2018-07-06 05:40:14 -0500 received badge ● Supporter (source) 2018-07-05 16:52:29 -0500 received badge ● Nice Question (source) 2018-07-05 09:17:08 -0500 commented question Assumptions and inequalities Thanks. About my first question: Could the reason be that sqrt(3) is not rational? (I have no idea). About my second question: I also tried without assumptions in other ways, like by using solve or solve_ineq. But I have similar problems. Anyway, an alternative procedure that works (that is, an answer to the second question), for me would be considered as a full answer (and very appreciated). 2018-07-05 07:24:16 -0500 received badge ● Student (source) 2018-07-05 02:59:49 -0500 received badge ● Editor (source) 2018-07-04 15:33:27 -0500 asked a question Assumptions and inequalities Hello all. I have some expressions like sums of ratios of real polynomials in a variable t. Mathematically, by assuming t real in a specific interval, each such expression is either always positive, or always non-negative. For Sage, this is sometimes the case, sometimes not: as you can see, the first one is correct, the second one not  var('t') expr1 = -1 + (t^2 - 1)/t^2 + 1/t^2 expr2 = (t^2 - 1)/(t^2 - 3) with assuming(t > 0, t < 1/2): print(bool(expr1 <= 0), bool(expr1 > 0)) print(bool(expr2 <= 0), bool(expr2 > 0))  Output: (True, False) \n (False, False) Questions: Why? How can I avoid this problem? (An answer to the second question would be enough for me) Thanks in advance :)