Re: Inner product can be modified?

*To*: mathgroup at smc.vnet.net*Subject*: [mg21464] Re: [mg21445] Inner product can be modified?*From*: Ken Levasseur <Kenneth_Levasseur at uml.edu>*Date*: Tue, 11 Jan 2000 04:17:45 -0500 (EST)*Organization*: UMass Lowell Mathematical Sciences*References*: <200001100856.DAA21012@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Denis: In developing a series of abstract algebra packages (AbstractAlgebra - http://www.central.edu/homepages/hibbarda/EAAM/eaam.html). I found Inner quite useful. For example, if X={X1, X2, ...,Xn} is a list of sets, the test to determine whether a={a1,a2,...,an} is in the cartesian product of the sets is Inner[MemberQ[#1,#2]&,X,a,And] Here's a specific example: In[1]:= X = Map[Range[1, #] &, Range[2, 5]] Out[1]= {{1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}} In[2]:= randompoint := Table[Random[Integer, {1, 5}], {4}] candidates = Table[randompoint, {10}] Out[3]= {{5, 4, 4, 2}, {5, 4, 5, 2}, {2, 3, 1, 2}, {3, 5, 1, 4}, {3, 4, 5, 5}, {2, 2, 1, 3}, {2, 1, 1, 3}, {5, 3, 2, 3}, {1, 2, 1, 4}, {4, 1, 3, 1}} In[4]:= Select[candidates, Inner[MemberQ[#1, #2] &, X, #, And] &] Out[4]= {{2, 3, 1, 2}, {2, 2, 1, 3}, {2, 1, 1, 3}, {1, 2, 1, 4}} A similar function, to determine whether an n-tuple, a, is a unit in the direct product of rings would be Inner[UnitQ[#1,#2]&,X,a,And], where X would be {R1,R2,...,Rn} and each Ri is what we call a Ringoid. Ken Levasseur Math. Sciences UMass Lowell Denis Cousineau wrote: > > Hi, > > I've seen in the documentation that the command > Inner[] > can be modified so that it is not necessarily the > sum (Plus) that is executed on the elements. > > Is is done frequently in mathematics? I discover that > I needed to do that in my own application, but though > I was doing a crazy thing, so if other did, I would > like to know. > > What kind of application requires a different aggregate > operation than Plus? > Is is well-known? > Do you have an easy-to-access reference where this > is done? > > Thank you for your help. > Denis > > P.S. mail and post reply appreciated. > -- > > Denis Cousineau, Postdoc ***************************** > Cognitive psychology * * > Indiana University * Etudiant devant l'eternel * > Psychology Building * * > Bloomington, 47405 ***************************** > > Office: (812) 856-5217 Fax: (812) 855-1086 > E-mail: decousin at indiana.edu http://Prelude.PSY.UMontreal.CA/~cousined