Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

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

Search the Archive

Re: PolynomialGCD

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60291] Re: [mg60276] PolynomialGCD
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 10 Sep 2005 06:46:40 -0400 (EDT)
  • References: <200509090807.EAA16029@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 9 Sep 2005, at 17:07, jonspalmer at gmail.com wrote:

> Is there anyway to get PolynomialGCD to work with Complex numbers? For
> example get:
>
> PolynomialGCD[(x+y) I, (x+y) 2 I]
>
> to return:
>
> (x+y) I
>
>
> ?
>
> Many thanks
> Jon Palmer
>
>

It looks to me you have found prehistoric bug. But first let me point  
out that in general PolynomialGCD cannot be expected to work over  
real or complex numbers. PolynomialGCD is mathematically defined but  
it does not make sense to try to compute it by means of the Euclidean  
algorithm because a crucial step in the algorithms demands  
determining if a real or complex expression is 0 and this cannot be  
done exactly. On the other hand there is no problem with using the  
Euclidean algorithm over any algebraic extension of the rationals,  
and you can do it with PolynomialGCD by means of the option Extension- 
 >{a sequence of algebraic numbers}.
  However, this has nothing to do with the problem here. In fact just  
replace I by 1+I and everything works fine:


PolynomialGCD[(x + 1)*(I + 1), (x + 1)*2*(I + 1)]


(1 + I)*x + (1 + I)




here PolynomialGCD simply treats I as a variable, which is exactly  
what the documentation tells you it will do:

PolynomialGCD[poly1, poly2, ? ] will by default treat algebraic  
numbers that appear in the polyi as independent variables.

So we have to conclude that


PolynomialGCD[(x+y) I, (x+y) 2 I]


x+y

is a bug and one that must have been with us since time immemorial.  
In the immortal words of a former contributor this list it is a "bug  
the long liver" ;-)

Andrzej





  • Prev by Date: Re: Precedence
  • Next by Date: Re: A very EZ Question! Make a Graph!
  • Previous by thread: PolynomialGCD
  • Next by thread: Re: PolynomialGCD