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Re: How to declare Integers?

Sean Ross wrote:
> Le Van Tri wrote:
> >
> > Dear Joe Oswald and Sean Ross,
> >
> > About your idea of having variable typing instead of pattern matching in
> > Mathematica
> > I think that idea is nice but some what "obsolete" - by which I mean
> > variable typing
> > is obsolete by the coming out of pattern matching. Why ? In traditional
> > languages
> > like Fortran, C++, Lisp, Scheme, ML, ... variable typing was done statically
> > at compile
> > time. By using pattern matching, that could be done dynamically at run time.
> > Which
> > way is better ?
> Perhaps the term variable "typing" is ill-advised since it sounds the
> same as what is done in C++ or Fortran.  No, what we are after is
> something like this:
> Declare[symbol,Integer];
> Sin[symbol Pi x]
> and have it return zero for all x even with no explicit value assigned
> to symbol.
> I want to be able to tell mathematica that a certain symbol is Real,
> Complex, Imaginary, greater than 2, Integer etc. and have every single
> function in the language react appropriately taking that declaration as
> an assumption.  I want Integrals to be appropriate to Real only or
> Integer only arguments etc.  In essence I want global assumptions or
> conditions on symbols with every built-in function looking at those
> restrictions or assumptions and responding appropriately.
> You can't do that yet with pattern matching.

I have a similar problem, but it is less involved with the built in 
mathematica function since it deals with functions I defined in a 
I need to be able to declare proberties of four vectors, (more or less
the same as usual vectors except relativistic). I still haven't decided
on how to declare a given symbol to represent a four vector. I see two 

i) I tag all my symbols, so if k is supposed to be fourvector, I use
everywhere, and can use definitions like

Energy[a_?(FreeQ[#,Fv] b_]:=a Energy[b]  

b) I put all my four vectors in the context Fv` and I would write

Energy[a_ b_?(Context[#]==="Fv`")]:= a Energy[b] 

(This is just an example which in fact does not work since b could be
sum of two four vectors)

Which alternative do you think is better ?


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