Every once in awhile, we talk about making Maxima "infinity correct."
Among other things, an infinity correct Maxima would do inf - inf -->
und. I think Raymond even once started an infinity correct Maxima
branch. My guess is that infinity correct multiplication and
exponentiation operators would break quite a few limit calculations.
I think I've pointed things like the following before--one more time:
Try tracing simplus and evaluate:
integrate(1/(x^2*sqrt(x^2-a^2)),x,a,inf);
Maxima calls simplus 634 times; in the list of calls to simplus,
you'll see
1> (SIMPLUS ((MPLUS) $INF ((MTIMES SIMP) -1 $INF)) 1 T)
<1 (SIMPLUS 0)
Yikes! You'll also see the same sums done a dozen or more times in a
row.
I have an *experimental* simplus function that tries to be infinity
correct. Richard Fateman wrote parts of this code, but the infinity
correctness is due to me. This code also uses sorting to speed up
lengthy sums with many distinct terms; for short sums, the
alternative simplus function is slower (in the test suite, about 98.7%
of the summands have fewer than eight terms).
If it's OK with everybody, I'll place this code in a new folder, say
/share/contrib/altsimp. Last I checked, this code makes it through the
test suite with three errors. Maybe this code would be a distraction;
maybe it would be helpful. Algorithmically, simplus is pretty simple.
Barton
And by the way, with my infinity correct addition, Maxima calls
simplus 642 times to evaluate integrate(1/(x^2*sqrt(x^2-a^2)),x,a,inf).
It still gets the correct value. Because my code is not infinity
correct for multiplication, some things don't work:
(%i5) inf - inf;
(%o5) inf-inf
Some things do:
(%i6) inf + minf;
(%o6) und
With an infinity correct multiplication, the test suite might
report many errors.