Re: Problem overriding simple built-in functions[2]

*To*: mathgroup at smc.vnet.net*Subject*: [mg28861] Re: Problem overriding simple built-in functions[2]*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Wed, 16 May 2001 03:28:09 -0400 (EDT)*References*: <9dld4j$o9b@smc.vnet.net> <9dqdrf$4jr@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Apologies for the misposting of the following addendum (it went to Subject: Re: column * row ??(2)). I should have added the following alternative way of dealing with the problem arising from the attribute Flat noted at the end of my previous posting on this topic [copied below]. ClearAttributes[GCD, {Listable, Protected}] SetAttributes[GCD,{OneIdentity}] GCD[x_List]:= GCD@@x GCD[{3,6}] 3 Protect[GCD -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Allan Hayes" <hay at haystack.demon.co.uk> wrote in message news:9dqdrf$4jr at smc.vnet.net... > One way out of this difficulty is to define > > MyGCD[x___]:= GCD@@Flatten[{x}] > > This gives > > MyGCD[{3,6}] > > 3 > > Another possibility is suggested at the end of the following discussion. > > > Here is what seems to be happening with the examples that you give. > > In Mathematica 4.1 we have > > atts=Attributes[GCD] > > {Flat,Listable,Orderless,Protected} > > [though in Help Browser, Listable is not mentioned] > > After > > Unprotect[GCD]; > GCD[x_List]:=GCD@@x > > I get, as you report, > > GCD[{3,6}] > > {3,6} > > The explanation is that the attribute Listable is used before any rules for > GCD are looked for. > So the main steps in the evaluation are > > GCD[{3,6}] > {GCD[3],GCD[6]} because of the attribute Listable > {3,6} > > That new assignment was never used. > > With regard to > > Apply[GCD,{3,6}] > > 3 > > The mains steps are > > Apply[GCD,{3,6}] > GCD[3,6] > 3 > > > HOWEVER: it is not sufficient to clear the attribute, Listable: > > ClearAttributes[GCD, Listable]; > > We still get > > GCD[{3,6}] > > GCD[{3,6}] > > This is due to the attribute Flat: > > Starting with GCD[{3,6}] a peculiarity of the attribute Flat is that > x_ in GCD[x_List]:=GCD@@x is matched to a held GCD[{3,6}] in the > expression > GCD[GCD[{3,6}]] which evaluates to GCD[{3,6}] without further evaluation > > But we can do something about this: > > Clear the old definition: > > GCD[x_List]:=. > > Use instead > > GCD[{x___}] := GCD[x] > > Now we get > > GCD[{3,6}] > > 3 > > > -- > Allan > --------------------- > Allan Hayes > Mathematica Training and Consulting > Leicester UK > www.haystack.demon.co.uk > hay at haystack.demon.co.uk > Voice: +44 (0)116 271 4198 > Fax: +44 (0)870 164 0565 > > "Jean-Christophe Deschamps" <jchd at worldnet.fr> wrote in message > news:9dld4j$o9b at smc.vnet.net... > > Hi, > > > > I'm told the following occurs under Mathematica v4.0: > > > > In[1]:= GCD[{3, 6}] > > Out[1]= {3, 6} > > In[2]:= GCD[x_List] := Apply[GCD, x] > > In[3]:= GCD[{3, 6}] > > Out[3]= GCD[{3, 6}] > > In[4]:= Apply[GCD, {3, 6}] > > Out[4]= 3 > > > > Why is it so? It looks like the override is ignored, but why? > > > > The same exerpt seems to work fine under version 2.x. > > > > > > > > > > > > >