Re: Re: Product
- To: mathgroup at smc.vnet.net
- Subject: [mg87664] Re: [mg87592] Re: Product
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Tue, 15 Apr 2008 05:51:48 -0400 (EDT)
- References: <200804110542.BAA04653@smc.vnet.net> <200804121059.GAA00044@smc.vnet.net> <ftsd2p$bca$1@smc.vnet.net> <200804140941.FAA07966@smc.vnet.net> <234CB1EF-7890-4173-94F9-8998DFC54BED@mimuw.edu.pl> <f831b3d60804140842o15ca844dpaa3832a8a2b55de9@mail.gmail.com>
On 15 Apr 2008, at 00:42, Szabolcs Horv=E1t wrote: > 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 Horv=E1t Yes, you are right, of course. (I gues I should stop posting replies whose conents consist of the first thing that comes to my mind, but I usually do not have the time for much more). Level specifications are certianly not the reason for having Total (though I find them a bit more convenient to use - which is what made me make that silly claim). I guess the reason was just the feeling that the syntax of Apply and Plus was just a bit too convoluted. Andrzej
- References:
- Product
- From: "Steven" <steven_504@telenet.be>
- RE: Product
- From: "Jose Luis Gomez" <jose.luis.gomez@itesm.mx>
- Re: Product
- From: Szabolcs Horvát <szhorvat@gmail.com>
- Product