Re: Re: Product

*To*: mathgroup at smc.vnet.net*Subject*: [mg87639] Re: [mg87592] Re: Product*From*: "Szabolcs HorvÃt" <szhorvat at gmail.com>*Date*: Tue, 15 Apr 2008 05:47:00 -0400 (EDT)*References*: <200804110542.BAA04653@smc.vnet.net>

On Mon, Apr 14, 2008 at 3:13 PM, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > > > But of course in principle there is nothing that would make it > > impossible to introduce a special case for functions like Times and > > Plus, and make them work with packed arrays. So this alone does not > > make it necessary to introduce a new syntax/new function, like Total[]. > > > > Well, I never claimed that it did. I didn't mean that you did :-) > It seems to me that WRI wanted to add > new functionality to Mathematica and modifying Plus would break too many > things. For example, Total, in version 6 accepts level specifications, so: > > Total[{{a, b}, {c, d}}, {2}] > {a + b, c + d} > > while > > Apply[Plus, {{a, b}, {c, d}}, {2}] > {{a, b}, {c, d}} > > The key thing, in my opinion, is that Total[list] is just a spacial case of > Total (=Total[list,1]) and the general case of Total would be quite hard or > impossible to define using Apply and Plus. > Actually one just needs to shift the level specification by 1, so Total[{{a, b}, {c, d}}, {2}] is equivalent to Apply[Plus, {{a, b}, {c, d}}, {1}] Generally, Total[expression, {n}] is equivalent to Apply[Plus, expression, {n-1}] and Total[expression, n] is equivalent to Apply[Plus, expression, {0, n-1}] Szabolcs HorvÃ¡t

**References**:**Product***From:*"Steven" <steven_504@telenet.be>