Cannot solve very simple equation.
in [Mathematica]
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From: negatron on 16 Dec 2009 06:22 NSolve[x^2 + 1 == 2^x] "Solve::tdep: "\!\(\* StyleBox[\"\\\"The equations appear to involve the variables to be solved for in an essentially non-algebraic way.\\\"\", \"MT\"]\) "" Am I forgetting something trivial here?
From: Alois Steindl on 16 Dec 2009 06:35 negatron <lokieffect(a)gmail.com> writes: > NSolve[x^2 + 1 == 2^x] > > "Solve::tdep: "\!\(\* > StyleBox[\"\\\"The equations appear to involve the variables to be > solved for in an essentially non-algebraic way.\\\"\", \"MT\"]\) "" > > Am I forgetting something trivial here? > Hello, from the Help page: NSolve[lhs==rhs,var] gives a list of numerical approximations to the roots of a polynomial equation. Although your equation looks quite simple, it isn't polynomial. Alois -- Alois Steindl, Tel.: +43 (1) 58801 / 32558 Inst. for Mechanics and Mechatronics Fax.: +43 (1) 58801 / 32598 Vienna University of Technology, A-1040 Wiedner Hauptstr. 8-10
From: Bob Hanlon on 17 Dec 2009 07:21 NSolve is intended primarily for polynomial equations (although you also left out the variable). Use FindRoot eqn = x^2 + 1 == 2^x; Plot[eqn, {x, -1, 5}] soln = Union[FindRoot[eqn, {x, #}] & /@ Range[-1, 5] // Chop, SameTest -> (Abs[(x /. #1) - (x /. #2)] < 10^-12 &)] {{x->0},{x->1.},{x->4.25746}} Bob Hanlon ---- negatron <lokieffect(a)gmail.com> wrote: ============= NSolve[x^2 + 1 == 2^x] "Solve::tdep: "\!\(\* StyleBox[\"\\\"The equations appear to involve the variables to be solved for in an essentially non-algebraic way.\\\"\", \"MT\"]\) "" Am I forgetting something trivial here?
From: DrMajorBob on 17 Dec 2009 07:24 Plot[fns = {x^2 + 1, 2^x}, {x, -2, 2}] From that, I get starting points for FindRoot. FindRoot[x^2 + 1 - 2^x, {x, .01}] {x -> -1.66744*10^-16} FindRoot[x^2 + 1 - 2^x, {x, 1.01}] {x -> 1.} The first root is exactly 0, and the second is exactly 1, which you can easily verify by looking at the problem. Bobby On Wed, 16 Dec 2009 05:19:55 -0600, negatron <lokieffect(a)gmail.com> wrote: > NSolve[x^2 + 1 == 2^x] > > "Solve::tdep: "\!\(\* > StyleBox[\"\\\"The equations appear to involve the variables to be > solved for in an essentially non-algebraic way.\\\"\", \"MT\"]\) "" > > Am I forgetting something trivial here? > -- DrMajorBob(a)yahoo.com
From: negatron on 17 Dec 2009 07:25
On Dec 16, 6:35 am, Alois Steindl <Alois.Stei...(a)tuwien.ac.at> wrote: > Although your equation looks quite simple, it isn't polynomial. Hi, it's not indeed, however my presumption was that Mathematica should converge on a solution using non-algebraic means. Monte Carlo algorithms for example should achieve a solution rather instantly and they're quite trivial to implement. Wolfram Alpha for example gives the solution to this and any such equation without the slightest fuss about the nature of the expression, so I assumed I was making a trivial error. I've been informed using FindRoot is necessary. I was hoping NSolve would directly provide the numerical solution, but such is life :) Thanks. |