I want Mathematica to solve this equation (*) Integral from z to Q of 1 / K*(z-a)*(z-b) dz == t for Q, in terms of z, t, K, a, b, where all 5 of these are complex with a unequal to b. It's a theorem that even if the quadratic polynomial denominator is replaced more generally by *any* function V(z) analytic for all z in C, and |t| < eps, where eps = eps(z,V), then there is a solution Q = Q(z,t,K,a,b), and this is unique. (As long as the unspecified path of integration does not contain a point z_0 where V(z_0) = 0 -- which we assume.) In fact for the case of the quadratic polynomial, Q = Q(z,t,K,a,b) is defined for all (z,t) in CxC. In fact, the solution is a linear fractional transformation of z, in K, a, b, t: (a e^(-Lt) - b e^(Lt)) z + ab (e^(Lt) - e^(-Lt)) (**) Q(z,t,K,a,b) == ----------------------------------------------------- (e^(-Lt) - e^(Lt)) z + (a e^(Lt) - b e^(-Lt)) where L := K / 2(a-b). But no way can I get Mathematica to come up with anything remotely as simple, no less (**). The commands I used are just: << In[1]:= f[u_] := K*(u-a)*(u-b) In[2]:= FullSimplify[Solve[Integrate[f[u],{u,z,Q}] == t, Q]]
but I suspect, or at least hope, there are smarter ways to get Mathematica to simplify its answer. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele