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

• To: mathgroup at smc.vnet.net
• Subject: [mg119966] Re: Why does Solve give me no solutions for this in Version 8.0.1?
• From: Phil J Taylor <xptaylor at gmail.com>
• Date: Sat, 2 Jul 2011 05:01:27 -0400 (EDT)

```I hadn't realized that this was possible. The documentation had indicated
that Solve required at least two arguments. Thanks, the simplest solution
works best for me in this case.
====

Solve[eqns]
====
On Fri, Jul 1, 2011 at 11:54 AM, Daniel Lichtblau <danl at wolfram.com> wrote:

> On 06/30/2011 07:40 PM, 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: {{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 {}.
>>
>
>
> There are no generic solutions: each separate system forces equations
> involving non-Solve variables. See
> Documentation Center > Solve > Options > MaxExtraConditions
>
> You could do e.g.
>
> In:= Solve[eqns, b, MaxExtraConditions -> Infinity]
>
> Out= {{b ->
>   ConditionalExpression[j + n + o,
>    d - j - k - o == 0 && f + j + k + n + o + p == 38 &&
>
>     m + n + o + p == 38 && e - k - n - o - p - r == -38 &&
>     g + k + o + r == 38 && i + j + k + n + o + r == 38 &&
>     c - k - o - p - r - s == -38 && h - n - o - p - r - s == -38 &&
>     l + p + s == 38 && a + j + k + n + 2 o + p + r + s == 76 &&
>     q + r + s == 38]}}
>
> I'd suggest instead just doing
>
> Solve[eqns]
>
> An addition to being simpler to input, you will not have a "solution set"
> where r is in terms of l, and l is in terms of r.
>
> If you want to specify a set of variables to solve for in terms of all the
> rest, that shopuld be fine too. I'd make sure it is large enough that there
> are no remaining relations in terms of non-specified variables (or again
> you'll get {}). Alternatively you could set MaxExtraConditions to some high
> value.
>
>
> Daniel Lichtblau
> Wolfram Research
>

```

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