redundant ideal generator

[bcwhite]

I'm using Macaulay to examine rings of the form k + x^n k[[x]].
I started by creating the ring R = k + x^3 k[[x]]. I constructed this in Macaulay by taking k[[x_3,x_4,x_5]], where x_n is meant to represent x^n, and modding out by the ideal

I=ideal(x_3^3-x_4*x_5,x_4^2-x_3*x_5,x_5^2-x_3^2*x^4). 

When I computed the colon ideal A_1 : A_2, where

A_1=ideal(x_3,x_5)  
A_2=ideal(x_3^2,x_3*x_4)

I got the result

                 2   2
o7 = ideal (x , x , x ). 
             4   5   3

This appears to be a bug, since:

i9 : x_4*x_3^2

      2
o9 = x
      5

which shows that (x_5)^2 is a redundant generator for the ideal. I hoped that Macaulay would return the minimum generating set of the ideal, which it generally does successfully. Is this actually the intended behavior, or is Macaulay failing to detect that the one generator can be found from the others?

This is not a functional error, since the ideal returned was the correct ideal, simply with a redundant generator.

[DanGrayson]

I think you'll have better luck if you make the ring homogeneous, with

R =
QQ[x_3,x_4,x_5,Degrees=>{3,4,5}]/ideal(x_3^3-x_4_x_5,x_4^2-x_3_x_5,x_5^2-x_3^2*x_4)

On Wed, May 29, 2013 at 5:32 PM, bcwhite notifications@github.com wrote:

I'm using Macaulay to examine rings of the form k + x^n k[[x]].
I started by creating the ring R = k + x^3 k[[x]]. I constructed this in
Macaulay by taking k[[x_3,x_4,x_5]], where x_n is meant to represent x^n,
and modding out by the ideal

I=ideal(x_3^3-x_4_x_5,x_4^2-x_3_x_5,x_5^2-x_3^2*x^4).

When I computed the colon ideal A_1 : A_2, where

A_1=ideal(x_3,x_5)
A_2=ideal(x_3^2,x_3*x_4)

I got the result

             2   2

o7 = ideal (x , x , x ).
4 5 3

This appears to be a bug, since:

i9 : x_4*x_3^2

  2

o9 = x
5

which shows that (x_5)^2 is a redundant generator for the ideal. I hoped
that Macaulay would return the minimum generating set of the ideal, which
it generally does successfully. Is this actually the intended behavior, or
is Macaulay failing to detect that the one generator can be found from the
others?

This is not a functional error, since the ideal returned was the correct
ideal, simply with a redundant generator.

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Reply to this email directly or view it on GitHubhttps://github.com//issues/34
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[DanGrayson]

Making the ring homogeneous removes the redundant generator, so I'm closing this issue. Feel free to reopen if there is still a problem.