Re: Bug in NSolve?

*To*: mathgroup at smc.vnet.net*Subject*: [mg33855] Re: Bug in NSolve?*From*: lalu_bhatt at yahoo.com (Bhuvanesh)*Date*: Sat, 20 Apr 2002 02:49:43 -0400 (EDT)*References*: <a9oe60$d9r$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski <andrzej at tuins.ac.jp> wrote: > Unlike Solve, NSolve returns only one root when it finds multiple roots > it considers to be sufficiently close to be identical. In fact it seems > that it applies Union to the final result. So when you use more > precision the roots which were considered as distinct due to possible > error become identified and appear only once. <snipped> > Why do Solve and NSolve behave differently here? Well, it seems to me > that it is probably a matter of "philosophy". Solve is basically an > "algebraic function" and from the algebraic point of view the > multiplicity of roots is an important property of a solution. But most > people looking for numerical solutions would be I think inclined to > consider multiple roots as "the same". But there should be two solutions, right? Solve returns: In[1]:= Solve[4877361379 x^2 -9754525226 x + 4877163849==0,x] 4877262613 - I Sqrt[2] 4877262613 + I Sqrt[2] Out[1]= {{x -> ----------------------}, {x -> ----------------------}} 4877361379 4877361379 The two solutions *are* close, as you wrote. -- Bhuvanesh, Wolfram Research.