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Re: Problems with Mathematica 8.0 Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114824] Re: Problems with Mathematica 8.0 Solve
  • From: Roman Pearce <rpearcea at gmail.com>
  • Date: Fri, 17 Dec 2010 23:50:19 -0500 (EST)
  • References: <id2eh3$d1i$1@smc.vnet.net>

On Nov 30, 1:01 am, Daniel Lichtblau <d... at wolfram.com> wrote:
> Version 8 Solve attempts to compute a lexicographic Groebner basis over
> a field of fractions in the parameters. I gather this turns out to be
> very difficult for this example, and it hangs here. I do not know
> offhand whether this indicates a limitation of our Groebnerbasis code,
> or this is just an intrinsically difficult computation.

Unless evaluation and interpolation are used extensively, computing
over the field of fractions is intrinsically harder.  The gain is that
you remove content from all the polynomials in each step, which may
help simplify the system.  In practice you can just preprocess the
generators because once the Groebner algorithms start running this is
quite rare.  A fast modular method over Q using a block order, with
parameters below the original variables, is often better for a small
number of parameters.


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