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/