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. ==== I'd suggest instead just doing 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[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 {}. >> > > > 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[563]:= Solve[eqns, b, MaxExtraConditions -> Infinity] > > Out[563]= {{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 >