       Re: Differencing two equations

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• Subject: [mg129757] Re: Differencing two equations
• From: Murray Eisenberg <murrayeisenberg at gmail.com>
• Date: Mon, 11 Feb 2013 04:36:32 -0500 (EST)
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```Yeah, Mathematica stubbornly refuses to thread Equal over the difference. I seem to recall that there are good design reasons for that.

The following works, but of course is more involved than one might like:

Equal @@ Subtract @@@ {a == r, b == s}

Which is an abbreviated form of:

Apply[Equal, Apply[Subtract, {a == r, b == s}, 1]]

Essentially, you're taking out the equalities and after subtractions putting an equality back.

On Feb 10, 2013, at 3:24 AM, g.c.b.at.home at gmail.com wrote:

> I'm brand new to Mathematica, so I apologize for the naive questions...
>
> I'm trying to figure out how to difference two equations.  Basically if I have:
> a==r
> b==s
>
> I'd like to get:
> a-b == r-s
>
> What I'm getting is more like (a==r) - (b==s).  I'm not sure how that's a useful result, but is there a function to do what I'm looking for?
>
> A quick search of the archives seem to bring up ways of doing this from using transformation rules to swap heads to unlocking the Equals operator and hacking its behavior.  I'd like to avoid doing that kind of rewiring for a simple operation, and I'd like to keep the syntax clean.
>
> The Core Language documentation makes a big point of how everything is basically a list with different heads.  In this case, what I'm trying to do would work if it were treated as a list ({a,b}-{r,s} returns {a-b,r-s}) but doesn't work under Equal.
>
> Thanks for any suggestions.

---
Murray Eisenberg                                    murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
710 North Pleasant Street                         fax   413 545-1801
Amherst, MA 01003-9305

```

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