2021-12-09 09:40:16 +0200 received badge ● Nice Question (source) 2021-12-06 11:28:26 +0200 commented answer Some straightforward square root fractions are not simplified Thanks! The takeaway message, the way I see it as a Sage beginner, is that it can always be useful to check with Sympy i 2021-12-06 11:25:59 +0200 marked best answer Some straightforward square root fractions are not simplified I'm a Sage beginner who's trying to apply it to a set of equations I'm working on. In that process, I came across an issue where SageMath 9.4 is not simplifying some very straightforward square root fractions in my expressions. Let me show you a minimal example: x = var('x') sqrt(1-x)/(1-x)  $$-\frac{\sqrt{-x + 1}}{x - 1}$$ What I was expecting to get, of course, is $1 / \sqrt{1 - x}$. Calling simplify() or full_simplify() on the expression doesn't make a difference; I still get the same thing out. I experimented with other square root fractions as well to see if this issue recurs: sqrt(x)/x  $$1/\sqrt{x}$$ sqrt(1+x)/(1+x)  $$1/\sqrt{1+x}$$ sqrt(x-1)/(x-1)  $$1/\sqrt{x-1}$$ So in other words, Sage automatically simplifies all of the other expressions I tried in exactly the way that I would expect. To try out things a bit further, I tried to see if it helps to apply Sympy: ( sqrt(1-x)/(1-x) )._sympy_().simplify()  $$1/\sqrt{1-x}$$ That works. (The simplify() argument is essential here; otherwise, the fraction is not automatically simplified.) So, is there some subtle finesse here that I'm not understanding, or did I stumble across a bug in Sage's simplification algorithms? 2021-12-06 11:25:59 +0200 received badge ● Scholar (source) 2021-12-06 11:25:56 +0200 received badge ● Supporter (source) 2021-12-03 18:29:18 +0200 received badge ● Student (source) 2021-12-03 18:27:38 +0200 asked a question Some straightforward square root fractions are not simplified Some straightforward square root fractions are not simplified I'm a Sage beginner who's trying to apply it to a set of e