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Re: How to declare Integers?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg13464] Re: How to declare Integers?
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Sun, 26 Jul 1998 02:33:29 -0400
*Organization*: University of Western Australia
*References*: <000001bda94e$c10efc90$338e5981@sumba.cs.uwm.edu> <6ocuh1$hd8@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Sean Ross wrote:
> 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.
To indicate how difficult this can be in general, consider the following
sum:
Sum[(j^n y^j)/j!, {j, 0, Infinity}]
If n is an Integer, n >=0, then this sum reduces to
E^y Sum[StirlingS2[n, m] y^m, {m, 0, n}]
Is this the sort of thing you expect to happen automatically? You might
feel that the second form is more complicated than the first -- but it
is actually much more useful.
Another example is, how would you like BesselJ[n+1/2,x] to be
represented?
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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