Services & Resources / Wolfram Forums
MathGroup Archive
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: ModularArithmetic

  • To: mathgroup at
  • Subject: [mg32232] Re: [mg32217] ModularArithmetic
  • From: Andrzej Kozlowski <andrzej at>
  • Date: Wed, 9 Jan 2002 03:17:21 -0500 (EST)
  • Sender: owner-wri-mathgroup at

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

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
> gabrieli at
> gabrielic at
> gabrielic at
> web pages:
> =========================================================================
> =====
> "If you can't explain your research to your grandmother, then you
> don't understand it yourself"
> Richard Feynman
> "Update your bumper stickers, kids: Mac OS 8 = Windows 2010"
> David Pogue
> =========================================================================
> =====
Andrzej Kozlowski
Toyama International University

  • Prev by Date: Re: Wrestling with Mathematica on Trig Simplification
  • Next by Date: Re: How to call BinomialDistribution from within a package?
  • Previous by thread: ModularArithmetic
  • Next by thread: How to call BinomialDistribution from within a package?