One last point, sorry for the barrage of posts. If it is already known that b is an integer then you would not have to
ask, but in some cases when it is not known you get a wrong answer because it does not ask, like below.
(%i1) limit(x^(2*b),x,minf);
Is b positive, negative, or zero?
p;
(out1) minf
Rich
--------------------------------------------------
From: "Richard Hennessy" <rich.hennessy at verizon.net>
Sent: Thursday, January 28, 2010 3:11 PM
To: "Barton Willis" <willisb at unk.edu>
Cc: "Maxima List" <maxima at math.utexas.edu>
Subject: Re: [Maxima] limit code
> Here is one last example.
>
> (%i1) limit(a*x^b,x,minf);
> Is b positive, negative, or zero?
> p;
> (out1) a*(-1)^b*('limit(x^b,x,inf))
> (%i2) ev(%,nouns);
> Is b positive, negative, or zero?
> p;
> (out2) inf*a*(-1)^b
>
> I want to propose that an extra question (or maybe two) be asked when the domain in real. Is b an integer? You could
> be more specific and ask if it is an even or odd integer too but that may be unnecessary.
>
> Here is another bug.
>
> (%i1) limit(x^(2*b),x,minf);
> Is b positive, negative, or zero?
> p;
> (out1) minf
>
> You could ask if b is an integer and if yes then the answer would be inf. So this answer is wrong too.
>
> Rich
>
>
> --------------------------------------------------
> From: "Richard Hennessy" <rich.hennessy at verizon.net>
> Sent: Thursday, January 28, 2010 2:42 PM
> To: "Barton Willis" <willisb at unk.edu>
> Cc: "Maxima List" <maxima at math.utexas.edu>
> Subject: Re: [Maxima] limit code
>
>> Here is one example where the bug manifests itself as an error.
>>
>> (%i1) display2d:false;
>> (out1) false
>> (%i2) limit(a*x^b,x,inf);
>> Is b positive, negative, or zero?
>> z;
>> (out2) 0
>> (%i3) limit(a*x^0,x,inf);
>> (out3) a
>>
>>
>> Here it returns a noun which can be handled better.
>>
>> (%i1) display2d:false;
>> (out1) false
>> (%i2) limit(a*x^b,x,inf);
>> Is b positive, negative, or zero?
>> p;
>> (out2) a*('limit(x^b,x,inf))
>> (%i3) ev(%,nouns);
>> Is b positive, negative, or zero?
>> p;
>> (out3) inf*a
>> (%i4) limit(a*x^b,x,minf);
>> Is b positive, negative, or zero?
>> p;
>> (out4) a*(-1)^b*('limit(x^b,x,inf))
>> (%i5) ev(%,nouns);
>> Is b positive, negative, or zero?
>> p;
>> (out5) inf*a*(-1)^b
>>
>> It should ask if b is an integer. Then if so
>>
>> (%i4) limit(a*x^b,x,inf)
>> Is b an integer?
>> y;
>> Is b positive, negative, or zero?
>> p;
>> Is a positive, negative, or zero?
>> (out4) inf
>>
>> Here is Barton's error.
>>
>> limit(f(a*x),x,inf),
>> f(infinity)
>>
>> I think $infinity is being returned because the sign of a is undetermined so it could be $minf or $inf so someone
>> made it return $infinity which is wrong. $infinity means complex infinity, not "unknown sign but still infinite".
>>
>> Rich
>>
>> --------------------------------------------------
>> From: "Barton Willis" <willisb at unk.edu>
>> Sent: Thursday, January 28, 2010 6:54 AM
>> To: "Maxima List" <maxima at math.utexas.edu>
>> Cc: "Richard Hennessy" <rich.hennessy at verizon.net>
>> Subject: Re: [Maxima] limit code
>>
>>> Better example (independent of limsubst)
>>>
>>> (%i1) limit(a*x,x,inf);
>>> (%o1) infinity
>>>
>>> Barton
>>>
>>> -----maxima-bounces at math.utexas.edu wrote: -----
>>>
>>>
>>>>Maybe Richard is refereeing to the (unreported?) bug:
>>>>
>>>> (%i7) limit(f(a*x),x,inf), limsubst : true;
>>>> 1> (RATLIM ((MTIMES SIMP) $A $X))
>>>> <1 (RATLIM $INFINITY)
>>>> (%o7) f(infinity)
>>>
>>>