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

Zhenyu Zeng
Posted 1 year ago

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

enter image description here

From this output, enter image description here 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?
POSTED BY: Zhenyu Zeng
1 Reply
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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.
POSTED BY: Gianluca Gorni
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