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MathGroup Archive 1998

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Together chokes with Prime Modulus > 46337

  • To: mathgroup at
  • Subject: [mg15155] Together chokes with Prime Modulus > 46337
  • From: "Ersek, Ted R" <ErsekTR at>
  • Date: Wed, 16 Dec 1998 03:11:26 -0500
  • Sender: owner-wri-mathgroup at

One of the great things about Mathematica is that you can do exact
calculations with very large numbers.  For example:


In the next line Together works in modulo 46337 and I get the answer in
a flash! 
(note 46337 is a prime number)  

Together[1/x+1/(x+1), Modulus->46337] Out[2] (2*(23169 + x))/(x*(1 + x))

Next try using Together with any prime modulus larger than 46337 and
Mathematica will choke.

I would have guessed the functions that use the Modulus option could
work in modulo prime where the prime modulus has a hundred digits or
more with no problem.  Instead Mathematica flat-out quits for modulo
greater than 46337.

Is it impractical to make a version that will do modular algebra with a
large modulus?

I can evaluate NextPrime[10^10000] and I doubt Mathematica will refuse
to try it.  I might have to wait over a year for an answer.  I might
run out of memory before I get an answer, but I expect Mathematica will
not give up. Using Modulus 46337 Together hasn't even got to the point
where it takes a little while, but it will refuse to work with a
modulus any larger.  Why?

Ted Ersek

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