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[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