Fourier-Motzkin Elimination

Question

Is there any method available in mathematica to eliminate variable from set of inequalities? I tried Eliminate function available, but I guess it works on equalities only.

Answer 1

I'll borrow an example from another response. Recast as an existance problem in the variable you want to eliminate, then use Resolve.

sol = 
 Resolve[Exists[y, 
   And @@ {x >= 4 y, x <= 3 + 4 y, x >= 0, x <= 63, y >= 0, y <= 15}]]

(* x \[Element] 
  Reals && ((-3 + x <= 0 && -x <= 0) || (-60 + x <= 0 && -x <= 
      0) || (-63 + x <= 0 && 3 - x <= 0) || (-63 + x <= 0 && 
     60 - x <= 0)) *)

Answer 2

You might want to have a look at Reduce :

sol = Reduce[{x >= 4 y, x <= 3 + 4 y, x >= 0, x <= 63, y >= 0, y <= 15}, {y}, Integers] ;

You can then build a function with :

ysol[x_] =  Piecewise[Transpose[{sol[[All, 2, 2]] /. Or -> List, 
                                 sol[[All, 1]] /. Or -> List}]];

DiscretePlot[ysol[x], {x, 0, 63}]