[Maxima] Complicated objects in Maxima
fateman at eecs.berkeley.edu
Fri May 18 09:43:52 CDT 2012
On 5/18/2012 6:53 AM, Steve Haflich wrote:
> When code asks a question about
> a node, the answer becomes class based.
> Under such a regimen, an operation that simplifies an expression that is
> the addition of two subexpressions would become a generic operation that
> uses the classes of its argument subexpression, and what is known about
> itself as represented by its own class.
I think this is similar to the representation in Maple, at least in the
data structuring direction,
though probably not in the method dispatch.
That is, in Maple, there are structures like
"power" with 2 more slots, so that x^y would be [power_tag,x,y].
a+b+c would be [plus_tag,3,a,b,c] where the 3 is an argument count.
There is, I guess, a tag for f(x,y) like
Years ago the count tag space was 16 bits, leading to problems for sums
of more than 2^16 terms.
It has been enlarged.
Nevertheless the use of lists is hardly inevitable. Also, instead of
storing the "head" of the expression
plus, times, sin, cos,log.... explicitly as a lisp atom in the
expression, it could be stored somewhere
implicitly. This would mean in maxima lisp terms, computing (type_of
E) instead of (caar E).
and having (simplify ....) be a method associated with E, rather than
essentially (apply (get (caar E) 'op) E).
An issue that messes up this situation is that the identification of the
appropriate method in maxima is
often dependent on information that is not in the heads or types of the
arguments. For example,
the setting of relevant flags. A simple method might need to look at
flags like numer, expop, radsimp, etc.
The point here is that the "right thing to do" does not just fall out in
the wash because you are using
object-oriented programming. OO could have some benefit in an overall
organizational sense; (at least I hope
it would), and it probably would not make the program much slower. It
might make some data structures
larger, and others smaller.
People have implemented systems along these lines, more or less. e.g.
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