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2020-12-20 04:41:09 +0200 | answered a question | Assumption seems to break integrate(); is this a bug? The issue seems to have been fixed in more recent versions of Sage! Based on my experience, it seemed to be a problem in versions 8.6 and 8.9, but not in 9.2. Since upgrading to 9.2 I can no longer reproduce this issue. If you are experiencing a similar issue, I would recommend upgrading to a current version if possible. (If that is not possible, a couple of work-arounds are suggested in the Question.) Also, if you are using Sage online through CoCalc it may give you an option to upgrade to a current version. You can check what version you are running, by opening a notebook and executing a
command. Thank you very much to the Sage Development Team! |

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2020-07-12 01:48:31 +0200 | asked a question | Assumption seems to break integrate(); is this a bug? Consider the following Sage code (tested using Sage 8.6): Output (as expected): Next: Output (again, no problem): Now suppose we give Sage a little more information. The following assumptions should guarantee that we're integrating over a real interval, and that the second (or "top") endpoint is strictly greater than the first ("bottom") endpoint. (Though as we have seen, Sage does not really need this information.) So,
Personally, I found it surprising: I expected that, if a command worked with no assumptions, then it should still work after adding assumptions (consistent assumptions that only narrow the scope of the problem).
I also get a similar kind of problem if I do the following: It seems to me that $1 < a < 3$ implies $0 < a < 4$, which implies that $-a^2 + 4a > 0$. (The graph of the quadratic is a downward-opening parabola, with roots at $0$ and $4$.) I am not surprised that Sage has trouble constructing this argument, so I am not surprised that the So, I speculate that maybe the In our case, I think Sage assumes by default that By the way, the following works just fine: Or, this also works: Asked also at Math Stackexchange, but did not receive an answer there. Apologies if this kind of cross-posting is frowned upon. |

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