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Simplification


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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