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Re: A Problem with Simplify
On 21 =C1=D0=D2, 11:26, Andrzej Kozlowski <a... at mimuw.edu.pl> 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:= 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?