Re: Modifying equations

• To: mathgroup at smc.vnet.net
• Subject: [mg59164] Re: Modifying equations
• From: dh <dh at metrohm.ch>
• Date: Sun, 31 Jul 2005 01:30:39 -0400 (EDT)
• References: <dcf38r\$lfr\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Kalle,
see below.
sincerely Daniel

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}] ?
this can be done e.g. by a rule:
r = HoldPattern[Sum[f1_, {i, 0,
n}] + Sum[f2_, {i, 0, n}]] :> Sum[f1 + f2, {i, 0, n}];
The HoldPattern is needed because f1 and f2 do not explicitely mention i
and Mathematica would otherwise take f1 and f2 as independent of i.
Application of this rule gives the result you want:
Sum[a[i], {i, 0, n}] + Sum[b[i], {i, 0, n}] /. r

note that your example a_i and b_i is WRONG. Either you can define a and
b as functions od i and would write a[i] and b[i] or you take it as
arrays: a[[i]], b[[i]]

>
> Thanks.
>
>

```

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