# Question:Maple returns an incomplete set of solutions (Environment Variable problem?)

## Question:Maple returns an incomplete set of solutions (Environment Variable problem?)

Maple
Hello, this is my first post here and I'm relatively new to Maple. I'm using version 10 (fully updated) and have been struggling for the better part of the past two days with what should be a simple fix. I have two functions which I am equating, and then using Solve to put it in terms of one of the variables. Maple is consistently, and for a range of different functions, returning incomplete solution sets. Sometimes it is aware the set is incomplete whereas other times it is not, returning only a single result where there should be two (or more). I have seen one other post on here where a similar problem was encountered, but the user did not include a specific enough example, it seems, to be helped. So here are a couple of chunks of Maple code that cause the problem in version 10 (NOTE: we also have a machine running Maple 6, which does not seem to suffer this problem and returns all solutions, every time). First example: ``` S_Z := 2 - (4 * Z) / ( 4 * Z^2 + 1)^(1/2); S_Zmid1 := int(S_Z,Z=H..H+midZ); S_Zmid2 := int(S_Z,Z=H+midZ..infinity); Zmid := solve(S_Zmid1 = S_Zmid2,midZ); ``` The last line should return two solutions, however only the following solution is returned: Zmid := -1/8*(-8*H^2-3+4*sqrt(4*H^2+1)*H)/(-2*H+sqrt(4*H^2+1)) In this case, Maple does not seem to be aware that it is turfing a solution (though for my purposes, the solution it is returning is the correct one at least). Second example: ``` S_z := 2 - (4 * (z/s)) / ( 4 * (z/s)^2 + 1)^(1/2); S_zmid1 := int(S_z,z=h..h+midz); S_zmid2a := int(S_z,z=h+midz..infinity); #the second integral evaluates to infinity by Maple, so let's just do the indefinite #integral, and then do our own evaluation: S_zmid_indefinite := int(S_z,z); #evaluated to... S_zmid2b := ((s^2) + (4*(h+midz)^2))^(1/2) - 2*h - 2*midz; #Which can now be equated together to solve for zmid: zmid := solve(S_zmid1 = S_zmid2b,midz); ``` This time there are four possible solutions (which I ended up arduously working out on paper to be sure of when comparing to our old version 6 machine which variously returns only 2 of the 4 at any one time), only 1 of which is useful. Maple consistently returns only 1 of those 4 solutions, and it is non-physical so it is useless to me. In this instance, it is also aware that it is throwing out some solutions. The following is what is returned by the last line: Warning, solutions may have been lost zmid := -1/4*sqrt((4*h^2+s^2)/s^2)*s-1/2*h The Maple documentation (solve,details) suggests this may be an environment variable issue, although I have tried setting _EnvExplicit to each of the four options, and also tried setting _EnvTryHard to true, none of which had any effect whatsoever (although, Maple's documentation is completely unclear on how to actually set these variables... I tried a variety of methods that normally work for such variables, but none made a difference). Is it possible I need to change the variables in a buried config file somewhere? Is this possibly a bug - and then hopefully one with a workaround? It is not time critical anymore since we verified the results the old-fashioned way, but it is obviously important for us to be able to trust future solution results where alternate verification may not be reasonable. Any thoughts and/or advice is much appreciated. ﻿