• To: mathgroup at smc.vnet.net
• Subject: [mg14392] Re: [mg14342] Adding equations
• From: Daniel Lichtblau <danl>
• Date: Sun, 18 Oct 1998 15:09:58 -0400
• References: <199810150428.AAA18222@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```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

In[29]:= Thread[Plus[a==b,c==d], Equal] Out[29]= a + c == b + d

Another common approach is to use the automatic threading capability of
e.g. Plus over the head List. To do so you may change Equal to List,
operate, then change back.

In[30]:= ((a==b) + (c==d) /. Equal->List) /. List->Equal Out[30]= a + c
== b + d

Daniel Lichtblau
Wolfram Research

```