Re: re-inventing the wheel... scope of assumptions.



Daniel Lichtblau wrote:
.... description of macsyma, then mathematica handling of assumptions
....
That seems to cover a good deal of the syntax and scope rules of
what might be plausible for assumptions, although why certain commands
like Simplify have extra arguments looks like a relic of a time when
Assumptions were not properly integrated into Mathematica.
Why not Assuming[.... , Simplify[...]]
instead of Simplify[..., Assumptions -> ...].

The details of what calculations are actually done with assumptions
are probably unstated and may vary from time to time, e.g. to what
extent are non-linear inequalities handled? Can one say Assume H is a Hilbert Space ?

I indicated in my earlier note that assumptions HAVE been added relatively recently to the post-1980 CAS. But designing them
in from the beginning might have resulted in a nicer system.

Are all issues now handled correctly? I doubt it. Is Macsyma's
design from 1978 or so superior to the more recent ad-hoc additions
to CAS? Not necessarily. Are the implementation details in Macsyma
(or Maxima) superior to those in other CAS? Probably not -- the details
are all pretty much undescribed in any case. But Macsyma has a good
excuse for not doing a great job on this topic: the design for the
simplifier was pretty much set up by 1968, running in an environment
that had the computing power of a cell phone.




I don't know if this addresses all possible issues of points of
similarity or difference between current Mathematica assumptions usage
and that of Maxima.

One large set of issues is how good the assumption mechanism is in
actual use. Can collections of them be simplified, as one issue.

For example, both Macsyma and Mathematica
know that if n is an integer, then abs(sin((2*n+1)*pi/2)) is 1.
But given assumptions a<=0 && a>=0, it seems that Mathematica does
not know if a==0. Macsyma does, at least if asked is(a=0);


I think it gives some idea, though. I'll get off
your feet now.

thanks.
RJF

.

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