_SAGE_VAR_minus and Maxima limit direction

[Jan Marucha]

`integrate()' function on non-elementary integrals outputs sometimes a limit function, ie:

In: k = var("m", domain='positive', latex_name=r"\hat k" );

In: N_nr = integrate(k^2/(exp(k)+1), (k, 0, oo))

Out: `limit(1/3*k^3 - k^2*log(e^k + 1) - 2*k*dilog(-e^k) + 2*polylog(3, -e^k), k, +Infinity, minus) + 3/2*zeta(3)`

Analytically, the part under the limit is equal to 0 (compare to mathematica's  N_nr = Integrate[k^2/(Exp[k] + 1), {k, 0, Infinity}]

On simplify, the engine tries to evaluate the limit using maxima and fails

In: N_nr.simplify()

Out: TypeError: ECL says: Error executing code in Maxima: limit: direction must be either 'plus' or 'minus'; found: _SAGE_VAR_minus

Something seems to be off from putting this sage expression to maxima.

Version: Sage 9.3
OS: Windows 10 Pro, 21H2, x64

[Nils Bruin]

That's a fairly straightforward thing to fix: it just means that the sage-to-maxima interface needs to learn how to translate "plus" and "minus" in limit expressions.

The easiest way would be to tell the interface that "plus" and "minus" are symbols that need a hardcoded translation. A more subtle version would put a special translation in place for a symbolic "limit" to treat the direction argument separately.

Perhaps a slightly cleaner way of triggering the error:

function('f')

limit(f(x),x=0,dir="-").simplify()

Someone should file a bug report.

[kcrisman]

https://trac.sagemath.org/ticket/33692