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Question: How can I prove if the set is empty

Question:How can I prove if the set is empty

HelenaRib 83 Maple
linear student
March 06 2009
1

I have a little problem. I have some linear unequalities and I wan't to prove if the following set is empty.
S:={(a,c) | (a-2*b-d+2*c)*delta <= d-c-a+b, a-b >= d-c, a>=0, b>=0}

b:=2;
d:=5;
delta:=2;

I have proved it like this:
solve({(a-2*b-d+2*c)*delta <= d-c-a+b, a-b >= d-c, a>=0, b>=0}, [a,c]);                  

But this is sometimes really slow if  the set is not empty, because it gives me the piecewise definition where it is defined for a and c. And in my programm I have to prove such sets really often (more than 200 times).
Is there a better way to prove whether such a set is empty??


Thanks for your help

Helena
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