* The two-loop helicity amplitudes for qqb -> VV' -> 4 leptons
* T. Gehrmann, A. von Manteuffel, L. Tancredi
***
* In this FORM-readable file we present the inversion of formula (2.15).
* These relations are needed to express the coefficients $\tau_j$ defined
* in (2.14) in terms of the coefficients $A_j$ defined in (2.11):
* $\tau_j = \sum_{i=1}^{10} B^{-1}_{ji} A_i$ .
***
* We use the following definition of the Mandelstam variables:
* s = (p1+p2)^2, t=(p1-p3)^2, u=(p2-p3)^2, p3^2=ma2, p4^2=mb2,
* and 'd' is the dimensional regularisation parameter.
***
* In these files we use the notation
* Num(n?) = n ;
* Den(n?) = 1/n ;
***

id tau1 =

       + A10 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1
          )

       + A9 * (
          - 1/2*Num(mb2 - u)*Num(mb2*ma2 - t*u)*Num(ma2 + 2*mb2 - 2*u - t
         )*mb2^-1
          )

       + A8 * (
          - 1/4*Num(mb2 - u)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A7 * (
          + 1/4*Num(mb2 - u)*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A6 * (
          + 1/4*Num(ma2 - t)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A5 * (
          - 1/4*Num(mb2 - u)^2*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A4 * (
          - 1/8*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2
          - t*u)*Num(2*mb2*ma2 + mb2^2 - u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A3 * (
          + 1/8*Num(mb2 - u)^2*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - 
         u*ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A2 * (
          + 1/8*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - 
         u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A1 * (
          - 1/8*Num(mb2 - u)^2*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*mb2^-1*
         ma2^-1
          );

id tau2 =

       + A10 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1
          )

       + A9 * (
          + 1/2*Num(mb2*ma2 - t*u)*Num(3*mb2*ma2 + 2*mb2^2 - 2*u*mb2 + t*
         ma2 - t*mb2 - 2*t*u - t^2)*mb2^-1
          )

       + A8 * (
          - 1/4*Num(mb2 - t)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A7 * (
          + 1/4*Num(mb2 - t)*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A6 * (
          - 1/4*Num(mb2 - t)^2*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A5 * (
          + 1/4*Num(ma2 - t)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A4 * (
          + 1/8*Num(mb2 - t)^2*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - 
         u*ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A3 * (
          - 1/8*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2
          - t*u)*Num(2*mb2*ma2 + mb2^2 - u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A2 * (
          - 1/8*Num(mb2 - t)^2*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*mb2^-1*
         ma2^-1
          )

       + A1 * (
          + 1/8*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - 
         u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          );

id tau3 =

       + A10 * (
          + 1/2*Num(mb2*ma2 - t*u)*Num(3*mb2*ma2 + 2*mb2^2 + u*ma2 - u*
         mb2 - u^2 - 2*t*mb2 - 2*t*u)*mb2^-1
          )

       + A9 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1
          )

       + A8 * (
          + 1/4*Num(mb2 - u)*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A7 * (
          - 1/4*Num(mb2 - u)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A6 * (
          + 1/4*Num(ma2 - u)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A5 * (
          - 1/4*Num(mb2 - u)^2*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A4 * (
          + 1/8*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - 
         u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A3 * (
          - 1/8*Num(mb2 - u)^2*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*mb2^-1*
         ma2^-1
          )

       + A2 * (
          - 1/8*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2
          - t*u)*Num(2*mb2*ma2 + mb2^2 - u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A1 * (
          + 1/8*Num(mb2 - u)^2*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - 
         u*ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          );

id tau4 =

       + A10 * (
          - 1/2*Num(mb2 - t)*Num(mb2*ma2 - t*u)*Num(ma2 + 2*mb2 - u - 2*t
         )*mb2^-1
          )

       + A9 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1
          )

       + A8 * (
          + 1/4*Num(mb2 - t)*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A7 * (
          - 1/4*Num(mb2 - t)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A6 * (
          - 1/4*Num(mb2 - t)^2*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A5 * (
          + 1/4*Num(ma2 - u)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A4 * (
          - 1/8*Num(mb2 - t)^2*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*mb2^-1*
         ma2^-1
          )

       + A3 * (
          + 1/8*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - 
         u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A2 * (
          + 1/8*Num(mb2 - t)^2*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - 
         u*ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A1 * (
          - 1/8*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2
          - t*u)*Num(2*mb2*ma2 + mb2^2 - u*mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          );

id tau5 =

       + A10 * (
          - Num( - 4*mb2*ma2^2 - 5*mb2^2*ma2 + 5*u*mb2*ma2 + 6*t*mb2*ma2
          + 2*t*mb2^2 + 2*t*u*ma2 + t*u*mb2 - 3*t*u^2 - 2*t^2*mb2 - 2*t^2*u
          + 2*d*mb2*ma2^2 + 2*d*mb2^2*ma2 - 2*d*u*mb2*ma2 - 3*d*t*mb2*ma2
          - d*t*mb2^2 - d*t*u*ma2 + d*t*u^2 + d*t^2*mb2 + d*t^2*u)*mb2^-1
          )

       + A9 * (
          + Num(mb2 - u)*Num(mb2*ma2 + 2*u*ma2 + 2*u*mb2 - 2*u^2 - 3*t*u
          - d*u*ma2 - d*u*mb2 + d*u^2 + d*t*u)*mb2^-1
          )

       + A8 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A7 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A6 * (
          - 1/2*Num(2*mb2*ma2 + mb2^2 - u*mb2 - t*mb2 - t*u)*Num( - 2*ma2^2
          - 3*mb2*ma2 + 2*u*ma2 + 2*t*ma2 + t*u + d*ma2^2 + d*mb2*ma2 - d
         *u*ma2 - d*t*ma2)*mb2^-1*ma2^-1
          )

       + A5 * (
          + 1/2*Num(mb2 - u)^2*Num( - 2*ma2^2 - 3*mb2*ma2 + 2*u*ma2 + 2*t*
         ma2 + t*u + d*ma2^2 + d*mb2*ma2 - d*u*ma2 - d*t*ma2)*mb2^-1*ma2^-1
          )

       + A4 * (
          + 1/4*Num(ma2 - u)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A3 * (
          - 1/4*Num(mb2 - u)^2*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A2 * (
          + 1/4*Num(ma2 - t)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A1 * (
          - 1/4*Num(mb2 - u)^2*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          );

id tau6 =

       + A10 * (
          + Num(mb2 - t)*Num(mb2*ma2 + 2*t*ma2 + 2*t*mb2 - 3*t*u - 2*t^2
          - d*t*ma2 - d*t*mb2 + d*t*u + d*t^2)*mb2^-1
          )

       + A9 * (
          - Num( - 4*mb2*ma2^2 - 5*mb2^2*ma2 + 6*u*mb2*ma2 + 2*u*mb2^2 - 2*
         u^2*mb2 + 5*t*mb2*ma2 + 2*t*u*ma2 + t*u*mb2 - 2*t*u^2 - 3*t^2*u
          + 2*d*mb2*ma2^2 + 2*d*mb2^2*ma2 - 3*d*u*mb2*ma2 - d*u*mb2^2 + d*u^2
         *mb2 - 2*d*t*mb2*ma2 - d*t*u*ma2 + d*t*u^2 + d*t^2*u)*mb2^-1
          )

       + A8 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A7 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A6 * (
          + 1/2*Num(mb2 - t)^2*Num( - 2*ma2^2 - 3*mb2*ma2 + 2*u*ma2 + 2*t*
         ma2 + t*u + d*ma2^2 + d*mb2*ma2 - d*u*ma2 - d*t*ma2)*mb2^-1*ma2^-1
          )

       + A5 * (
          - 1/2*Num(2*mb2*ma2 + mb2^2 - u*mb2 - t*mb2 - t*u)*Num( - 2*ma2^2
          - 3*mb2*ma2 + 2*u*ma2 + 2*t*ma2 + t*u + d*ma2^2 + d*mb2*ma2 - d
         *u*ma2 - d*t*ma2)*mb2^-1*ma2^-1
          )

       + A4 * (
          - 1/4*Num(mb2 - t)^2*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A3 * (
          + 1/4*Num(ma2 - u)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          )

       + A2 * (
          - 1/4*Num(mb2 - t)^2*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A1 * (
          + 1/4*Num(ma2 - t)*Num(mb2*ma2 - t*u)*Num(2*mb2*ma2 + mb2^2 - u*
         mb2 - t*mb2 - t*u)*mb2^-1*ma2^-1
          );

id tau7 =

       + A10 * (
          + Num(ma2 - t)*Num( - 3*mb2*ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*mb2 + 
         t*u + d*mb2*ma2 + d*mb2^2 - d*u*mb2 - d*t*mb2)*mb2^-1
          )

       + A9 * (
          - Num( - 3*mb2*ma2^2 - 4*mb2^2*ma2 + 4*u*mb2*ma2 + 5*t*mb2*ma2
          + 2*t*mb2^2 + t*u*ma2 - 2*t*u^2 - 2*t^2*mb2 - t^2*u + d*mb2*ma2^2
          + d*mb2^2*ma2 - d*u*mb2*ma2 - 2*d*t*mb2*ma2 - d*t*mb2^2 + d*t*u*
         mb2 + d*t^2*mb2)*mb2^-1
          )

       + A8 * (
          - 1/2*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2 - t*u)*Num( - 3*mb2*
         ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*mb2 + t*u + d*mb2*ma2 + d*mb2^2 - d*
         u*mb2 - d*t*mb2)*mb2^-1*ma2^-1
          )

       + A7 * (
          + 1/2*Num(ma2 - t)^2*Num( - 3*mb2*ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*
         mb2 + t*u + d*mb2*ma2 + d*mb2^2 - d*u*mb2 - d*t*mb2)*mb2^-1*ma2^-1
          )

       + A6 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A5 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A4 * (
          - 1/4*Num(mb2 - t)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A3 * (
          - 1/4*Num(mb2 - u)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A2 * (
          + 1/4*Num(mb2 - t)*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A1 * (
          + 1/4*Num(mb2 - u)*Num(ma2 - t)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          );

id tau8 =

       + A10 * (
          - Num( - 3*mb2*ma2^2 - 4*mb2^2*ma2 + 5*u*mb2*ma2 + 2*u*mb2^2 - 2*
         u^2*mb2 + 4*t*mb2*ma2 + t*u*ma2 - t*u^2 - 2*t^2*u + d*mb2*ma2^2
          + d*mb2^2*ma2 - 2*d*u*mb2*ma2 - d*u*mb2^2 + d*u^2*mb2 - d*t*mb2*
         ma2 + d*t*u*mb2)*mb2^-1
          )

       + A9 * (
          + Num(ma2 - u)*Num( - 3*mb2*ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*mb2 + 
         t*u + d*mb2*ma2 + d*mb2^2 - d*u*mb2 - d*t*mb2)*mb2^-1
          )

       + A8 * (
          + 1/2*Num(ma2 - u)^2*Num( - 3*mb2*ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*
         mb2 + t*u + d*mb2*ma2 + d*mb2^2 - d*u*mb2 - d*t*mb2)*mb2^-1*ma2^-1
          )

       + A7 * (
          - 1/2*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2 - t*u)*Num( - 3*mb2*
         ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*mb2 + t*u + d*mb2*ma2 + d*mb2^2 - d*
         u*mb2 - d*t*mb2)*mb2^-1*ma2^-1
          )

       + A6 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A5 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A4 * (
          + 1/4*Num(mb2 - t)*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A3 * (
          + 1/4*Num(mb2 - u)*Num(ma2 - u)^2*Num(mb2*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A2 * (
          - 1/4*Num(mb2 - t)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          )

       + A1 * (
          - 1/4*Num(mb2 - u)*Num(mb2*ma2 - t*u)*Num(ma2^2 + 2*mb2*ma2 - u*
         ma2 - t*ma2 - t*u)*mb2^-1*ma2^-1
          );

id tau9 =

       + A10 * (
          - 2*Num( - 7*mb2*ma2^2 - 16*mb2^2*ma2 + 8*u*mb2*ma2 + 8*t*mb2*
         ma2 + 3*t*u*ma2 + 12*t*u*mb2 - 4*t*u^2 - 4*t^2*u + 3*d*mb2*ma2^2
          + 9*d*mb2^2*ma2 - 3*d*u*mb2*ma2 - 3*d*t*mb2*ma2 - d*t*u*ma2 - 7
         *d*t*u*mb2 + d*t*u^2 + d*t^2*u - d^2*mb2^2*ma2 + d^2*t*u*mb2)*mb2^-1
          )

       + A9 * (
          + 2*Num( - 3*mb2*ma2^2 - 6*mb2^2*ma2 + 2*u*mb2*ma2 - 2*u^2*ma2 - 
         2*u^2*mb2 + 2*u^3 + 2*t*mb2*ma2 + t*u*ma2 + 4*t*u*mb2 + 2*t*u^2
          + d*mb2*ma2^2 + 5*d*mb2^2*ma2 - d*u*mb2*ma2 + d*u^2*ma2 + d*u^2*
         mb2 - d*u^3 - d*t*mb2*ma2 - 4*d*t*u*mb2 - d*t*u^2 - d^2*mb2^2*ma2
          + d^2*t*u*mb2)*mb2^-1
          )

       + A8 * (
          + Num(ma2 - u)*Num( - 3*mb2*ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*mb2 + 
         t*u + d*mb2*ma2 + d*mb2^2 - d*u*mb2 - d*t*mb2)*mb2^-1
          )

       + A7 * (
          - Num( - 3*mb2*ma2^2 - 4*mb2^2*ma2 + 4*u*mb2*ma2 + 5*t*mb2*ma2
          + 2*t*mb2^2 + t*u*ma2 - 2*t*u^2 - 2*t^2*mb2 - t^2*u + d*mb2*ma2^2
          + d*mb2^2*ma2 - d*u*mb2*ma2 - 2*d*t*mb2*ma2 - d*t*mb2^2 + d*t*u*
         mb2 + d*t^2*mb2)*mb2^-1
          )

       + A6 * (
          - Num( - 4*mb2*ma2^2 - 5*mb2^2*ma2 + 6*u*mb2*ma2 + 2*u*mb2^2 - 2*
         u^2*mb2 + 5*t*mb2*ma2 + 2*t*u*ma2 + t*u*mb2 - 2*t*u^2 - 3*t^2*u
          + 2*d*mb2*ma2^2 + 2*d*mb2^2*ma2 - 3*d*u*mb2*ma2 - d*u*mb2^2 + d*u^2
         *mb2 - 2*d*t*mb2*ma2 - d*t*u*ma2 + d*t*u^2 + d*t^2*u)*mb2^-1
          )

       + A5 * (
          + Num(mb2 - u)*Num(mb2*ma2 + 2*u*ma2 + 2*u*mb2 - 2*u^2 - 3*t*u
          - d*u*ma2 - d*u*mb2 + d*u^2 + d*t*u)*mb2^-1
          )

       + A4 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1
          )

       + A3 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - u)*Num(mb2*ma2 - t*u)*mb2^-1
          )

       + A2 * (
          + 1/2*Num(mb2*ma2 - t*u)*Num(3*mb2*ma2 + 2*mb2^2 - 2*u*mb2 + t*
         ma2 - t*mb2 - 2*t*u - t^2)*mb2^-1
          )

       + A1 * (
          - 1/2*Num(mb2 - u)*Num(mb2*ma2 - t*u)*Num(ma2 + 2*mb2 - 2*u - t
         )*mb2^-1
          );

id tau10 =

       + A10 * (
          + 2*Num( - 3*mb2*ma2^2 - 6*mb2^2*ma2 + 2*u*mb2*ma2 + 2*t*mb2*ma2
          + t*u*ma2 + 4*t*u*mb2 - 2*t^2*ma2 - 2*t^2*mb2 + 2*t^2*u + 2*t^3
          + d*mb2*ma2^2 + 5*d*mb2^2*ma2 - d*u*mb2*ma2 - d*t*mb2*ma2 - 4*d*
         t*u*mb2 + d*t^2*ma2 + d*t^2*mb2 - d*t^2*u - d*t^3 - d^2*mb2^2*ma2
          + d^2*t*u*mb2)*mb2^-1
          )

       + A9 * (
          - 2*Num( - 7*mb2*ma2^2 - 16*mb2^2*ma2 + 8*u*mb2*ma2 + 8*t*mb2*
         ma2 + 3*t*u*ma2 + 12*t*u*mb2 - 4*t*u^2 - 4*t^2*u + 3*d*mb2*ma2^2
          + 9*d*mb2^2*ma2 - 3*d*u*mb2*ma2 - 3*d*t*mb2*ma2 - d*t*u*ma2 - 7
         *d*t*u*mb2 + d*t*u^2 + d*t^2*u - d^2*mb2^2*ma2 + d^2*t*u*mb2)*mb2^-1
          )

       + A8 * (
          - Num( - 3*mb2*ma2^2 - 4*mb2^2*ma2 + 5*u*mb2*ma2 + 2*u*mb2^2 - 2*
         u^2*mb2 + 4*t*mb2*ma2 + t*u*ma2 - t*u^2 - 2*t^2*u + d*mb2*ma2^2
          + d*mb2^2*ma2 - 2*d*u*mb2*ma2 - d*u*mb2^2 + d*u^2*mb2 - d*t*mb2*
         ma2 + d*t*u*mb2)*mb2^-1
          )

       + A7 * (
          + Num(ma2 - t)*Num( - 3*mb2*ma2 - 2*mb2^2 + 2*u*mb2 + 2*t*mb2 + 
         t*u + d*mb2*ma2 + d*mb2^2 - d*u*mb2 - d*t*mb2)*mb2^-1
          )

       + A6 * (
          + Num(mb2 - t)*Num(mb2*ma2 + 2*t*ma2 + 2*t*mb2 - 3*t*u - 2*t^2
          - d*t*ma2 - d*t*mb2 + d*t*u + d*t^2)*mb2^-1
          )

       + A5 * (
          - Num( - 4*mb2*ma2^2 - 5*mb2^2*ma2 + 5*u*mb2*ma2 + 6*t*mb2*ma2
          + 2*t*mb2^2 + 2*t*u*ma2 + t*u*mb2 - 3*t*u^2 - 2*t^2*mb2 - 2*t^2*u
          + 2*d*mb2*ma2^2 + 2*d*mb2^2*ma2 - 2*d*u*mb2*ma2 - 3*d*t*mb2*ma2
          - d*t*mb2^2 - d*t*u*ma2 + d*t*u^2 + d*t^2*mb2 + d*t^2*u)*mb2^-1
          )

       + A4 * (
          - 1/2*Num(mb2 - t)*Num(mb2*ma2 - t*u)*Num(ma2 + 2*mb2 - u - 2*t
         )*mb2^-1
          )

       + A3 * (
          + 1/2*Num(mb2*ma2 - t*u)*Num(3*mb2*ma2 + 2*mb2^2 + u*ma2 - u*
         mb2 - u^2 - 2*t*mb2 - 2*t*u)*mb2^-1
          )

       + A2 * (
          + 1/2*Num(mb2 - t)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1
          )

       + A1 * (
          + 1/2*Num(mb2 - u)*Num(ma2 - t)*Num(mb2*ma2 - t*u)*mb2^-1
          );