#1051 bug in limit, asks sign of IND, encountered in integrator

[Anonymous]

quoted from the mailing list:

On 12/11/06, Daniel Lakeland <dlakelan@street-artists.org> wrote:
>integrate(abs(sin(x)/x),x,0,inf) asks the seemingly stupid question:
>Is ind positive, negative, or zero?
>
>the user has absolutely no idea what maxima is asking... I'm going to
>assume that it has something to do with a change of variable deep
>within the integrator... but it's completely opaque to me.

This is definitely a bug, and should be reported. Integrate is
calling limit, and the bug is actually in the limit routine:

limit( abs(sin(x))/x , x , inf) => asks sign of ind

IND is supposed to be used by Limit as a return value meaning that the
limit set is bounded, e.g. limit(sin(x),x,inf) => ind, but obviously
here it's gotten its wires crossed.

I suggest you write up the limit bug with a note that definite
integration encounters it.

[Dan Gildea]

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Fixed in limit.lisp rev 1.40.

(%i3) limit( abs(sin(x))/x , x , inf) ;
(%o3) ind

[Raymond Toy]

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Why is limit(abs(sin(x))/x, x, inf) ind? Shouldn't it be zero? abs(sin(x))/x is surely bounded between 0 and 1/x.

Am I missing something?

Reopening.

[Dan Gildea]

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oops, sorry.
in limit.lisp rev 1.41:

limit(abs(sin(x))/x, x, inf) => 0

however:
limit(abs(sin(x))/sin(x), x, inf) => 1
still not correct