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Re: Defining N for a new entity

• To: mathgroup at smc.vnet.net
• Subject: [mg66740] Re: [mg66719] Defining N for a new entity
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Sun, 28 May 2006 06:08:23 -0400 (EDT)
• References: <200605280103.VAA23345@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Giuseppe Bilotta wrote:
> Hello,
>
> I'm try to build a Mathematica toolbox to work with Stolfi's affine
> expression. Until now, I've had no problems: I use AffineExpression[c,
> {{i, xi}, ...}] (where c and xi are Reals and the i are Integers) to
> represent c + \sum xi e_i and I can define addition, multiplication,
> quotient and everything else without any problems.
>
> Recently, I've begun using these entities in more complex expression,
> and in particular as elements of matrices to be fed to LinearSolve.
>
> In the specific context, LinearSolve seems to apply N to all of its
> arguments, but as a side-effect of this the indices (i in the
> expressions above) are turned into Reals, so that for example
>
> AffineExpression[ .5, {{1, .2},{2, .1}}]
>
> comes out as
>
> AffineExpression[ .5, {{1., .2}, {2., .1}}]
>
> This has aesthetical and functional disadvantages (my codes also
> exploits the fact that the indices are integer), so I have to apply
> Rationalize or some other such function to re-convert the indices into
> Integers.
>
> So I was looking for a way to tell Mathematica that applying N to an
> AffineExpression should only actually apply it to c and xi, something
> like
>
> N[AffineExpression[c_, dev_]] :=
>   AffineExpression[N[c], MapAt[N,#,{2}]&/@ dev]
>
> but if I actually do this and then call
>
> AffineExpression[1, {{1, 1}}]
> N[%]
>
> the Mathematica kernel (5.2.0.0) dies without any message.
>
> Does anybody have an idea of what could the reason be? And what could
> I do as a workaround?
>

One idea is to use the attribute NHoldRest (or if you change your data
structure, NHoldFirst). For example:

SetAttributes[AffineExpression, NHoldRest]

In[42]:= N[AffineExpression[.5, {{1, .2}, {2, .1}}]]

Out[42]= AffineExpression[0.5, {{1, 0.2}, {2, 0.1}}]

Carl Woll
Wolfram Research



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