lexsegmentIdeal -- Create a lexsegment ideal.

Consider a polynomial ring in N variables. For any hilbert function, there is a unique lexsegment ideal. Furthermore, this ideal has graded Betti numbers that are at least as large as those of any other ideal with that hilbert function.

The Hilbert function of a lexsegment ideal is determined by the values in the degrees that are at and below the largest degree of any generator. As a result, it makes sense to specify the Hilbert function through the largest degree of a generator and then truncate the rest of the function.

This function returns the lexsegment ideal with the given Hilbert function.

Note: this method is significantly faster than the similar lexIdeal from the package LexIdeals.

i1 : lexsegmentIdeal (QQ[x_1..x_4], {1,2,3,3,3,3})

                     3
o1 = ideal (x , x , x )
             1   2   3

o1 : Ideal of QQ[x , x , x , x ]
                  1   2   3   4

i2 : lexsegmentIdeal (QQ[x_1..x_4], {1,2,3,3,3,3,0}) --Artinian

                     3   2 4     5   6
o2 = ideal (x , x , x , x x , x x , x )
             1   2   3   3 4   3 4   4

o2 : Ideal of QQ[x , x , x , x ]
                  1   2   3   4

i3 : lexsegmentIdeal (QQ[x_1..x_5], {1,5,15,35})

o3 = ideal 0

o3 : Ideal of QQ[x , x , x , x , x ]
                  1   2   3   4   5