Re: Number Theory - Chinese Remainder Theorem
- To: mathgroup at smc.vnet.net
- Subject: [mg27966] Re: [mg27954] Number Theory - Chinese Remainder Theorem
- From: BobHanlon at aol.com
- Date: Tue, 27 Mar 2001 01:26:04 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Needs["NumberTheory`NumberTheoryFunctions`"];
?ChineseRemainder
Bob Hanlon
In a message dated 2001/3/26 5:51:19 AM, lee.stone at hqasc.army.mil writes:
>I am studying the Chinese Remainder Theorem. I am using have been using
>the
>following code to solve CRT problems.
>
>PairwiseQ[m-List] := Apply[LCM, m] == Apply[Times, m]
>
>CRT[a_, m_] := Module[{M = Apply[Times, m]},
>If[PairwiseQ[m], Mod[Apply[Plus, a * PowerMid[M/m, -1, m] * M/m], M],
> {}]]
>
>I would like modify this code to also be able to solve moduli that are
>not
>relatively prime and to return the empy set ({}) if the congurences have
>no
>solution.
>