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sqfr

Run Example
(%i1)sqfr(x^3-9);
                                     3
(%o1)                               x  - 9
(%i2) remainder(expand((x^3+1)^3-2),a^3-9,a);
                              9      6      3
(%o2)                        x  + 3 x  + 3 x  - 1
(%i3) h:expand((x^2+2*x+5)^2*(x-1)^3*(x+2)*(x+1)^1);
       9      8       7      6       5       4       3       2
(%o3) x  + 4 x  + 10 x  + 6 x  - 20 x  - 42 x  - 26 x  + 82 x  + 35 x - 50
(%i4) g:gcd(h,diff(h,x));
                               4      2
(%o4)                         x  + 2 x  - 8 x + 5
(%i5) c[1]:rat(h/g);
                       5      4      3      2
(%o5)/R/              x  + 4 x  + 8 x  + 6 x  - 9 x - 10
(%i6) d[1]:rat(diff(h,x)/g-diff(c[1],x));
                          4       3       2
(%o6)/R/               4 x  + 16 x  + 28 x  + 32 x + 16
(%i7) i:1;
(%o7)                                  1
(%i8) while c[i]#1 do (/*print("c[",i,"]=",c[i]),*//*print("d[",i,"]=",d[i]),*/f[i]:gcd(c[i],d[i]),if f[i]#1 then (print("f[",i,"]=",f[i])),c[i+1]:rat(c[i]/f[i]),d[i+1]:rat(d[i]/f[i]-diff(c[i+1],x)),i:i+1);
         2
f[ 1 ]= x  + 3 x + 2 
         2
f[ 2 ]= x  + 2 x + 5 
f[ 3 ]= x - 1 
(%o8)                                done
(%i9) 
Run Example
sqfr((expand((x-2)^3*(x^2+1))));
                                      3   2
(%o1)                          (x - 2)  (x  + 1)
(%i2) 
Run Example
sqfr: 14=x-4;
(%o1)                             14 = x - 4
(%i2) 

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