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 > > > ========================================================================= > ===== > > "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 JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/