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#541 rat/factor exponents are fixnums (doc)
It does not seem to be documented anywhere that the
exponents in a CRE expression are fixnums. For example,
rat(x^(2^31)) => x. This also affects functions which
use Rat internally, e.g. factor, ratsubst....
This is not a bug, but it is an important documentation
lacuna.
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Hmm, with Maxima 5.9.1 (cvs circa 200410) I see
rat(x^(2^31));
=> Exponent out of range
so it appears something has changed in the not-too-distant past.
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a) I can reproduce this in the current Windows GCL version
Maxima version: 5.9.1
Maxima build date: 7:34 9/24/2004
host type: i686-pc-mingw32
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL 2.6.5
b) In Dodier's configuration, "Exponent out of range"
presumably indicates that the exponent could not be
converted to a fixnum. It is a *good thing* that an error
message was generated in this case (rather than silently
giving an incorrect response), though the message should be
more user-friendly. But in any case, the exponents are
still restricted to fixnums.
c) For another dramatic failure due to this issue, try
rat((x^2^30+1)*(x^2^30)) => 1/x^2147483648+x^1073741824
d) Given current processor speeds, I recommend that we
convert exponents to general numbers. At the very least, we
should be giving overflow errors and not blindly generating
garbage.
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Could this be a gcl problem? I also get "Exponent out of
range" when using cmucl.