> with(CurveFitting):
> f:=(x-1)*(x+2)^2*(x-1/2);
                                     2 /    1\
                 f := (x - 1) (x + 2)  |x - -|
                                       \    2/
> f:=expand(f);
                      4   5  3   3  2          
                f := x  + - x  - - x  - 4 x + 2
                          2      2             
> factor(f);
                  1                          2
                  - (2 x - 1) (x - 1) (x + 2) 
                  2                           
> solve(f,x);
                             1        
                          1, -, -2, -2
                             2        
> g:=x^3-1;
                                3    
                          g := x  - 1
> factor(g);
                              / 2        \
                      (x - 1) \x  + x + 1/
> factors(g);
               [   [[ 2           ]            ]]
               [1, [[x  + x + 1, 1], [x - 1, 1]]]
> g1:=factors(g)[2][1][1];
                               2        
                        g1 := x  + x + 1
> alias(a=RootOf(g1));
                               a
> factor(g1,a);
                      (x - a) (x + 1 + a)
> h:=x^5+x^4+x^3+x^2+x+1;
                       5    4    3    2        
                 h := x  + x  + x  + x  + x + 1
> solve(h);
      1   1    (1/2)    1   1    (1/2)  1   1    (1/2)  1   1    (1/2)
-1, - - + - I 3     , - - - - I 3     , - + - I 3     , - + - I 3     
      2   2             2   2           2   2           2   2         
> factor(h);
                       / 2        \ / 2        \
               (x + 1) \x  - x + 1/ \x  + x + 1/
> factor(h,a);
        (x - a) (x + 1 + a) (x - 1 - a) (x + a) (x + 1)
> 
> #### Parembolh ####
> 
> f:=PolynomialInterpolation([[0,1],[1,3],[2,2]],x);
                            3  2   7      
                     f := - - x  + - x + 1
                            2      2      
> #### Sxhma tou Shamir ####
> 
> secret:=7;
                          secret := 7
> f:=2*x^2+3*x+secret;
                              2          
                      f := 2 x  + 3 x + 7
> share[1]:=[1,subs(x=1,f)];
                      share[1] := [1, 12]
> share[2]:=[2,subs(x=2,f)];
                      share[2] := [2, 21]
> share[3]:=[3,subs(x=3,f)];
                      share[3] := [3, 34]
> share[4]:=[4,subs(x=4,f)];
                      share[4] := [4, 51]
> PolynomialInterpolation([share[1],share[2],share[3]],x) mod 11;
                            2          
                         2 x  + 3 x + 7