Re: Simplification

*To*: mathgroup at smc.vnet.net*Subject*: [mg75444] Re: Simplification*From*: "Michael Weyrauch" <michael.weyrauch at gmx.de>*Date*: Tue, 1 May 2007 03:20:58 -0400 (EDT)*References*: <f146na$m9e$1@smc.vnet.net>

Hello, I do not have a real solution, but just a quick remark... in principle such simplifications are easy, if one recognizes that both numerator an denominator of your expression can be written as a geometric series. oo = Product[Cos[(2^j*Pi)/1023], {j, 0, 9}]/Product[Cos[(2^j*Pi)/1025], {j, 0, 9}] num = Expand[Numerator[TrigToExp[oo]]] den = Expand[Denominator[TrigToExp[oo]]] num1 = -1 - Sum[(-a)^n, {n, 0, nnum}] /. {a -> (-1)^(1/1023), nnum -> 1022} den1 = 1 - Sum[(-a)^n, {n, 0, nden}] /. {a -> (-1)^(1/1025), nden -> 1024} Obviously, num1==num and den1==den and num1/den1 -1 since both sums are zero. While the equalities of num==num1 and den==den1 can be seen with significantly reduced vision on both eyes, Mathematica would not show it to me. Why?? Since I do not have available the other CAS you are talking about, it would be interesting to explain what the convert() command is intended to do... Michael "dimitris" <dimmechan at yahoo.com> schrieb im Newsbeitrag news:f146na$m9e$1 at smc.vnet.net... > This appeared in another forum. > > (Converting to Mathematica InputForm.) > > In[2]:= > oo = Product[Cos[(2^j*Pi)/1023], {j, 0, 9}]/Product[Cos[(2^j*Pi)/ > 1025], {j, 0, 9}]; > > The expression can be simplified to -1. > > Indeed, adopted by someone's reply, in another CAS, we simply have > > Product(cos(Pi*2^j/1023), j= 0..9)/ Product(cos(Pi*2^j/1025), j= > 0..9): > p:=value(%): > convert(p, sin): > simplify(%); > -1 > > However, no matter what I tried I was not able to succeed in > simplifying above expression > to -1 with Mathematica, in reasonable time. Futhermore, even the much > more simpler of > showing oo==-1 didn't work. > > So I would really appreciate if someone pointing me out: > 1) A way to show (in Mathematica!) that oo is simplified to -1 > 2) That the equality oo==-1 (or oo-1==0 alternatively) can be > simplified > to True. > > Any ideas? > > BTW, I found the function convert of the other CAS, very useful. > Has anyone implementated a similar function in Mathematica? > (I ain't aware of a Mathematica built-in function, similar to convert > from the other CAS.) > > Dimitris > >