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Norm bound when finding an integer relation via FindIntegerNullVector

When using FindIntegerNullVector in WolframAlpha online to get an integer relation $a=(a_1,\ldots,a_n)$ between numbers $x_i$, an optional parameter $d$ can be given in order to get a vector $a$ of norm not greater than $d$, if it exists.

I'm not sure if I understand correctly how this works, something odd is happening: for some numbers $x_i$ with $n=4$ I get the solution $a=(1,1,1,-1)$, which has norm $\|a\|=\sqrt{4}=2$ (the norm is the $2$-norm). Now I search with $d<2$, but I keep getting the same solution of norm $2$ for some values of $d$ (e.g. $\sqrt{3}$, $5/3$, $1.68$). You can see it for example in

https://www.wolframalpha.com/input/?source=nav&i=FindIntegerNullVector%5B%7B-24,15,10,1%7D,sqrt%7B3%7D%5D

Am I doing something wrong, or is this a bug?

POSTED BY: Jose Brox
2 Replies

None of the above, really. Mathematica gives a warning message with that result. W|A appears to be suppressing it. Might be a smallish bug, depending on one's view of such things.

To see the message, try the computation using the Wolfram Cloud:

https://www.wolframcloud.com/

POSTED BY: Daniel Lichtblau

Thank you for your answer. Can you please copy the warning message here? I have no access to Mathematica.

POSTED BY: Jose Brox
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