yeah's profile - activity

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).

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 :)