Simplify is a nice fast function that cleans up simple inequalities. For example:
Simplify[c (a - b) > 0, Assumptions -> c > 0]
a > b
But I need the output inequality of the form
expr > 0, and ultimately I want to extract
expr. So I wrote a tiny function that gets it:
getGtrZero[expr_, assump_] := Part[#, 1] - Part[#, 2] &@Simplify[expr > 0, assump]
getGtrZero[c (a - b), c > 0]
a - b
This seems to be working ok, but this crucially requires that the output uses the function
Greater. Is this a robust way to get the simplified
expr that is going to be greater than zero?
Assumptions about input inequality: The input inequality will always have head
Greater and will be a comparison of two simple polynomials of various symbols (involving only plus, minus and times).