Question: Minimum positive integer solution of system


I have a question, if it is possible please guide me. I tried for this problem but I failed.

I have a set of linear equations that I want to find the "minimum" "positive" "integer" solution to it. This system may contain free parameters in some cases that they should be set an integer in such a way that they yield our goal namely "Minimum positive solution".

I used isolve but it does not work for this case.

Indeed I especially want that maple use isolve it and then search that if there are "freevars" (in the solution: produced by maple when we use isolve code) or not, if yes then set number such that all solutions be the minimum positive integer set that we can have, indeed, the "freevars" should not set manually, but by the Maple. In the case that there is no "freevar", then maple should give me the minimum positive integer that we can have.

Note that the result must be a unique set of solutions.

For example, one of such systems that I am concerning is as follows which contains freevar in solution when we use isolve.

sys := [a[1] = 2*a[5], a[1] = a[4], 4*a[1]+2*a[3] = a[6]+2*a[7], 2*a[2]+2*a[3] = 2*a[6], a[2] = a[4]+a[5], 2*a[2]-a[1] = 2*a[4]]

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