Re: Beginner--getting rid of dot products with zero

*To*: mathgroup at smc.vnet.net*Subject*: [mg66946] Re: Beginner--getting rid of dot products with zero*From*: Peter Pein <petsie at dordos.net>*Date*: Sun, 4 Jun 2006 02:01:32 -0400 (EDT)*References*: <e5ot50$i6t$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

smanky at gmx.de schrieb: > sorry that my question was apparently not clear. > > i have no problem with computing the derivatives. the expressions with Total[] etc all make sense. > > however, the derivatives include ugly terms that are simply zero. there are terms of the following form > > 0.{exp, exp, exp} > > or > > {exp, exp, exp}.0 > > in both cases the whole thing is zero and they should drop out... > > i am surprised that mathematica is not getting rid of them by itself, or at least when i use Simplify[]. so i am looking for a clever way to tell mathematica that it should disregard those terms. > > thanks, > > ~s > > p.s. if it is still not clear, or you just want to see for yourself, run: > > finish = 2; > i = Table[i, {i, finish}]; > > d1[k1_, k2_] = Exp[k1*i + k2*i^2]; > d2[k1_, k2_] = Total[Exp[k1*i + k2*i^2]]; > > w[k1_, k2_, i] = d1[k1, k2]/d2[k1, k2]; > > q[k1_, k2_] = x.w[k1, k2, i]; > > > L[k1_, k2_, alpha_, beta_ ] = Total[Log[q[k1, k2]]] + Total[(y - alpha - beta*q[k1, k2])^2/q[k1, k2]]; > > \!\(Simplify[∂\_beta\ L[k1, \ k2, \ alpha, \ beta]]\) > > Link to the forum page for this post: > http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Special:Forum_ViewTopic&pid=10811#p10811 > Posted through http://www.mathematica-users.org [[postId=10811]] > > Hello Stephan, I don't know what you expect when applying a dot-product to a scalar (x) and a vector, but one of the following should do what you want: either define x,y as vectors: x = {x1, x2}; y = {y1, y2}; Simplify[D[L[k1, k2, a, b], a]] --> {(2*E^(-k1 - 3*k2)*(a*(1 + E^(k1 + 3*k2))^2 + 2*b*E^(k1 + 3*k2)*x1 - (1 + E^(k1 + 3*k2))^2*y1))/x1, (2*E^(-k1 - 3*k2)*(a*(1 + E^(k1 + 3*k2))^2 + 2*b*E^(k1 + 3*k2)*x2 - (1 + E^(k1 + 3*k2))^2*y2))/x2} or use scalar multiplication in the definition of q[]: q[k1_, k2_] = x*w[k1, k2, i]; Simplify[D[L[k1, k2, a, b], a]] --> (2*E^(-k1 - 3*k2)*(a*(1 + E^(k1 + 3*k2))^2 + 2*b*E^(k1 + 3*k2)*x - (1 + E^(k1 + 3*k2))^2*y))/x hth, Peter