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 > >