Re: Re: Cross results?

*To*: mathgroup at smc.vnet.net*Subject*: [mg63230] Re: [mg63205] Re: [mg63201] Cross results?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 20 Dec 2005 04:19:27 -0500 (EST)*References*: <200512181234.HAA24522@smc.vnet.net> <200512191200.HAA10926@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

I now think that a more convincing explanation why 0.* x does not return 0. than the one I gave below (about the unknown size of x and the possibility that it could be infinity) is that in an expression like 0.*x, where x is a symbol, Mathematica can't even be sure the symbol stands for a simple number! For example, x could stand for an interval and then we get things like: 0.*x /. x -> Interval[{-1, 1}] Interval[{-2.2250738585072014*^-308, 2.2250738585072014*^-308}] Andrzej Kozlowski On 19 Dec 2005, at 21:00, Andrzej Kozlowski wrote: > > On 18 Dec 2005, at 21:34, Virgil Stokes wrote: > >> I have the following >> >> x=. >> Cross[{10 Sin[x],-10 Cos[x],2.5},{0.12 Sin[x],-0.12 Cos[x], 0.0}] >> >> which gives, >> >> {0.3 Cos[x], 0.3 Sin[x], 0.Cos[x]Sin[x]} >> >> why does it not set the last term to 0.0? > > It would never make sense to set 0.0 * u to 0.0, where u is a > symbol since there is nothing known about the size of u. In general, > u could be arbitrarily large and in fact it can even be Infinity. Of > course for real x the value of 0. Cos[x]*Sin[x] will be approximately > 0, but by taking x to be a purely imaginary number of huge modulus we > can make Cos[x]*Sin[x] also have arbitrarily large modulus. In fact, > taking x= I Infinity we get: > > > 0. Sin[x]*Cos[x]/.x->I*Infinity > > Indeterminate expression DirectedInfinity, encountered. > > > Indeterminate > > > In any case, as a rule Mathematica never replaces 0.* non numeric > symbolic expression by 0. With numeric symbols the situation is of > course quite different (for the obvious reasons): > > > 0.*Pi > > > 0. > > Andrzej Kozlowski >

**References**:**Re: Cross results?***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>