Re: Together chokes with Prime Modulus > 46337

• To: mathgroup at smc.vnet.net
• Subject: [mg15132] Re: Together chokes with Prime Modulus > 46337
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Wed, 16 Dec 1998 03:11:10 -0500
• References: <754vbm\$jfg@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Ted,
I get an explicit message:

\$Version

"Microsoft Windows 3.0 (April 25, 1997)"

Together[1/x+1/(x+1),Modulus\[Rule]1299709]

Together::"modm":
"Modulus \!\(1299709\) is too large for this implementation."

Together[1/x + 1/(1 + x), Modulus -> 1299709]

Allan

---------------------
Allan Hayes
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

Ersek, Ted R wrote in message <754vbm\$jfg at smc.vnet.net>...
>One of the great things about Mathematica is that you can do exact
>calculations with very large numbers.  For example:
>
>In[1]:=
>3^123-7^69
>Out[1]=
>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[2]:=
>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?
>
>
>Cheers,
>Ted Ersek
>
>

```

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