Re: Maxima, WolframAlpha, mma

Thierry Mataigne <[email protected]> Fri, 3 Jul 2026 11:51:42 +0200
Newsgroups gmane.comp.mathematics.maxima.general
Message-ID <CAAueMa2b7M0FC47RnYG+ZKY88Ewu3s+MiaT+gzABq0sDQF08tQ@mail.gmail.com>
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This is interesting . Maple (2021) did not find the limit either. However,
Claude AI finds it immediately and explains why it exists and is 0, which
is easy to guess. ChatGPT first says it does not exist, then when I point
out its mistake, gives the correct answer. Both LLMs provide a correct
proof using bounds and the squeeze theorem. Gemini gives a more convoluted
proof  which seems incorrect (it requires that sin(1/x)>0), but ends up
with 0. Unfortunately, CAS tools do not explain how they find their answers
and why they fail to find them. Should they?
Thierry


Le ven. 3 juil. 2026 =C3=A0 09:38, David Scherfgen via Maxima-discuss <
[email protected]> a =C3=A9crit :

> Nice! The result seems to be correct.
> It's nice to see a case where Maxima outperforms the commercial CAS.
> Good job, "Limit Man"!
>
> [image: Limit-Man.jpg]
>
> Am Do., 2. Juli 2026 um 20:49 Uhr schrieb Barton Willis via Maxima-discus=
s
> <[email protected]>:
>
>> Maxima:
>>
>> (%i2) limit((sin(1/x)/2)^(1/x^2),x,0);
>> (%o2) 0
>>
>> WolframAlpha:
>>
>> Limit[(Sin[1/x]/2)^(1/x^2),x -> 0]
>> (insufficient time to determine limit)
>>
>> Mma 14.1:
>>
>> Limit[(Sin[1/x]/2)^(1/x^2), x -> 0]
>> Underscript[\[Limit], x->0]2^(-(1/x^2)) Sin[1/x]^(1/x^2)
>>
>> --Barton
>>
>> *"I=E2=80=99m too busy working on my own grass to notice that yours is g=
reener." *
>>  Unknown
>>
>> *"You wouldn=E2=80=99t worry so much about what others think of you if y=
ou
>> realized how seldom they do." * Eleanor Roosevelt
>> _______________________________________________
>> Maxima-discuss mailing list
>> [email protected]
>> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>>
> _______________________________________________
> Maxima-discuss mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>

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<div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-family:verdana,=
sans-serif;font-size:small">This is interesting . Maple (2021) did not find=
 the limit either. However, Claude AI finds it immediately and explains why=
 it exists and is 0, which is easy to guess. ChatGPT first says it=C2=A0doe=
s not exist, then when I point out its mistake, gives the correct answer. B=
oth LLMs provide a correct proof using bounds and the squeeze theorem. Gemi=
ni gives a more convoluted proof=C2=A0 which seems incorrect (it requires t=
hat sin(1/x)&gt;0), but ends up with 0. Unfortunately, CAS tools do not exp=
lain how they find their answers and why they fail to find them. Should the=
y?</div><div class=3D"gmail_default" style=3D"font-family:verdana,sans-seri=
f;font-size:small">Thierry</div><div class=3D"gmail_default" style=3D"font-=
family:verdana,sans-serif;font-size:small"><br></div></div><br><div class=
=3D"gmail_quote gmail_quote_container"><div dir=3D"ltr" class=3D"gmail_attr=
">Le=C2=A0ven. 3 juil. 2026 =C3=A0=C2=A009:38, David Scherfgen via Maxima-d=
iscuss &lt;<a href=3D"mailto:[email protected]">maxima-d=
[email protected]</a>&gt; a =C3=A9crit=C2=A0:<br></div><blockquo=
te class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px =
solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr">Nice! The result =
seems to be correct.<div><span style=3D"background-color:transparent">It&#3=
9;s nice to see a case where Maxima outperforms the commercial CAS.</span><=
/div><div>Good job, &quot;Limit Man&quot;!</div><div><br></div><div><img sr=
c=3D"cid:ii_mr4iuswf1" alt=3D"Limit-Man.jpg" width=3D"562" height=3D"450"><=
br></div></div><br><div class=3D"gmail_quote"><div dir=3D"ltr" class=3D"gma=
il_attr">Am Do., 2. Juli 2026 um 20:49=C2=A0Uhr schrieb Barton Willis via M=
axima-discuss &lt;<a href=3D"mailto:[email protected]" t=
arget=3D"_blank">[email protected]</a>&gt;:<br></div><bl=
ockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-lef=
t:1px solid rgb(204,204,204);padding-left:1ex"><div>




<div dir=3D"ltr">
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">Ma=
xima:</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
(%i2) limit((sin(1/x)/2)^(1/x^2),x,0);</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">(%=
o2) 0</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)"><b=
r>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
WolframAlpha:</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
Limit[(Sin[1/x]/2)^(1/x^2),x -&gt; 0]</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
(insufficient time to determine limit)</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
Mma 14.1:</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
Limit[(Sin[1/x]/2)^(1/x^2), x -&gt; 0]</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
Underscript[\[Limit], x-&gt;0]2^(-(1/x^2)) Sin[1/x]^(1/x^2)</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
--Barton</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<i>&quot;I=E2=80=99m too busy working on my own grass to notice that yours =
is greener.&quot; </i>=C2=A0Unknown</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style=3D"font-family:Georgia,serif;font-size:12pt;color:rgb(0,0,0)">
<i>&quot;You wouldn=E2=80=99t worry so much about what others think of you =
if you realized how seldom they do.&quot;
</i>=C2=A0Eleanor Roosevelt</div>
</div>

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=3D"noreferrer" target=3D"_blank">https://lists.sourceforge.net/lists/listi=
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</div></blockquote></div>
_______________________________________________<br>
Maxima-discuss mailing list<br>
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nfo/maxima-discuss</a><br>
</blockquote></div>

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