Re: Overriding the definition of Plus so that it does exact arithmetic: Bug or Feature?

• To: mathgroup at smc.vnet.net
• Subject: [mg120257] Re: Overriding the definition of Plus so that it does exact arithmetic: Bug or Feature?
• From: Dana DeLouis <dana01 at me.com>
• Date: Fri, 15 Jul 2011 04:09:05 -0400 (EDT)

```> This works as expected,  e.g.

> P[0.1, -1/10]  returns 1/180143985094819840

Not sure, but is this a good alternative?

p[v___]:=Total[Rationalize[List@v,0]]

p[0.1,-1/10]
0

p[a,1./3,1.1,2.3,5.6,2/3.]
10+a

= = = = = = = = = =
HTH  : >)
Dana DeLouis
\$Version
8.0 for Mac OS X x86 (64-bit) (November 6, 2010)

On Jul 14, 5:24 am, Richard Fateman <fate... at cs.berkeley.edu> wrote:
> Consider the definition of the new function P which is supposed to be
> exactly like Plus, except that converts all "Real" floats to exact
> rational numbers before adding them up.
>
> P[a_Real,b__]:= Plus[Rationalize[SetAccuracy[a, Infinity]], b];
> SetAttributes[P, Attributes[Plus]]
>
> P[c__]:= Plus[c]
>
> This works as expected,  e.g.
>
> P[0.1, -1/10]  returns 1/180143985094819840
>
> which is the difference between the closest double-float to 0.1,
> and the exact number 1/10.
>
> Given this, let's put EXACTLY the same definition on Plus
>
> Unprotect[Plus];
> Plus[a_Real,b__]:= Plus[Rationalize[SetAccuracy[a, Infinity]], b];
> Protect[Plus];
>
> 0.1-1/10  gives 0.   (wrong)
> 0.1+x gives 3602879701896397/36028797018963968 + x  (hm, right).
>
> My guess is that any Rules inserted on Plus by the user are checked
> AFTER the built-in simplifications attached to Plus. I consider this a
> bug. Any workaround come to mind, if you consider this a feature :)
>
> RJF

```

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