Re: Modifying equations

• To: mathgroup at smc.vnet.net
• Subject: [mg59179] Re: Modifying equations
• From: Konstantin <no.email at no.email>
• Date: Sun, 31 Jul 2005 01:30:49 -0400 (EDT)
• References: <dcf38r\$lfr\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Unprotect[Equal];
Equal /: Plus[Equal[a_, b_], Equal[c_, d_]] := Equal[a + c, b + d];
Equal /: Plus[Equal[a_, b_], c_] := Equal[a + c, b + c];
Equal /: Times[Equal[a_, b_], c_] := Equal[a*c, b*c];
Protect[Equal];

Note, however, that unprotecting system symbols is generally not a good
idea as you can mess up a lot of things.

Kalle Rutanen wrote:

> Hello
>
> My intention is to write a mathematical paper which derives results step by
> step. So here is my first question:
>
> Given the equations
> eqn1 = a == b
> eqn2 = c == d
>
> How can I combine these to form (for example)
> a + c == b + d ?
>
> I tried the obvious eqn1 + eqn2, but that does not seem to work...
>
> Second question:
>
> Given this:
> Sum[a_i, {i, 0, n}] + Sum[b_i, {i, 0, n}]
> How can I make Mathematica combine the sums giving:
> Sum[a_i + b_i, {i, 0, n}] ?
>
> Thanks.
>
>

```

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