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Re: Differencing two equations

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  • Subject: [mg129770] Re: Differencing two equations
  • From: David Bailey <dave at removedbailey.co.uk>
  • Date: Tue, 12 Feb 2013 03:24:22 -0500 (EST)
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On 10/02/2013 08:35, 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.
>

I would define a function thus:

equationSubtract[x1_ == y1_, x2_ == y2_] := (x1 - x2) == (y1 - y2);

(If you use it a lot, you might want to put it somewhere do it is auto 
loaded).

In[9]:= equationSubtract[a == r, b == s]

Out[9]= a - b == r - s

A slightly better version might have a third optional argument to supply 
a multiplier:

equationSubtract[x1_ == y1_, x2_ == y2_,
   m_: 1] := (x1 - m x2) == ( y1 - m y2);

In[5]:= equationSubtract[a == r, b == s, 2]

Out[5]= a - 2 b == r - 2 s

This function would still handle the 2-argument case.

In general, I don't believe in writing complicated syntax to do an 
individual algebraic manipulation (because if you get it wrong, you may 
not notice the wrong answer!). It is better to write a function once, 
test it, and use it when you need it - as I have done here.

David Bailey
http://www.dbaileyconsultancy.co.uk





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