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Re: Simplify With Assumptions

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]

        1 + 2 x
Out[1]= --------

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

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