(1) -> f:=differentiate(complexNormalize(log(tan(%pi/2*tanh(x)))),x);
Type:
Expression(Integer)
(2) -> output lines(formatExpression(f)$Format1D).1
(-8*%pi*(%e^x)^2*%e^((%pi*sqrt(-1)*(%e^x)^2+(-%pi)*sqrt(-1))/((%e^x)^2+1)))/(
(sqrt(-1)*(%e^x)^4+2*sqrt(-1)*(%e^x)^2+sqrt(-1))*(%e^((%pi*sqrt(-1)*(%e^x)^2+
(-%pi)*sqrt(-1))/((%e^x)^2+1)))^2+(-sqrt(-1))*(%e^x)^4+-2*sqrt(-1)*(%e^x)^2-s
qrt(-1))
Type:
Void
(3) -> limit(f,x=%plusInfinity)
(3) 2
Type:
Union(OrderedCompletion(Expression(Integer)),...)
On Wed, 23 Nov 2022 at 12:48, Waldek Hebisch <[email protected]>
wrote:
> On Wed, Nov 23, 2022 at 05:21:42PM +0800, Qian Yun wrote:
> > FYI, it can be correctly solved by "mrv_limit" which uses Gruntz
> > algorithm. However I don't know why this code path is not enabled
> > for this function. (see "is_exp_log" in limitps.spad).
> >
> > - Qian
> >
> > (1) -> )expose MrvLimitPackage
> > MrvLimitPackage is now explicitly exposed in frame frame1
> > (1) -> f := D(log(tan(%pi/2*tanh(x))), x);
> >
> > Type:
> > Expression(Integer)
> > (2) -> mrv_limit(f, x=%plusInfinity)
> >
> > (2) 2
>
> This is due to 'tan'. Termination of Gruntz algorithm depends
> on having exp-log function, for trigonometric functions
> Gruntz may fail. This is easy case, but ATM we have no way
> to distinguish it from problematic cases.
>
> --
> Waldek Hebisch
>
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