsubst,sin,trigexpand] [coeff,cos,makelist,ratsubst,sin,solve,sum,trigexpand] [constant,cos,declare,ratsimp,ratsubst,solve,sqrt] [constant,cos,declare,ratsimp,ratsubst,sqrt] [constant,cos,declare,ratsubst,solve,sqrt] [cos,derivabbrev,diff,eliminate,lhs,ratsimp,ratsubst,sin,solve,true] [cos,derivabbrev,diff,lhs,ratsimp,ratsubst,sin,solve,true] [cos,diff,exp,ratsubst,sin] [cos,display2d,false,makelist,mod,ratsubst,sin,sqrt,sum,trigexpand] [cos,display2d,false,ratsubst,sin,sqrt,sum,trigexpand] [cos,expand,factor,ratsubst,sin,sqrt,trigexpand] [cos,factor,plot2d,rat,ratsubst,sin,trigexpand] [cos,factor,rat,ratsubst,sin,trigexpand] [cos,makelist,ratsubst,sin,sum,trigexpand] [cos,plot2d,rat,ratsubst,sin,trigexpand] [cos,rat,ratsubst,sin,trigexpand] [cos,ratsubst,remainder,sin,trigexpand] [cos,ratsubst,sin,sum,trigexpand] [cos,ratsubst,sin,trigexpand] [denom,lhs,num,ratsubst,rhs,solve] [denom,lhs,ratsubst,rhs,solve] [determinant,matrix,ratsubst,rhs,solve] [determinant,matrix,ratsubst,simp,solve] [diff,exp,ratsimp,ratsubst] [diff,ic1,ode2,ratsubst] [diff,ratsubst] [display2d,false,print,ratsubst] [expand,makelist,product,ratsubst] [expand,product,ratsubst] [expand,ratsubst] [load,matrix,rank,ratsubst,solve] [load,matrix,rank,ratsubst] [ratsimp,ratsubst] [ratsubst,solve,sqrt] [ratsubst,solve] [ratsubst,sqrt] [ratsubst]

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