Apart1

Description

Apart1[expr, x] is equivalent to Apart[expr, x], but it is faster than Apart if explicit complex numbers (I's) are in exp.

See also:  Apart2, Apart3.

Examples

t = 
      1/4*(1 - x)^4*x*(21 + 13*x + 3*x^2) - 
        1/24*11*I*Pi*(1 - x)^4*
          x*(21 + 13*x + 3*x^2) + ((1 - x)^4*
              x^2*(21 + 13*x + 
                  3*x^2))/(36*(-1 + x)^4) - (I*
              Pi*(1 - x)^4*
              x^2*(21 + 13*x + 
                  3*x^2))/(12*(-1 + x)^4) - (7*(1 - 
                    x)^4*x^3*(21 + 13*x + 
                  3*x^2))/(48*(-1 + x)^4) + (3*I*
              Pi*(1 - x)^4*
              x^3*(21 + 13*x + 
                  3*x^2))/(8*(-1 + x)^4) + (11*(1 - 
                    x)^4*x^4*(21 + 13*x + 
                  3*x^2))/(24*(-1 + x)^4) - (3*I*
              Pi*(1 - x)^4*
              x^4*(21 + 13*x + 
                  3*x^2))/(4*(-1 + x)^4) - (49*(1 - 
                    x)^4*x^5*(21 + 13*x + 
                  3*x^2))/(144*(-1 + x)^4) + (11*I*
              Pi*(1 - x)^4*
              x^5*(21 + 13*x + 3*x^2))/(24*(-1 + x)^4) + 
        1/4*(1 - x)^4*x*(21 + 13*x + 3*x^2)*Zeta2 + 
        11/24*(1 - x)^4*x*(21 + 13*x + 3*x^2)*Log[x] + 
        1/4*I*Pi*(1 - x)^4*x*(21 + 13*x + 3*x^2)*
          Log[x] + ((1 - x)^4*x^2*(21 + 13*x + 3*x^2)*
              Log[x])/(12*(-1 + x)^4) - (3*(1 - x)^4*
              x^3*(21 + 13*x + 3*x^2)*
              Log[x])/(8*(-1 + x)^4) + (3*(1 - x)^4*
              x^4*(21 + 13*x + 3*x^2)*
              Log[x])/(4*(-1 + x)^4);

Timing[a1 = Apart1[t, x]; ]

Timing[a2 = Apart[t, x]; ]

a1 - a2 // Expand

Clear[t, a1, a2]