Query regarding Trim of an ideal

[Shrikant Shekhar 1910404]

Dear all,

In the $R = QQ[x,y,z]/ideal(x^4-y^2, x^4-z^2, x*y, x*z, y*z)$, I am considering the ideals m = ideal(x,y,z); m2 = trim (m*m). I am getting output "ideal (z^2 , x^2 )" for  trim (m*m). But in the ring R, we have z^2=x^2*x^2. 

So my question is why trim(m*m) is not the ideal(x^2)?

I am attaching a screenshot for your reference. Thanks for your kind help.

[jche...@gmail.com]

The basic issue is that the ring R is not (standard) graded. A lot of minimization routines in M2, like trim, prune, etc. may behave unexpectedly for objects that are not graded. In this particular case though there is a nonstandard grading (namely deg(y) = deg(z) = 2*deg(x)), and with this grading trim(m*m) will give the expected answer (x^2).

Justin

i1 : R = QQ[x,y,z, Degrees => {1,2,2}]/ideal(x^4-y^2, x^4-z^2, x*y, x*z, y*z)

o1 = R

o1 : QuotientRing

i2 : isHomogeneous R

o2 = true

i3 : m = ideal(x,y,z); trim(m*m)

o3 : Ideal of R

                    2
o4 = ideal x

o4 : Ideal of R