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MathGroup Archive 2007

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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
>
> 



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