Re: Bug in Det[ ], once more
- To: mathgroup at smc.vnet.net
- Subject: [mg15651] Re: [mg15592] Bug in Det[ ], once more
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Sat, 30 Jan 1999 04:28:46 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica's entire mod p arithmetic seems to break down for primes of
about this magnitude. For example, recently Ted Ersek wrote to point
out that Together[ ,Modulus->p] breaks down for p larger than 46337 and
we noticed that most other algebraic functions suffer from the same
defect. Daniel Lichtblau explained that all this is due to limitations
of the current inplementation of modular arithmetic. The bug noticed
buy you appears to be somewhat different (its a "bug" rather than a
"limitation") but the closeness of the value of p at which it occurs to
the one where functions like Factor, PolynomialGCD etc fail suggests
that there may be a relationship. Definitely Mathematica's modular
arithmetic is not useable and should be fixed.
As to whether there are any ways round this problem: I think it depends
on the concrete problem you are trying to solve. In the example you
mention the way round is obvious: just do it by hand. In some other
cases I can imagine it might be possible to use the
ChineseRemainedrTheorem from the NumberTheoryFunctions package.
On Thu, Jan 28, 1999, David Jedelsky <david.jedelsky at vsb.cz> wrote:
>In Mathematica 3.0
>
>Det[{{1,1},{1,1}},Modulus->48611]
>
>gives the result 1 instead of 0.
>It probably holds for all Modulus equal to other primes grater or equal
>to Prime[4793] and for all matrices with some equal rows.
>
>I need this type of computations and I waste a lot of time on this bug.
>I cannot find any help in Wolfram documents.
>
>Is there any patch or other possibility to correct this bug? (
>Mod[Det[m],p] is really no help )
>
>Thanks
> David Jedelsky
>
>------------
>david.jedelsky at vsb.cz
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp/
http://eri2.tuins.ac.jp/
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