Why doesn't "Reduce" function combine some results succinctly？

Questions
,
1

Hello,

For example,

TraditionalForm@
 Reduce[x + 3 y + 3 z + 4 d + 5 f + 6 g == 18 && 
   x + 3 y + 4 z + 8 g == 12 && x + 7 z + 6 d == 15 && x >= 0 && 
   y >= 0 && z >= 0 && d >= 0 && f >= 0 && g >= 0, {x, y, z, d, f, g},
   Backsubstitution -> True]

will produce

Screenshot2024-01-08202144.png
Screenshot2024-01-08202144.png1114×1192 47.4 KB

From this output,

Screenshot2024-01-08202423.png
Screenshot2024-01-08202423.png802×110 3.81 KB

these two results can’t be combined to one as the latter can be expressed by the former if change y<224/85 to y<=224/85. So, why doesn’t Mathematica combine this sort of expressions?

2

Strange. Define

a = (x == 12/5 && 
    4/5 < y < 224/85 && (9 y)/56 <= z <= -(3/20) (-16 + 5 y) && 
    d == -(7/30) (-9 + 5 z) && f == 1/60 (-9 y + 56 z) && 
    g == 1/40 (48 - 15 y - 20 z));
b = (x == 12/5 && y == 224/85 && z == 36/85 && d == 273/170 && 
    f == 0 && g == 0);
c = (x == 12/5 && 
    4/5 < y <= 224/85 && (9 y)/56 <= z <= -(3/20) (-16 + 5 y) && 
    d == -(7/30) (-9 + 5 z) && f == 1/60 (-9 y + 56 z) && 
    g == 1/40 (48 - 15 y - 20 z));

Both

Reduce[Or[a, b] && Not[c]]
Reduce[Not@Or[a, b] && c]

give False very quickly. I would expect the following to give True quickly:

Reduce[Equivalent[Or[a, b], c]]

Instead, it gives a complicated expression.