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divide

divide(-12*x**4+20*x*...

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divide

divide(x^9+6*x^4-0*x+...

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divide-num-ratsimp

num : 1-1/z-4/z^2+4/z^3;

num:ratsimp(num*z^3);

den : 1-11/4/z+13/8/z...

Calculate

divide

divide(x^3-x^2+x+5,x+1);

x^3-x^2+x+5,x=-11;

divide(5*x^4+30*x^3-4...

Calculate

divide-gcd

divide(X^3-3*X+1,3*X^...

f:gcd(X^2-1,X-1,X);

f;

Calculate

divide-num-ratsimp

num : 1-1/z-4/z^2+4/z^3;

num:ratsimp(num*z^3);

den : 1-11/4/z+13/8/z...

Calculate

divide-ev-expand-simp

answer_1: ev(expand((...

answer_2: ev(expand((...

ev(answer_1+answer_2,...

Calculate

divide-factor-solve

factor (x^3-2*x^2+10*...

divide (6*x^3+5*x-8, ...

solve(x^3-2*x^2+10*x+...

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divide

divide (4*x^3 + x + 1...

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divide

divide (16*a^9+2*b^9-...

divide (x + y, x - y);

Calculate

divide

Run Example
(%i1)factorC(_f,_z):=block([s,n,m,fp,j],fp:1,/* This commented code was meant to use themore robust solver to_poly_solve, but I couldn't understand how to handle multiplicitiesss:args(to_poly_solve(_f,_z)),s:create_list(ss[k][1],k,1,length(ss)),*/s:solve(_f,_z),m:multiplicities,n:length(s),for j:1 thru n do  if lhs(s[j])#0  then fp:fp*(_z-(rhs(s[j])))^m[j], fp:fp*divide(_f,fp)[1],fp);
(%o1) factorC(_f, _z) := block([s, n, m, fp, j], fp : 1, s : solve(_f, _z), 
m : multiplicities, n : length(s), for j thru n 
                                             m
                                              j
do if lhs(s ) # 0 then fp : fp (_z - rhs(s ))  , fp : fp divide(_f, fp) , fp)
           j                              j                            1
(%i2) partfracC(_f,_z):=block([d,fd],d:denom(_f),fd:factorC(d,_z),partfrac(1/fd,_z));
(%o2) partfracC(_f, _z) := block([d, fd], d : denom(_f), fd : factorC(d, _z), 
                                                                       1
                                                              partfrac(--, _z))
                                                                       fd
(%i3) O:partfracC(1/(x^5-1)^4,x);
               4 %i %pi           2 %i %pi             2 %i %pi
               --------           --------           - --------
                  5                  5                    5
(%o3) (41992 %e         + 42160 %e         + 42076 %e
             4 %i %pi                  4 %i %pi         2 %i %pi            4 %i %pi            4 %i %pi
           - --------                  --------         --------          - --------            --------
                5                         5                5                   5                   5
 + 41824 %e           + 42328)/((625 %e         - 625 %e         + 1875 %e           - 1875) (%e         x
 - 1))
           4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi
           --------          --------          - --------          - --------
              5                 5                   5                   5
 + (1082 %e         + 1018 %e         + 1114 %e           + 1114 %e
                    2 %i %pi           2 %i %pi           4 %i %pi
                    --------         - --------         - --------
                       5                  5                  5
 + 1082)/((- 1250 %e         + 625 %e           + 625 %e          )
    4 %i %pi
    --------
       5           2
 (%e         x - 1) )
        4 %i %pi        2 %i %pi          2 %i %pi          4 %i %pi
        --------        --------        - --------        - --------
           5               5                 5                 5
   28 %e         + 20 %e         + 12 %e           + 20 %e           + 20
 + ----------------------------------------------------------------------
                   2 %i %pi         4 %i %pi     4 %i %pi
                 - --------         --------     --------
                      5                5            5           3
          (625 %e           - 625 %e        ) (%e         x - 1)
               4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
               --------         --------         - --------         - --------
                  5                5                  5                  5
 + 1/((- 125 %e         - 125 %e         - 125 %e           - 125 %e
           4 %i %pi                      4 %i %pi          2 %i %pi
           --------                      --------          --------
              5           4                 5                 5
 + 500) (%e         x - 1) ) - (- 1544 %e         - 1880 %e
          2 %i %pi           4 %i %pi
        - --------         - --------
             5                  5
 - 32 %e           - 368 %e           - 956)
            4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi     2 %i %pi
            --------          --------          - --------          - --------     --------
               5                 5                   5                   5            5
/((- 4375 %e         - 6875 %e         + 6875 %e           + 4375 %e          ) (%e         x - 1))
         4 %i %pi         2 %i %pi          2 %i %pi          4 %i %pi
         --------         --------        - --------        - --------
            5                5                 5                 5
 + (42 %e         + 170 %e         + 42 %e           - 54 %e           + 170)
           4 %i %pi          2 %i %pi           2 %i %pi            4 %i %pi
           --------          --------         - --------          - --------
              5                 5                  5                   5
/((- 625 %e         + 1875 %e         - 625 %e           - 2500 %e           + 1875)
    2 %i %pi
    --------
       5           2
 (%e         x - 1) )
        4 %i %pi       2 %i %pi          2 %i %pi         4 %i %pi
        --------       --------        - --------       - --------
           5              5                 5                5
 - (4 %e         - 4 %e         - 12 %e           + 4 %e           - 12)
         4 %i %pi           2 %i %pi           4 %i %pi           2 %i %pi
         --------         - --------         - --------           --------
            5                  5                  5                  5           3
/((625 %e         - 625 %e           + 625 %e           - 625) (%e         x - 1) )
       2 %i %pi           4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
     - --------           --------         --------         - --------         - --------
          5                  5                5                  5                  5
 + %e          /((- 125 %e         - 125 %e         + 500 %e           - 125 %e
           2 %i %pi
           --------
              5           4
 - 125) (%e         x - 1) )
            4 %i %pi           2 %i %pi             2 %i %pi
            --------           --------           - --------
               5                  5                    5
 - (41824 %e         + 42076 %e         + 42160 %e
             4 %i %pi                  4 %i %pi         2 %i %pi            4 %i %pi
           - --------                  --------         --------          - --------
                5                         5                5                   5
 + 41992 %e           + 42328)/((625 %e         - 625 %e         + 1875 %e           - 1875) (x
     4 %i %pi
     --------
        5
 - %e        ))
           4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi
           --------          --------          - --------          - --------
              5                 5                   5                   5
 + (1114 %e         + 1082 %e         + 1082 %e           + 1114 %e
                    2 %i %pi           2 %i %pi           4 %i %pi
                    --------         - --------         - --------
                       5                  5                  5
 + 1018)/((- 1250 %e         + 625 %e           + 625 %e          )
        4 %i %pi
        --------
           5     2
 (x - %e        ) )
        4 %i %pi        2 %i %pi          2 %i %pi          4 %i %pi
        --------        --------        - --------        - --------
           5               5                 5                 5
   20 %e         + 20 %e         + 20 %e           + 12 %e           + 28
 - ----------------------------------------------------------------------
                    2 %i %pi         4 %i %pi         4 %i %pi
                  - --------         --------         --------
                       5                5                5     3
           (625 %e           - 625 %e        ) (x - %e        )
       4 %i %pi           4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
     - --------           --------         --------         - --------         - --------
          5                  5                5                  5                  5
 + %e          /((- 125 %e         - 125 %e         - 125 %e           - 125 %e
               4 %i %pi
               --------
                  5     4
 + 500) (x - %e        ) )
         4 %i %pi         2 %i %pi            2 %i %pi           4 %i %pi
         --------         --------          - --------         - --------
            5                5                   5                  5
 - (32 %e         + 956 %e         + 1544 %e           + 368 %e
                    4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi
                    --------          --------          - --------          - --------
                       5                 5                   5                   5
 + 1880)/((- 4375 %e         - 6875 %e         + 6875 %e           + 4375 %e          ) (x
     2 %i %pi
     --------
        5
 - %e        ))
          4 %i %pi        2 %i %pi          2 %i %pi           4 %i %pi
          --------        --------        - --------         - --------
             5               5                 5                  5
 + (170 %e         + 42 %e         + 42 %e           + 170 %e           - 54)
           4 %i %pi          2 %i %pi           2 %i %pi            4 %i %pi
           --------          --------         - --------          - --------
              5                 5                  5                   5
/((- 625 %e         + 1875 %e         - 625 %e           - 2500 %e           + 1875)
        2 %i %pi
        --------
           5     2
 (x - %e        ) )
          4 %i %pi        2 %i %pi         2 %i %pi         4 %i %pi
          --------        --------       - --------       - --------
             5               5                5                5
 - (- 4 %e         + 12 %e         + 4 %e           - 4 %e           + 12)
         4 %i %pi           2 %i %pi           4 %i %pi               2 %i %pi
         --------         - --------         - --------               --------
            5                  5                  5                      5     3
/((625 %e         - 625 %e           + 625 %e           - 625) (x - %e        ) )
       4 %i %pi           4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
     - --------           --------         --------         - --------         - --------
          5                  5                5                  5                  5
 + %e          /((- 125 %e         - 125 %e         + 500 %e           - 125 %e
               2 %i %pi
               --------
                  5     4
 - 125) (x - %e        ) )
         4 %i %pi         2 %i %pi           2 %i %pi          4 %i %pi
         --------         --------         - --------        - --------
            5                5                  5                 5
   120 %e         + 120 %e         - 132 %e           + 36 %e           + 36
 - -------------------------------------------------------------------------
                4 %i %pi         2 %i %pi            2 %i %pi
                --------         --------          - --------
                   5                5                   5
         (625 %e         + 625 %e         - 1250 %e          ) (x - 1)
        4 %i %pi        2 %i %pi          2 %i %pi         4 %i %pi
        --------        --------        - --------       - --------
           5               5                 5                5
   36 %e         + 36 %e         - 60 %e           + 4 %e           + 4
 + --------------------------------------------------------------------
             4 %i %pi         2 %i %pi            2 %i %pi
             --------         --------          - --------
                5                5                   5             2
      (625 %e         + 625 %e         - 1250 %e          ) (x - 1)
        4 %i %pi          4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
        --------          --------         --------         - --------         - --------
           5                 5                5                  5                  5
 - (8 %e        )/((500 %e         - 125 %e         - 125 %e           - 125 %e
                      4 %i %pi
                      --------
               3         5
 - 125) (x - 1) ) + %e
         4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
         --------         --------         - --------         - --------
            5                5                  5                  5
/((500 %e         - 125 %e         - 125 %e           - 125 %e           - 125)
        4
 (x - 1) )
(%i4) tex(O);
$${{41992\,e^{{{4\,i\,\pi}\over{5}}}+42160\,e^{{{2\,i\,\pi}\over{5}}}
 +42076\,e^ {- {{2\,i\,\pi}\over{5}} }+41824\,e^ {- {{4\,i\,\pi
 }\over{5}} }+42328}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}-625\,e
 ^{{{2\,i\,\pi}\over{5}}}+1875\,e^ {- {{4\,i\,\pi}\over{5}} }-1875
 \right)\,\left(e^{{{4\,i\,\pi}\over{5}}}\,x-1\right)}}+{{1082\,e^{{{
 4\,i\,\pi}\over{5}}}+1018\,e^{{{2\,i\,\pi}\over{5}}}+1114\,e^ {- {{2
 \,i\,\pi}\over{5}} }+1114\,e^ {- {{4\,i\,\pi}\over{5}} }+1082}\over{
 \left(-1250\,e^{{{2\,i\,\pi}\over{5}}}+625\,e^ {- {{2\,i\,\pi}\over{
 5}} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }\right)\,\left(e^{{{4\,i\,
 \pi}\over{5}}}\,x-1\right)^2}}+{{28\,e^{{{4\,i\,\pi}\over{5}}}+20\,e
 ^{{{2\,i\,\pi}\over{5}}}+12\,e^ {- {{2\,i\,\pi}\over{5}} }+20\,e
 ^ {- {{4\,i\,\pi}\over{5}} }+20}\over{\left(625\,e^ {- {{2\,i\,\pi
 }\over{5}} }-625\,e^{{{4\,i\,\pi}\over{5}}}\right)\,\left(e^{{{4\,i
 \,\pi}\over{5}}}\,x-1\right)^3}}+{{1}\over{\left(-125\,e^{{{4\,i\,
 \pi}\over{5}}}-125\,e^{{{2\,i\,\pi}\over{5}}}-125\,e^ {- {{2\,i\,\pi
 }\over{5}} }-125\,e^ {- {{4\,i\,\pi}\over{5}} }+500\right)\,\left(e
 ^{{{4\,i\,\pi}\over{5}}}\,x-1\right)^4}}-{{-1544\,e^{{{4\,i\,\pi
 }\over{5}}}-1880\,e^{{{2\,i\,\pi}\over{5}}}-32\,e^ {- {{2\,i\,\pi
 }\over{5}} }-368\,e^ {- {{4\,i\,\pi}\over{5}} }-956}\over{\left(-
 4375\,e^{{{4\,i\,\pi}\over{5}}}-6875\,e^{{{2\,i\,\pi}\over{5}}}+6875
 \,e^ {- {{2\,i\,\pi}\over{5}} }+4375\,e^ {- {{4\,i\,\pi}\over{5}} }
 \right)\,\left(e^{{{2\,i\,\pi}\over{5}}}\,x-1\right)}}+{{42\,e^{{{4
 \,i\,\pi}\over{5}}}+170\,e^{{{2\,i\,\pi}\over{5}}}+42\,e^ {- {{2\,i
 \,\pi}\over{5}} }-54\,e^ {- {{4\,i\,\pi}\over{5}} }+170}\over{\left(
 -625\,e^{{{4\,i\,\pi}\over{5}}}+1875\,e^{{{2\,i\,\pi}\over{5}}}-625
 \,e^ {- {{2\,i\,\pi}\over{5}} }-2500\,e^ {- {{4\,i\,\pi}\over{5}} }+
 1875\right)\,\left(e^{{{2\,i\,\pi}\over{5}}}\,x-1\right)^2}}-{{4\,e
 ^{{{4\,i\,\pi}\over{5}}}-4\,e^{{{2\,i\,\pi}\over{5}}}-12\,e^ {- {{2
 \,i\,\pi}\over{5}} }+4\,e^ {- {{4\,i\,\pi}\over{5}} }-12}\over{
 \left(625\,e^{{{4\,i\,\pi}\over{5}}}-625\,e^ {- {{2\,i\,\pi}\over{5
 }} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }-625\right)\,\left(e^{{{2\,i
 \,\pi}\over{5}}}\,x-1\right)^3}}+{{e^ {- {{2\,i\,\pi}\over{5}} }
 }\over{\left(-125\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi
 }\over{5}}}+500\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\,
 \pi}\over{5}} }-125\right)\,\left(e^{{{2\,i\,\pi}\over{5}}}\,x-1
 \right)^4}}-{{41824\,e^{{{4\,i\,\pi}\over{5}}}+42076\,e^{{{2\,i\,\pi
 }\over{5}}}+42160\,e^ {- {{2\,i\,\pi}\over{5}} }+41992\,e^ {- {{4\,i
 \,\pi}\over{5}} }+42328}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}-
 625\,e^{{{2\,i\,\pi}\over{5}}}+1875\,e^ {- {{4\,i\,\pi}\over{5}} }-
 1875\right)\,\left(x-e^{{{4\,i\,\pi}\over{5}}}\right)}}+{{1114\,e^{
 {{4\,i\,\pi}\over{5}}}+1082\,e^{{{2\,i\,\pi}\over{5}}}+1082\,e^ {- 
 {{2\,i\,\pi}\over{5}} }+1114\,e^ {- {{4\,i\,\pi}\over{5}} }+1018
 }\over{\left(-1250\,e^{{{2\,i\,\pi}\over{5}}}+625\,e^ {- {{2\,i\,\pi
 }\over{5}} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }\right)\,\left(x-e^{
 {{4\,i\,\pi}\over{5}}}\right)^2}}-{{20\,e^{{{4\,i\,\pi}\over{5}}}+20
 \,e^{{{2\,i\,\pi}\over{5}}}+20\,e^ {- {{2\,i\,\pi}\over{5}} }+12\,e
 ^ {- {{4\,i\,\pi}\over{5}} }+28}\over{\left(625\,e^ {- {{2\,i\,\pi
 }\over{5}} }-625\,e^{{{4\,i\,\pi}\over{5}}}\right)\,\left(x-e^{{{4\,
 i\,\pi}\over{5}}}\right)^3}}+{{e^ {- {{4\,i\,\pi}\over{5}} }}\over{
 \left(-125\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi}\over{5}}}
 -125\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\,\pi}\over{5}}
  }+500\right)\,\left(x-e^{{{4\,i\,\pi}\over{5}}}\right)^4}}-{{32\,e
 ^{{{4\,i\,\pi}\over{5}}}+956\,e^{{{2\,i\,\pi}\over{5}}}+1544\,e^ {- 
 {{2\,i\,\pi}\over{5}} }+368\,e^ {- {{4\,i\,\pi}\over{5}} }+1880
 }\over{\left(-4375\,e^{{{4\,i\,\pi}\over{5}}}-6875\,e^{{{2\,i\,\pi
 }\over{5}}}+6875\,e^ {- {{2\,i\,\pi}\over{5}} }+4375\,e^ {- {{4\,i\,
 \pi}\over{5}} }\right)\,\left(x-e^{{{2\,i\,\pi}\over{5}}}\right)}}+
 {{170\,e^{{{4\,i\,\pi}\over{5}}}+42\,e^{{{2\,i\,\pi}\over{5}}}+42\,e
 ^ {- {{2\,i\,\pi}\over{5}} }+170\,e^ {- {{4\,i\,\pi}\over{5}} }-54
 }\over{\left(-625\,e^{{{4\,i\,\pi}\over{5}}}+1875\,e^{{{2\,i\,\pi
 }\over{5}}}-625\,e^ {- {{2\,i\,\pi}\over{5}} }-2500\,e^ {- {{4\,i\,
 \pi}\over{5}} }+1875\right)\,\left(x-e^{{{2\,i\,\pi}\over{5}}}
 \right)^2}}-{{-4\,e^{{{4\,i\,\pi}\over{5}}}+12\,e^{{{2\,i\,\pi
 }\over{5}}}+4\,e^ {- {{2\,i\,\pi}\over{5}} }-4\,e^ {- {{4\,i\,\pi
 }\over{5}} }+12}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}-625\,e
 ^ {- {{2\,i\,\pi}\over{5}} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }-625
 \right)\,\left(x-e^{{{2\,i\,\pi}\over{5}}}\right)^3}}+{{e^ {- {{4\,i
 \,\pi}\over{5}} }}\over{\left(-125\,e^{{{4\,i\,\pi}\over{5}}}-125\,e
 ^{{{2\,i\,\pi}\over{5}}}+500\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e
 ^ {- {{4\,i\,\pi}\over{5}} }-125\right)\,\left(x-e^{{{2\,i\,\pi
 }\over{5}}}\right)^4}}-{{120\,e^{{{4\,i\,\pi}\over{5}}}+120\,e^{{{2
 \,i\,\pi}\over{5}}}-132\,e^ {- {{2\,i\,\pi}\over{5}} }+36\,e^ {- {{4
 \,i\,\pi}\over{5}} }+36}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}+
 625\,e^{{{2\,i\,\pi}\over{5}}}-1250\,e^ {- {{2\,i\,\pi}\over{5}} }
 \right)\,\left(x-1\right)}}+{{36\,e^{{{4\,i\,\pi}\over{5}}}+36\,e^{
 {{2\,i\,\pi}\over{5}}}-60\,e^ {- {{2\,i\,\pi}\over{5}} }+4\,e^ {- {{
 4\,i\,\pi}\over{5}} }+4}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}+
 625\,e^{{{2\,i\,\pi}\over{5}}}-1250\,e^ {- {{2\,i\,\pi}\over{5}} }
 \right)\,\left(x-1\right)^2}}-{{8\,e^{{{4\,i\,\pi}\over{5}}}}\over{
 \left(500\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi}\over{5}}}-
 125\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\,\pi}\over{5}}
  }-125\right)\,\left(x-1\right)^3}}+{{e^{{{4\,i\,\pi}\over{5}}}
 }\over{\left(500\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi
 }\over{5}}}-125\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\,
 \pi}\over{5}} }-125\right)\,\left(x-1\right)^4}}$$
(%o4)                                false
(%i5) 
Run Example
divide(x^4+7*x^3+2*x^2-3*x-5,3*x^2-x+1);
                           2
                        9 x  + 66 x + 37    110 x + 172
(%o1)                  [----------------, - -----------]
                               27               27
(%i2) 
Run Example
T1:x^2+8*x+15;
                                  2
(%o1)                            x  + 8 x + 15
(%i2) divide(T1,x-3);
(%o2)                            [x + 11, 48]
(%i3) T2:x^2-8*x+15;
                                  2
(%o3)                            x  - 8 x + 15
(%i4) divide(T2,x-3);
(%o4)                             [x - 5, 0]
(%i5) divide(T2,x-5);
(%o5)                             [x - 3, 0]
(%i6) divide(T2,x-4);
(%o6)                            [x - 4, - 1]
(%i7) T3:x^3+3*x^2+3*x+1;
                               3      2
(%o7)                         x  + 3 x  + 3 x + 1
(%i8) T4:x^2+2*x+1;
                                  2
(%o8)                            x  + 2 x + 1
(%i9) divide(T3,T4);
(%o9)                             [x + 1, 0]
(%i10) 

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