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MathGroup Archive 2005

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Re: Modifying equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59170] Re: Modifying equations
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sun, 31 Jul 2005 01:30:43 -0400 (EDT)
  • References: <dcf38r$lfr$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Kalle Rutanen schrieb:
> 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.
> 
> 
try

1. Thread[eq1 + eq2, Equal]
2.
Unprotect[Sum];
Sum /: Sum[a_, {n_, n0_, n1_}] + Sum[b_, {n_, n0_, n1_}] :=
    Sum[a + b, {n, n0, n}];
Protect[Sum];

Sum[Cos[n^2*x], {n, 0, m}] + Sum[Sin[n^2*x], {n, 0, m}]

-->
Sum[Cos[n^2*x] + Sin[n^2*x], {n, 0, n}]

-- 
Peter Pein
Berlin
http://people.freenet.de/Peter_Berlin/


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