TagSet and Unprotect
- To: mathgroup at smc.vnet.net
- Subject: [mg77594] TagSet and Unprotect
- From: dimitris <dimmechan at yahoo.com>
- Date: Wed, 13 Jun 2007 07:41:30 -0400 (EDT)
Following a idea by Raymond Manzoni let me prove that - PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4]=Pi^2/6 - (3*Log[2]^2)/2 Indeed Off[N::meprec] (*turn off a message*) PolyLog[2, z/(z + 1)] + PolyLog[2, z/(z - 1)] - (1/2)*PolyLog[2, z^2/ (z^2 - 1)] + (1/4)*Log[(1 + z)/(1 - z)]^2 == 0 (*an identity of dilogarithms*) (FunctionExpand[Expand[2*#1]] & ) /@ (% /. z -> -3^(-1)) (*Mathematica does the rest*) Reverse[(Plus @@ Cases[%, (a_)*PolyLog[x_, y_], Infinity] - #1 & ) /@ %] (1/4)*Log[(1 + z)/(1 - z)]^2 + PolyLog[2, z/(-1 + z)] + PolyLog[2, z/ (1 + z)] - (1/2)*PolyLog[2, z^2/(-1 + z^2)] == 0 -(Pi^2/6) + (3*Log[2]^2)/2 - PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4] == 0 -PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4] == Pi^2/6 - (3*Log[2]^2)/2 I try to add this result to Plus, so that in the following to have additional substitution. rul1 = {PolyLog[2, z_] /; z < -3 -> -PolyLog[2, 1/z] - Pi^2/6 - (1/2)*Log[-z]^2, PolyLog[2, z_] -> PolyLog[2, 1/(1 - z)] - Pi^2/6 + (1/2)*Log[1 - z]*Log[(1 - z)/z^2]}; o = Expand[3*PolyLog[2, -3] + PolyLog[2, -8] /. rul1] -((2*Pi^2)/3) - (3/2)*Log[9/4]*Log[4] - Log[8]^2/2 - PolyLog[2, - (1/8)] + 3*PolyLog[2, 1/4] That is, I want Mathematica to substitute - PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4] by Pi^2/6 - (3*Log[2]^2)/2 in the expression o. In the beggining I tried: Unprotect[PolyLog]; PolyLog /: -PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4] = Pi^2/6 - (3*Log[2]^2)/2 TagSet::tagpos : Tag PolyLog in -PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4] is \ too deep for an assigned rule to be found. Pi^2/6 - (3*Log[2]^2)/2 I understood the presence of this message. That's why I try to assign this equality to Plus. Unprotect[Plus]; Plus /: -PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4] = Pi^2/6 - (3*Log[2]^2)/2 TagSet::write: Tag Plus in-PolyLog[2, -(1/8)] + 3*PolyLog[2, 1/4] is Protected Now I don't understand the presence of this message. I can't assign an UpValue to a built in function? Can somebody explain me what is going on? And how I must work in order to overcome the problem? Thanks Dimitris
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