MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Is this a bug in NSolve in mathematica?

One would expect and hope that if you ask Mathematica to find the
roots of a polynomial, it should give the same (approximate) answers
whether you do this symbolically, then find numerical approximations
to these exact answers, or whether you do it numerically. Here's an
example which (in Mathematica 7, running on OS X) where this fails

poly = -112 + 1/q^28 + 1/q^26 - 1/q^24 - 6/q^22 - 14/q^20 - 25/q^18 -
  38/q^16 - 52/q^14 - 67/q^12 - 81/q^10 - 93/q^8 - 102/q^6 - 108/
  q^4 - 111/q^2 - 111 q^2 - 108 q^4 - 102 q^6 - 93 q^8 - 81 q^10 -
  67 q^12 - 52 q^14 - 38 q^16 - 25 q^18 - 14 q^20 - 6 q^22 - q^24 +
  q^26 + q^28;

Total[q^4 /. NSolve[poly == 0, q]] - Total[q^4 /. N[Solve[poly == 0,

(Note: this is actually a Laurent polynomial, and if you multiply
through by a large power of q the problem goes away.)

The last line here is just a demonstration that the solutions found
are very different; in fact it's the quantity we were trying to
compute in the problem we were working on.

If you look closely at the output of NSolve[poly == 0, q] and of
N[Solve[poly == 0, q], you'll see that NSolve only gives 54 roots
instead of the expected 56. It's not that it just missed a repeated or
anything; it's missing the two largest roots in magnitude
(approximately +/- 1.59)

Is this a bug in Mathematica? Does anyone have an explanation for why
this is happening?

(ps -- This is crossposted on,
if anyone would prefer to answer there.)

  • Prev by Date: Working with ppatterns
  • Next by Date: Re: working with lists
  • Previous by thread: Re: Working with ppatterns
  • Next by thread: Re: Is this a bug in NSolve in mathematica?