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Re: ModularArithmetic

• To: mathgroup at smc.vnet.net
• Subject: [mg32232] Re: [mg32217] ModularArithmetic
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Wed, 9 Jan 2002 03:17:21 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

It is a bit hard to answer  because the word "arithmetic" is ambiguous 
(does it include commutative algebra?). If by "arithmetic" you simply 
mean what is often called "modular arithmetic" then the answer is 
simple: just used the built in functions Mod, PowerMod and 
PolynomialMod. There are also useful functions in the 
NumberTheory`NumberTheoryFunctions` package, particularly the 
ChineseRemainder function. On the other hand if you want to do 
commutative algebra, like factoring polynomials (your original example) 
then most functions accept the option Modulus->n, but they usually 
expect n to be a prime number. (In your particular case even 
Factor[x^4 + 5*m^4, Modulus->3] would not work because Mathematica at 
this time cannot factor multivariate polynomials with respect to a 
modulus). Solve, SolveAlways, Reduce,ELiminate, Roots are among the 
functions that work with respect to an arbitrary modulus and you can do 
quite a lot with these.

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/


On Monday, January 7, 2002, at 05:16  PM, Carlo Gabrieli wrote:

> Hi MathGroup,
> is it possible to solve arithmetic expressions for example in Z_6
> with Mathematica?
>
> Thanks in advance
> Best Regards
> Carlo Gabrieli
> snail mail: Carlo Gabrieli
> Via San Giovanni d'Acri 15
> 30126 Lido di Venezia (VE)
> Tel.& FAX: 011-39-41-5264157
>
> e-mail: gabrieli at iuav.it
> gabrieli at flux.isdgm.ve.cnr.it
> gabrielic at libero.it
> gabrielic at inwind.it
>
> web pages: http://www.omitech.it/MERLIN/conn.htm
>
>
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Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/