do you want modular numbers to carry their modulus along
with them? (there are argument pro and con)
Tagging floats (in addition to the tag they already have
in CL) is going to cost in time and space. And when you
compute with LAPACK and its successors, there will be
a need to copy in and out..
These are considerations. Again, I'd recommend looking
at the recent Maple design before spending lots of time
on this.
RJF
Stavros Macrakis wrote:
>>I'd put my vote in for "do it once, do it right."...
>>are we going to use CLOS objects and introduce object
>>oriented programming to Maxima?
>>
>>
>
>What I have in mind is more modest than restructuring Maxima. It is
>just restructuring generalized numbers. Generalized numbers are things
>you can do arithmetic on but generally treat as atomic in symbolic
>expressions. Arithmetic on them should be efficient in time and space
>(though you can't require bounded size: consider bignums and rationals).
>Integers, floats, rationals, float complexes, integer complexes
>(Gaussian integers), bigfloats and the like are generalized numbers. So
>are real and complex intervals (of various flavors), IEEE floats (which
>include various kinds of infinity etc.), various other kinds of infinity
>and infinitesimal, modular integers, modular reals (clock arithmetic),
>fuzzy sets of different kinds, numeric differentials, etc. Maybe also
>non-scalars like numeric-entry matrices of various types, etc.
>
>I am intentionally *not* proposing that these all be unified with
>symbolic calculation in a grand universal-algebra object-oriented
>framework. That is an interesting, but vaster and more difficult,
>project.
>
>Different kinds of generalized number have different properties. For
>example, trichotomy fails for complexes and intervals, transitivity
>fails for modular numbers, various arithmetic identities fail for
>infinities and NaNs (inf-inf is not 0, etc.), etc.
>
>I believe it would be fairly straightforward and not too time-consuming
>to add at least scalar generalized numbers. I would do this by having a
>single CAAR covering all of them, e.g. gennum, with all additional
>information in the cdar and the cdr. I could identify all places where
>gennum needs to be handled by looking for all places which handle
>bigfloats (in fact, the bigfloat caar would be replaced by gennum). The
>hard part is generalizing the logic so that gennums where assumptions
>fail (x=x, x-x=0, etc.) are handled correctly.
>
>The gennum package would be object-oriented. I don't know if it's best
>to implement it in a traditional Lisp way or to use CLOS. If CLOS, I'd
>want to keep to a fairly simple subset....
>
> -s
>
>
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