Re: what's it worth to write a short program for polynomial multiplication?

On Jun 2, 1:04 pm, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:
.... snip

Alas, it is unlikely that the superfast subimbecile of
a computer will be able to do this at run time; even at
compile time, it is likely that the user will have to
tell the compiler what is provided and what is wanted.

a computer algebra system could run a program "what is a good
algorithm for "*"" at runtime.
in some sense, common lisp already does this for numeric types, and
with CLOS it can do it for polynomials etc.

Sparse polynomials and dense polynomials should be
handled differently, and it is usually the user who can
provide information on what is sparse and what is dense.

Perhaps the user could, but rarely is the user willing. Often the user
is not even available.


There is, I think, substantial evidence that the notion of object-
oriented choice of operator based on one operand, and in the typical
shallow way offered by most OO programming languages, is rather weak
for helping in determining the proper algorithm.

Why should not the object-oriented choice of operator use
the types of all the operands?

Good question. Most OO programming languages work that way. CLOS, the
Common Lisp Object System
is the one exception I am aware of, but perhaps there are more.

..... snip

This was the motivation for several programs of study in computer
algebra systems, and resulted in several system designs, including
most notably, Axiom/ Aldor.
I have observed that mathematicians, as well as physicists, may not be
as good as they think they are in designing computer programming
languages.

Has there been a real effort on this?

I think so.

Getting input from
all on what is wanted, and then trying to do as well as
one can.

You are welcome to try, again.

... snip..

Again, has anyone tried to produce an assembler which can
handle weakly typed arguments with type overrides?

Apparently you have, but I do not know of anyone promoting assembler
except as the target language for higher level languages.

I
tried it on two machines, the CYBER 205 and the VAX 780,
and came up with rather simple procedures. These ideas
will also work on the POWER machines and related one.

What I did was to look at the machine instructions from
a mathematical point of view and construct a simple grammar
from the lot. Seymour Cray's assembler languages are not
bad, but he did not try overloading.

Grammars for "machine architecture" have been explored, primarily to
make the instruction generation component of compilers more table- or
grammar- driven. I think work by Glanville..
http://portal.acm.org/citation.cfm?id=512785&dl=ACM&coll=portal

RJF
.

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