       Re: TagSet and Unprotect

• To: mathgroup at smc.vnet.net
• Subject: [mg77738] Re: TagSet and Unprotect
• From: dimitris <dimmechan at yahoo.com>
• Date: Fri, 15 Jun 2007 04:59:42 -0400 (EDT)
• References: <f4omjv\$7l3\$1@smc.vnet.net><f4r14b\$65e\$1@smc.vnet.net>

```So how can I overcome the situation?

Remember,

I have

> > o=(2*Pi^2)/3) - (3/2)*Log[9/4]*Log - Log^2/2 - PolyLog[2, -
> > (1/8)] + 3*PolyLog[2, 1/4]

> > I want Mathematica to substitute - PolyLog[2, -(1/8)] +
> > 3*PolyLog[2, 1/4]
> > by Pi^2/6 - (3*Log^2)/2 in the expression o.

???

Dimitris

and I want
/  Jens-Peer Kuska       :
> Hi,
>
> yes, you can't set an UpValue[] for a protected function
>
> Try
> Blub[x_?NumericQ] := "Ach"
>
> Protect[Blub]
>
> and
>
> Blub /: x_Blub + y_Blub := "Oh je!"
>
> Regards
>    Jens
>
>
> dimitris wrote:
> > 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
> >
> > 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 - 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
> >
> > 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 - Log^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 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
> >
> > 1/4] is \
> > too deep for an assigned rule to be found.
> > Pi^2/6 - (3*Log^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
> > 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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