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MathGroup Archive 1999

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Re(2): Re: Bug in Det[ ], once more

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15691] Re(2): [mg15651] Re: [mg15592] Bug in Det[ ], once more
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Mon, 1 Feb 1999 14:54:12 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On Sat, Jan 30, 1999, Daniel Lichtblau <danl at wolfram.com> wrote:

>Actually it is limitations in modular polynomial algebra e.g. taking
>gcds and factoring. Modular arithmetic per se is not suffering from bugs
>or limitations of any kind so far as I am aware.


I agree I should have said "algebra". I tend to automatically refer to
number theory as "arithmetic" (as in Serre "Cours D'Aritmetique") and
think of commutative algebra over algebraic number fields as "number
theory", hence "arithmetic". "Modular" just meant nonzero
characteristic. I suppose by "modular arithmetic" people usually mean
computations with remainders. However  all this reminds me of something
I have long wanted to ask for. I often do algebraic computations modulo
a fixed prime (often just 2).  So much so that sometimes  I find it
convenient to start such computations by defining:

$Pre=PolynomialMod[#,5]&
$Post=PolynomialMod[#,5]&

This works fine for simple computations like:

In[2]:=
Expand[(3+5x+11x^2)*(4-11x+23x^3)]
Out[2]=
             2      3      5
2 + 2 x + 4 x  + 3 x  + 3 x


The down side is that it in effect disables most algebraic functions,
like Together, Factor etc. I have tried other approaches but nothing I
have been able to think of is entirely satisfactory. What I would like
to do is to be able simply to enter
$Modulus= 5
 
and from that point on all algebraic operations should be done modulo 5.
When I next wanted to switch to characteristic zero I simply enter 
$Modulus=0

and everything works as normal. It seems to me that this should be
rather easy to implement, perhaps via a package, and would probably be
found useful by others.



Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp/
http://eri2.tuins.ac.jp/



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