Re: Extracting terms from an equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg69770] Re: [mg69697] Extracting terms from an equation*From*: János <janos.lobb at yale.edu>*Date*: Fri, 22 Sep 2006 01:04:56 -0400 (EDT)*References*: <200609211129.HAA07668@smc.vnet.net>

On Sep 21, 2006, at 7:29 AM, Coleman, Mark wrote: > Greetings, > > I'd like to find a general way to extract all of the terms from an > equation that involve a given variable. For instance, consider the > equation > > myEquation == Exp[a + b x^2 + c y^2 + d x y + e x^3]] > > I'd like to define a function such that > > myFunction[myEquation,x] returns the result {b x^2, d x y, e x^3} > > Thanks, > > -Mark Here is a newbie diving approach. I am sure it can be somehow functionalized, but not by me and not today: In[1]:= aa = myEq == Exp[a + b*x^2 + c*y^2 + d*x*y + e*x^3]; First I find all the unique positions where x can be found in the equation. In[2]:= mmbrs = Union[Flatten[ Table[Position[aa, x, i], {i, 1, Depth[aa]}], 1]] Out[2]= {{2, 2, 4, 2}, {2, 2, 2, 2, 1}, {2, 2, 3, 2, 1}} Then I dive deeper and deeper into every item where such position was found and chop away any surrounding layer that is not a "sum of parts". "Sum of part"s are those forms that have a Head of Plus. When I find such "sum of parts" than I just reach a level deeper and Sow your "pearl" right from there. In[3]:= Flatten[First[Last[ Reap[i = 1; While[ i <= Length[mmbrs], cur = mmbrs[[i]]; j = 1; While[ j <= Length[cur], If[Head[First[ Extract[aa, {Take[ cur, j]}]]] == Plus, Sow[Extract[ aa, {Take[cur, j + 1]}]]; Break[ ]]; j++; ]; i++; ]]]]] Out[3]= {d*x*y, b*x^2, e*x^3} János ---------------------------------------------- Trying to argue with a politician is like lifting up the head of a corpse. (S. Lem: His Master Voice)

**References**:**Extracting terms from an equation***From:*"Coleman, Mark" <Mark.Coleman@LibertyMutual.com>