Re: Modifying equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg59171] Re: [mg59135] Modifying equations*From*: "David Park" <djmp at earthlink.net>*Date*: Sun, 31 Jul 2005 01:30:43 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Kalle, One method is to use the Inner command. eqn1 = a == b; eqn2 = c == d; Inner[Plus, eqn1, eqn2, Equal] a + c == b + d In the following command we divide 3 times eqn1 by k times eqn2. Inner[3#1/(k#2) &, eqn1, eqn2, Equal] (3*a)/(c*k) == (3*b)/(d*k) Here are two other equations. eqn1 = a x + b == c; eqn2 = b y + d == f; In the following we give an annotated step by step calculation of x + y. (Copy the code into a Mathematica notebook and evaluate.) Print["Solving eqn1 for x"] # - b & /@ eqn1 xeqn = #/a & /@ % Print["Solving eqn2 for y"] # - d & /@ eqn2 yeqn = #/b & /@ % Print["Calculating x + y"] Inner[Plus, xeqn, yeqn, Equal] You may wish to look at the StepByStepEquations notebook on the Mathematica page of my web site below. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Kalle Rutanen [mailto:kalle_rutanen at nospam.hotmail.com] To: mathgroup at smc.vnet.net 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.