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Re: A Problem with Simplify

On 21 =C1=D0=D2, 11:26, Andrzej Kozlowski <a... at> wrote:
> And even in the purely algebraic cases  Reduce can easily take for
> ever. Or consider this:
>   Reduce[x^3 + Sin[x] == 0, x]
> During evaluation of In[34]:= Reduce::"nsmet" :  "This system cannot
> be solved with the methods available to Reduce"
> even though anyone can easily see that 0 is a solution (but Reduce is
> not allowed to return an incomplete solution).
> Adnrzej Kozlowski

I was surprised a bit. It is sad that even if I specify the Real
domain I may not give the only possible answer x=0:
Reduce[x + Sin[x] == 0, x, Reals]
Solve[x + Sin[x] == 0, x, Reals]

Now I understand the depth of the problem.

But speaking about Integrate, is it really necessarily to perform
Reduce[] on each step? The problem is to find the singularities on the
parameters of the argument function (I mean such values of the
parameters those degenerate the argument function). After this we
should keep track on arising new conditions on each step. It does not
mean to use Reduce. We need only understand what we really do and know
about limitations. As I think this is not so much complicated task and
may be fully implemented in Mathematica (if it is not implemented
already). On the final result we may need perform searching for the
singularities again - but only for checking the result!

But as I see first of all Wolfram Research should extend Reduce[] for
working with trigonometric functions. This is that we should wait for
nearest-future version of Mathematica. If we can not expect this -
what for we should pay money?

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