Re: Adding equations

• To: mathgroup at smc.vnet.net
• Subject: [mg14399] Re: [mg14342] Adding equations
• From: Jurgen Tischer <jtischer at col2.telecom.com.co>
• Date: Sun, 18 Oct 1998 15:10:04 -0400
• Organization: Universidad del Valle
• References: <199810150428.AAA18222@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Lawrence,
without checking for inconsistencies! Try these definitions

CircleTimes[a_,b_]:=Thread[Times[a,b],Equal]
CirclePlus[a_,b_]:=Thread[Plus[a,b],Equal]
Colon[a_,b_]:=Thread[Divide[a,b],Equal]

You can use the symbols (I can not show it in this damned ascii format)
which correspond to the names, and WR made them infix already.  The
nice thing is that those definitions solve your quest for applying
expressions also. You can even use them for simply add, sub and so on
numbers. Plus and Times work with multiple equations (I mean like
a==b==c).
The respective aliases are Esc c * Esc, Esc c + Esc, Esc : Esc.  If you
think you need them such a lot that it becomes a nuisance to type all
the time those aliases you could think in defining your own (shorter)
aliases, for example Esc 8 Esc and Esc = Esc are unused. You could
change to Backslash for Colon and had the easy alias Esc \ Esc, but you
loose the easy definition for division. I found

Backslash[a_,b_]:=Divide@@#&/@Thread[List[a,b],Equal]

will work, but less nice than Colon (for example 2\3 gives {2,3}).

Jurgen

Lawrence Walker wrote:
>
> Group:
>
> I've been trying to add two equations as follows:
>
> In[4]:=
>     a==b;
> In[5]:=
>     c==d;
> In[6]:=
>     %4+%5
> Out[6]=
>     (a==b)+(c==d)
>
> The result I was looking for is (a+c)==(b+d). The following works but it
> seems clumsy. In[7]:=
>     %4[[1]]+%5[[1]]==%4[[2]]+%5[[2]] Out[7]=
>     a+c==b+d
> Is there a way to elegantly add (sub, mult, div) two equations?  Also is
> there an elegant way to add (sub, mult, div) an expression to both
> sides of an equation?
>
> Lawrence Walker

```

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