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When one sets up an equation to solve one often needs to specify conditions on the variables such as 

{ x>0 && y>0 && z>0 }

This is not a problem if only a few variables are involved. However, it is another matter when say, 50 are required. Is there a compact form one can use? Using 

(...) && Table[x[[i]], {i,50}] > 0

within Reduce[] or Solve[] will not work.

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    $\begingroup$ Can you please format your question properly? Read this here which you find when you click on the question mark of the editor window. $\endgroup$
    – halirutan ♦
    Aug 5, 2013 at 22:10
  • $\begingroup$ Try (...) && (And @@ Table[...]) $\endgroup$
    – rm -rf ♦
    Aug 5, 2013 at 23:52
  • $\begingroup$ The second solution to this answer:How to find lattice points on a line segment? is another example like one can use Solve. Perhaps you could see also this Solve an equation in R+ $\endgroup$
    – Artes
    Aug 6, 2013 at 14:09

1 Answer 1

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One approach:

eqs = {x^2 + 4 y^2 + 9 z^2 + 16 t^2 == 354};

vars = Variables @ Level[eqs, -1]

Reduce[eqs ~Join~ Thread[vars > 0], {}, Integers]

{t, x, y, z}

(t == 1 && x == 1 && y == 8 && z == 3) || (t == 1 && x == 7 && y == 4 && z == 5) ||
(t == 2 && x == 1 && y == 4 && z == 5) || (t == 2 && x == 5 && y == 8 && z == 1) || 
(t == 2 && x == 7 && y == 2 && z == 5) || (t == 4 && x == 1 && y == 2 && z == 3) || 
(t == 4 && x == 5 && y == 4 && z == 1)
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  • $\begingroup$ This works for me. Thanks. $\endgroup$
    – TC Jones
    Aug 10, 2013 at 22:02
  • $\begingroup$ @TCJones You're welcome. Please consider voting for posts you find helpful and Accepting those that are fully satisfactory. $\endgroup$
    – Mr.Wizard
    Aug 10, 2013 at 23:14

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