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2021-05-22 15:06:15 +0100 | commented answer | Numerical approximation error involving cosh and sinh That is what I needed. Thanks! |
2021-05-21 15:59:59 +0100 | marked best answer | Numerical approximation error involving cosh and sinh Hi. I'm new to Sage and to computational mathematics in general. I have been trying to code something, but I am struggling to understand some numerical approximation errors. My problem seems to boil down to the following phenomenon: Which is as expected, $x=e^{-12\pi }$ is "very close" to 0. However, I do not understand why Sage gives me If I give it more bits of precision, then it works: But I can't understand why it is making such grotesque error. Sage knows $x$ is very small (it returned 0.000000000000000). So why did it approximate $5+x$ to 4? What is also weird, is that if I repeat the same computation with 4+x or 6+x instead, then it works just fine: My apologies if this is something trivial in computational maths, but can someone clarify what is going on here? In a situation like this, is there a way for me to know if I have given Sage enough bits of precision to get at least the first few digits correct? (Remark: I wrote |
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2021-05-21 15:59:49 +0100 | commented answer | Numerical approximation error involving cosh and sinh Now, with this in mind, I think I could code some kind of precision handling into many parts of my code. But I wonder, d |
2021-05-21 15:48:18 +0100 | commented answer | Numerical approximation error involving cosh and sinh Thanks you so much!! This answer was incredibly helpful. So, it was not a bug!! Though, is there a way for me to know if |
2021-05-20 18:58:02 +0100 | commented question | Numerical approximation error involving cosh and sinh So this is a bug? I was trying to do some computations with modular forms, but was getting some weird errors when evalua |
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2021-05-20 17:03:49 +0100 | asked a question | Numerical approximation error involving cosh and sinh Numerical approximation - Newbie question Hi. I'm new to SAGE and to computational mathematics in general. I have been t |