Re: Simplify With Assumptions

*To*: mathgroup at smc.vnet.net*Subject*: [mg17960] Re: Simplify With Assumptions*From*: Adam Strzebonski <adams>*Date*: Mon, 7 Jun 1999 02:51:18 -0400*Organization*: Wolfram Research, Inc.*References*: <7jahu5$jvo@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

This actually is a general problem with the Simplify heuristic, not with the assumptions. Simplify keeps only the best so far form of the expression, so one simplification may prevent another better simplification from happening. In this example the form with expanded base of the radical is simpler than the original form, but no longer is a Sqrt of a square, so it is not simplified further. If we replace t in the numerator with x so that it no longer cancels with the denominator we get the better simplification: In[1]:= Simplify[Sqrt[(1 + 2*x^2)^2/t^2], t > 0 && x > 0] 2 1 + 2 x Out[1]= -------- t I will keep this example in mind for future improvements in the Simplify heuristic. Adam Strzebonski Wolfram Research David Park wrote: > Simplify with assumptions in Version 4 is not everything one might > hope. > > Simplify[Sqrt[x^2], x > 0] > x > > But > > Simplify[Sqrt[(1 + 2*t^2)^2/t^2], t > 0] > Sqrt[4 + 1/t^2 + 4*t^2] > > not > > (1 + 2*t^2)/t > > Of course we can see for ourselves and PowerExpand. Yet one would have > > hoped that Mathematica would have handled this case automatically. > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/