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 ____________________________________________________________________