On 9/2/07, Nikos Apostolakis <[EMAIL PROTECTED]> wrote:
> > I'm interested in changing SAGE to use tlimswitch:true by default.
> > However, before I do that, I would like to know why Maxima sets
> > tlimswitch to false by default?  Does tlimswitch:true give incorrect
> > results in lots of interesting cases?  Or is it slower?   Or is it just 
> > inertia
> > that causes maxima to not have tlimswitch:true by default?
> >
>
> I asked in the maxima list and it seems that it's inertia, "the weight
> of history" as Rober Dodier put it.  They are considering to set
> this switch to true by default.
>

Excellent.  I want to change the sage-2.8.4 so it uses the tlimit command
to compute limits by default (that's the easiest thing to do)....

... OK, I tried this, then ran SAGE's extensive tests, and it turns
out the following limit computation fails, whereas with the normal
limit
command it worked fine:

(%i4) tlimit((5^x + 3^x)^(1/x), x, inf);

** - Continuable Error
two equal vars generated
If you continue (by typing 'continue'): Return from COMMON-LISP:BREAK loop
The following restarts are also available:
MACSYMA-QUIT   :R1      Maxima top-level
Break 1 [1]>

You might want to post this to the Maxima list.

See, using the normal limit command it works fine:
(%i1) limit((5^x + 3^x)^(1/x), x, inf);
(%o1)                                  5

----

It's weird seeing "MACSYMA" above in that error -- that was the name
of the commercial version of Maxima from the '80s.

For now, I'll change the SAGE limit command so it can be used as follows,
i.e., to have a taylor=True option:

sage: limit((tan(sin(x)) - sin(tan(x)))/x^7, x=0, taylor=True)
1/30

Anyway, this will be in sage-2.8.4.

 -- William

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