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Re: Why does Solve give me no solutions for this in Version 8.0.1?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119968] Re: Why does Solve give me no solutions for this in Version 8.0.1?
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Sat, 2 Jul 2011 05:01:48 -0400 (EDT)
  • References: <iuj54s$nnr$1@smc.vnet.net>

Phil J Taylor wrote:

> This system of equations for the Magic Hexagon is indeterminate.
>  Solve still provides useful information in  Version 6.0
>
> ClearAll[a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s];
> eqns = {
>    a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s
> - 190 == 0,
>    a + b + c - 38 == 0,
>    a + d + h - 38 == 0,
>    a + e + j + o + s - 38 == 0,
>    b + e + i + m - 38 == 0,
>    b + f + k + p - 38 == 0,
>    c + f + j + n + q - 38 == 0,
>    c + g + l - 38 == 0,
>    d + e + f + g - 38 == 0,
>    d + i + n + r - 38 == 0,
>    g + k + o + r - 38 == 0,
>    h + i + j + k + l - 38 == 0,
>    h + m + q - 38 == 0,
>    l + p + s - 38 == 0,
>    m + n + o + p - 38 == 0,
>    q + r + s - 38 == 0
>    };
>
> Join[
>  Solve[eqns, b], Solve[eqns, d], Solve[eqns, g],
>  Solve[eqns, m], Solve[eqns, p], Solve[eqns, j],
>  Solve[eqns, r], Solve[eqns, e], Solve[eqns, f],
>  Solve[eqns, i], Solve[eqns, k], Solve[eqns, n],
>  Solve[eqns, o], Solve[eqns, a], Solve[eqns, c],
>  Solve[eqns, h], Solve[eqns, l], Solve[eqns, q],
>  Solve[eqns, s]]
>
> Out[1]: {{b -> j + n + o}, {d -> j + k + o}, {g -> i + j + n},
>  {m -> f + j + k}, {p -> e + i + j}, {j -> -38 + d + g + r},
>  {r -> -38 + h + l + m + p}, {e -> -38 + h + k + q + r},
>  {f -> -38 + i + l + r + s}, {i -> -38 + f + p + q + s},
>  {k -> -38 + e + m + q + s}, {n -> -38 + g + h + k + l},
>  {o -> -38 + d + h + i + l}, {a -> -38 + i + m + n + q + r},
>  {c -> -38 + k + o + p + r + s}, {h -> -38 + n + o + p + r + s},
>  {l -> -38 + m + n + o + q +  r}, {q -> -38 + g + k + l + o + p},
>  {s -> -38 + d + h + i + m +  n}}
>
> Version 8.0.1 returns {}.

You can get back the behaviour of Solve (v.6), setting the Option
Method, which in 8.0.1 defaults to Automatic:

SetOptions[Solve,Method->"Legacy"]

Now Solve will give you the expected results.

-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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