redundant ideal generator about m2 HOT 2 CLOSED

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 [email protected] 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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from m2.

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

from m2.