Re: Exploiting relationships in manipulations: example with conjugate relationship

*To*: undisclosed-recipients:;*Subject*: [mg131340] Re: Exploiting relationships in manipulations: example with conjugate relationship*From*: Sune Jespersen <sunenj at gmail.com>*Date*: Sat, 29 Jun 2013 04:57:51 -0400 (EDT)*Approved*: Steven M. Christensen <steve@smc.vnet.net>, Moderator*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*Newsgroups*: comp.soft-sys.math.mathematica*References*: <20130628081233.8C1D769C6@smc.vnet.net> <CAEtRDSezcQXsrmSzzWO1yp-CPjGSeNncd9cfF6soHb3GYQvXBQ@mail.gmail.com>

Thanks. I meant ff[l][m] == Conjugate[ff[l][-m]]*(-1)^m). It seems your solution in this case produces an output fully identical (unchanged) to tel. For example, I wanted the 2nd element of tel I Sqrt[(2 =CF=80)/15] (ff[2][-1] + ff[2][1]) to become -2 Sqrt[(2 =CF=80)/15] Im(ff[2][1]). Sune On 28 Jun, 2013, at 17:42 , Bob Hanlon <hanlonr357 at gmail.com> wrote: > tel = {2/15 Sqrt[ > =CF=80] (5 ff[0][0] + 2 Sqrt[5] ff[2][0]), -I Sqrt[(2 =CF=80)/15] (ff[2][-1] + > ff[2][1]), > 1/15 Sqrt[ > =CF=80] (10 ff[0][0] - > Sqrt[5] (Sqrt[6] ff[2][-2] + 2 ff[2][0] + Sqrt[6] ff[2][2])), > Sqrt[(2 =CF=80)/15] (ff[2][-1] - ff[2][1]), -I Sqrt[(2 =CF=80)/15] (ff[2][-2] - > ff[2][2]), > 1/15 Sqrt[ > =CF=80] (10 ff[0][0] + > Sqrt[5] (Sqrt[6] ff[2][-2] - 2 ff[2][0] + Sqrt[6] ff[2][2]))}; > > In your text you state ff[l][m] == ff[l][-m] (-1)^m > > Simplify[tel, > Union[Cases[tel, ff[_][_], Infinity]] /. > ff[l_][m_] -> (ff[l][m] == ff[l][-m] (-1)^m)] > > {(2/15)*Sqrt[Pi]*(5*ff[0][0] + > 2*Sqrt[5]*ff[2][0]), 0, (2/15)*Sqrt[Pi]* > (5*ff[0][0] - Sqrt[5]*(ff[2][0] + > Sqrt[6]*ff[2][2])), -2*Sqrt[(2*Pi)/15]* > ff[2][1], 0, (2/15)*Sqrt[Pi]* > (5*ff[0][0] - Sqrt[5]*ff[2][0] + > Sqrt[30]*ff[2][2])} > > However, in your code you use ff[l][m] == = Conjugate[ff[l][-m]]*(-1)^m) > > Simplify[tel, > Union[Cases[tel, ff[_][_], Infinity]] /. > ff[l_][m_] -> (ff[l][m] == Conjugate[ff[l][-m]]*(-1)^m)] > > {(2/15)*Sqrt[Pi]*(5*ff[0][0] + > 2*Sqrt[5]*ff[2][0]), (-I)*Sqrt[(2*Pi)/15]* > (ff[2][-1] + ff[2][1]), (1/15)*Sqrt[Pi]* > (10*ff[0][0] - Sqrt[5]*(Sqrt[6]*ff[2][-2] + > 2*ff[2][0] + Sqrt[6]*ff[2][2])), > Sqrt[(2*Pi)/15]*(ff[2][-1] - ff[2][1]), > (-I)*Sqrt[(2*Pi)/15]*(ff[2][-2] - ff[2][2]), > (1/15)*Sqrt[Pi]*(10*ff[0][0] + > Sqrt[5]*(Sqrt[6]*ff[2][-2] - 2*ff[2][0] + > Sqrt[6]*ff[2][2]))} > > % === tel > > True > > > Bob Hanlon > > > > On Fri, Jun 28, 2013 at 4:12 AM, Sune <sunenj at gmail.com> wrote: > Hey all. > > I'm trying to get Mathematica to simplify a list of expressions involving complex symbolic variables with certain relations among them, and to take advantage of these relations while simplifying. > > To be more concrete, I could have a list such as > > tel={2/15 Sqrt[\[Pi]] (5 ff[0][0]+2 Sqrt[5] ff[2][0]),-I Sqrt[(2 \[Pi])/15] (ff[2][-1]+ff[2][1]),1/15 Sqrt[\[Pi]] (10 ff[0][0]-Sqrt[5] (Sqrt[6] ff[2][-2]+2 ff[2][0]+Sqrt[6] ff[2][2])),Sqrt[(2 \[Pi])/15] (ff[2][-1]-ff[2][1]),-I Sqrt[(2 \[Pi])/15] (ff[2][-2]-ff[2][2]),1/15 Sqrt[\[Pi]] (10 ff[0][0]+Sqrt[5] (Sqrt[6] ff[2][-2]-2 ff[2][0]+Sqrt[6] ff[2][2]))} > > However, there's a conjugate symmetry among the variables ff[l][m] that would enable a simpler looking expression. Specifically, ff[l][m]=ff[l][-m] (-1)^m, and I would like to have Mathematica take advantage of that and reduce expressions such as > > I Sqrt[(2 \[Pi])/15] (ff[2][-1]+ff[2][1]) > > to > > -Sqrt[(2 \[Pi])/15] 2*Im(ff[2][1]) > > > I've tried various combinations of ComplexExpand and FullSimplify; > > ComplexExpand[ > FullSimplify[tel, > And @@ Flatten[ > Table[ff[l][m] == Conjugate[ff[l][-m]]*(-1)^m, {l, 0, 4, 2}, {m, > 0, l}]]], Flatten[Table[ff[l][m] , {l, 2, 4, 2}, {m, -l, l}]]] > > (And also version with the two outermost commands interchanged) > but it doesn't do what I want. Of course, it may be that the rules for simplify are such that my sought expression is not considered a simpler version of the same expression. Could that be the case? Otherwise, I'd appreciate any suggestions on how to implement relations such as these in manipulation of expressions. > > Thanks, > Sune > >

**References**:**Exploiting relationships in manipulations: example with conjugate relationship***From:*Sune <sunenj@gmail.com>