Combined orderings
MickeyMouseII · Wed Sep 25, 2019 10:19 am
Dear members of the forum,
I am currently facing the following issue. I am working on a relative projective
space IP^r x IC^n, i.e. in the ring IC[s_0,...,s_r][x_1,...,x_n], where I consider
the s-variables as global, homogeneous variables, and the x-variables as local,
affine variables. This viewpoint suggests a mixed ordering such as
dp(r+1),ds(n).
For the relative projective space it is important, to work with the s-degree,
which is realized by the weights (1....,1,0,...,0), with r+1 ones and n zeroes.
I will say that an element a of S is s-homogeneous, when it is homogeneous
with respect to these weights.
Now, I am given an ideal I in S, whose generators are s-homogeneous and
I would like to compute a free resolution, which preserves the s-homogeneity.
Unfortunately, with the previously mentioned ordering, the command
mres(I,0)
does not produce a resolution with matrices with s-homogeneous entries.
Do you have any suggestions? That would be great!
Thank you very much,
MickeyMouseII
I am currently facing the following issue. I am working on a relative projective
space IP^r x IC^n, i.e. in the ring IC[s_0,...,s_r][x_1,...,x_n], where I consider
the s-variables as global, homogeneous variables, and the x-variables as local,
affine variables. This viewpoint suggests a mixed ordering such as
dp(r+1),ds(n).
For the relative projective space it is important, to work with the s-degree,
which is realized by the weights (1....,1,0,...,0), with r+1 ones and n zeroes.
I will say that an element a of S is s-homogeneous, when it is homogeneous
with respect to these weights.
Now, I am given an ideal I in S, whose generators are s-homogeneous and
I would like to compute a free resolution, which preserves the s-homogeneity.
Unfortunately, with the previously mentioned ordering, the command
mres(I,0)
does not produce a resolution with matrices with s-homogeneous entries.
Do you have any suggestions? That would be great!
Thank you very much,
MickeyMouseII