Well, it’s a bit more intricate than I thought initially :
sage: reset() sage: k = var("k") sage: Ex = (1 + (-1)^k)*x^k sage: sum(Ex,
k, 0, oo) sum(((-1)^k + 1)*x^k, k, 0, +Infinity)
Sage (i. e. Maxima) can’t solve it.
sage: sum(Ex, k, 0, oo, algorithm="giac") 1/(x + 1) - 1/(x - 1)
Giac does
sage: sum(Ex, k, 0, oo)._sympy_().doit() Piecewise((1/(1 - x), Abs(x) < 1),
(Sum(x**k, (k, 0, oo)), True)) + Piecewise((1/(x + 1), Abs(x) < 1),
(Sum((-1)**k*x**k, (k, 0, oo)), True))
Sympy does, gives an important precision (radius of convergence), but this
answer can’t (yet) be (automatically) translated to Sage
sage: Ex._mathematica_().Sum(mathematica([k, 0, oo])) {(1 + (-1)^k)*k*x^k,
0, (1 + (-1)^k)*x^k*Infinity}
Applying the Sum (Mathematica) method to the Ex object (automatically
translated to Mathematica) gives a nonsensical answer
sage: mathematica.Sum(*map(mathematica, (Ex, [k, 0, oo]))) {(1 +
(-1)^k)*k*x^k, 0, (1 + (-1)^k)*x^k*Infinity}
Ditto when calling the mathematica.Sum function to the (manually
translated) arguments.
sage: mathematica("Sum[%s, %s]"%tuple(map(lambda u:repr(mathematica(u)),
(Ex, [k, 0, oo])))) -2/(-1 + x^2)
But passing to the interpreter a (manually built) string representting the
function call works.
Not obvious to report…
Le dimanche 9 juillet 2023 à 23:45:59 UTC+2, Jan Groenewald a écrit :
> Debian 12, Sage 9.5 (debian package), Mathematica 13.3
>
> sage: mathematica("Sum[%s, %s]"%tuple(map(lambda u:repr(mathematica(u)),
> ((1+(-1
> ....: )^k)*x^k, [k , 0, oo]))))
> -2/(-1 + x^2)
>
> sage: mathematica.Sum(*map(mathematica, ((1+(-1)^k)*x^k, [k , 0, oo])))
> {(1 + (-1)^k)*k*x^k, 0, (1 + (-1)^k)*x^k*Infinity}
>
> On Sun, 9 Jul 2023 at 23:01, Emmanuel Charpentier <[email protected]>
> wrote:
>
>> Inspiration : this ask.sagemath.org question
>> <https://ask.sagemath.org/question/69855/compute-power-series/>.
>>
>> Using the Wolfram engine <https://www.wolfram.com/engine/> gives me a
>> curious and nonsensical conversion. Compare :
>> sage: mathematica("Sum[%s, %s]"%tuple(map(lambda u:repr(mathematica(u)),
>> ((1+(-1)^k)*x^k, [k , 0, oo])))) -2/(-1 + x^2) # Correct sage:
>> mathematica.Sum(*map(mathematica, ((1+(-1)^k)*x^k, [k , 0, oo]))) {(1 +
>> (-1)^k)*k*x^k, 0, (1 + (-1)^k)*x^k*Infinity} # Nonsensical
>>
>> I *think* that this signs a bug in the Mathematica conversion of sum.
>> Can someone check me with the “full blown” Mathematica interpreter before I
>> open an new issue ?
>>
>> Thanks in advance…
>>
>>
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