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MathGroup Archive 2000

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Re: making a function linear

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25491] Re: [mg25473] making a function linear
  • From: Ken Levasseur <Kenneth_Levasseur at uml.edu>
  • Date: Thu, 5 Oct 2000 23:50:12 -0400 (EDT)
  • Organization: UMass Lowell
  • References: <200010030226.WAA06503@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Murray:

The only approach I can think of uses Hold.   I understand what you mean
about tring to avoid using some variation of Hold, but in a way that
mirrors some of the problems I've had teaching students linear algebra. 
The impulse is to look at cx+y as a single vector to be mapped by T. 
You want them to look at it as a pattern or form;  so maybe Hold is
really natural.

Ken Levasseur
UMass Lowell  

Murray Eisenberg wrote:
> 
> For a function T not yet having any "definition by formula" (T[x_] :=
> ..... ), I want to specify the linearity rules:
> 
>   T[x_?VectorQ + y_?VectorQ] := T[x] + T[y]
> 
>   T[c_ x_?VectorQ] := c T[x]
> 
> Then, merely by specifying, say,
> 
>   a = {1, 2}; T[a] = {3, 4};
>   b = {5, 6}; T[b] = {7, 8};
> 
> evaluating
> 
>   T[2 a]
>   T[a + b]
> 
> would return results:
> 
>   {6, 8}
>   {10, 12}
> 
> The trouble is, of course, that Mathematica first evaluates 2 a and a +
> b when a and b have actual numeric values, so the two linearity rules
> never get used.
> 
> What is a SIMPLE way (if there is one) to accomplish this -- preferably
> some way to do it that does not explicitly require using some Hold
> variant?  (I need to be able to explain how to do it early in a linear
> algebra course where Mathematica is being introduced, and Hold, etc., I
> consider a definitely advanced topic.)
> 
> --
> Murray Eisenberg                     murray at math.umass.edu
> Mathematics & Statistics Dept.       phone 413 549-1020 (H)
> Univ. of Massachusetts                     413 545-2859 (W)
> Amherst, MA 01003-4515


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