       Together chokes with Prime Modulus > 46337

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

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

In:=
3^123-7^69
Out=
28018763581994152068926844488\
663468681310215695058256067220

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

In:=
Together[1/x+1/(x+1), Modulus->46337] Out (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?

Cheers,
Ted Ersek

```

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