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 Post subject: primary decomposition in Q[i]
PostPosted: Thu Aug 11, 2005 5:32 pm 
I am interested in computing the Primary decomposition of ideals in C[x,y]. For example i tried the following ideal:

I=(x^2+y^2)

in the polinomial ring Q[i][x,y] where i^2+1=0

the definition of the ring was as follows:

ring r=(0,i)(x,y),dp;minpoly=i^2+1;

PrimdecGTZ returns incorrectly the ideal itself, as if it was primary, while all the other primdec command from the primdec.lib and mprimdec.lib return rerror messages. My suispect is that we cannot compute the primary decomposistion with an algebraic extension of Q as coefficient ring. Anyone has any idea?

Thank you

Alberto Damiano

email: adamiano@gmu.edu
Posted in old Singular Forum on: 2004-05-05 17:17:36+02


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 Post subject: Re: primary decomposition in Q[i]
PostPosted: Thu Aug 11, 2005 8:39 pm 

Joined: Thu Aug 11, 2005 8:03 pm
Posts: 37
Location: RWTH Aachen, Germany
Dear Alberto Damiano,
Quote:
> I am interested in computing the Primary decomposition of ideals in C[x,y]. For example i tried the following ideal:
> I=(x^2+y^2)
> in the polinomial ring Q[i][x,y] where i^2+1=0
> the definition of the ring was as follows:
> ring r=(0,i)(x,y),dp;minpoly=i^2+1;

here you've forgotten a comma, it should be rather
Code:
ring r=(0,i),(x,y),dp;
minpoly=i^2+1;

Quote:
> PrimdecGTZ returns incorrectly the ideal itself, as if it was primary, while all the other primdec command from the primdec.lib and mprimdec.lib return rerror messages. My suispect is that we cannot compute the primary decomposistion with an algebraic extension of Q as coefficient ring. Anyone has any idea?
>

There should be an error in you Singular script, because the correct code
Code:
ring r=(0,i),(x,y),dp;
minpoly=i^2+1;
ideal I=x2+y2;
LIB "primdec.lib";
list L=primdecGTZ(I);
L;

gives always a correct answer (I've checked it extra with versions 2-0-4, 2-0-5 and even with the development version 2-1-2):

Code:
[1]:
   [1]:
       _[1]=x+(-i)*y
   [2]:
       _[1]=x+(-i)*y
[2]:
   [1]:
       _[1]=x+(i)*y
   [2]:
       _[1]=x+(i)*y



Quote:
> Thank you


If the given code produces something different from the given answer, please let us know your Singular version and also the version of primdec.lib.

Quote:
> Alberto Damiano


Best regards,

_________________
Viktor Levandovskyy


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