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Algebraic Integers


I am doing the algebraic manipulations with the numbers a+b*p, where a,b are integers
and p is essentially the irrational number (say Sqrt[2]). There is a number of rules allowing 
manipulation of the numbers without referring to the value of p (for example: p/: 1/p=p/2;)
I want function Min[] to calculate the minimum of the set of algebraic integers (a+b*p) the way
it works for ordinary numbers, but giving the answer in algebraic form:

In:= Min[3 p - 2, 5 p - 4]
Out:= 3 p -2 

Is there any _elegant_ solution for this problem?


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