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# roosTable -- Creates hashtable of Jan-Erik Roos' examples of quadratic ideals

- Usage:
    `H = roosTable ()`
- Outputs:
  - H, a hash table,

## Description

This is based on Main Theorem and Tables 3-7 in "Homological properties of the homology algebra of the Koszul complex of a local ring: Examples and questions" by Jan-Erik Roos, Journal of Algebra 465 (2016) 399-436. The ideals in this table exemplify 83 known cases of bi-graded Poincar\'e series of quadratic ideals of embedding dimension four in characteristic zero. The coefficient field is QQ.

    i1 : roosTable

    o1 = HashTable{1 => ideal 0                                                              }
                               2
                   2 => ideal x
                                2   2
                   3 => ideal (x , y )
                                2
                   4 => ideal (x , x*y)
                                2   2   2
                   5 => ideal (x , y , z )
                                2   2
                   6 => ideal (x , y  + x*z, y*z)
                                2    2   2    2
                   7 => ideal (x  + y , z  + u , x*z + y*u)
                                2   2
                   8 => ideal (x , y , x*z)
                                2        2
                   9 => ideal (x , x*y, y )
                                 2
                   10 => ideal (x , x*y, x*z)
                                 2   2   2   2
                   11 => ideal (x , y , z , u )
                                 2         2         2               2
                   12 => ideal (x  + x*y, y  + x*u, z  + x*u, z*u + u )
                                 2    2    2   2
                   13 => ideal (x  + z  + u , y , x*z, y*u + z*u)
                                      2   2    2
                   14 => ideal (x*z, y , z  + u , y*u + z*u)
                                      2         2
                   15 => ideal (x*z, y , y*z + u , y*u + z*u)
                                       2         2
                   16 => ideal (x*y + z  + y*u, y , y*u + z*u, x*z)
                                                 2
                   17 => ideal (x*z, y*z + x*u, y , y*u + z*u)
                                 2   2   2
                   18 => ideal (x , y , z , y*u)
                                      2              2
                   19 => ideal (x*z, y , y*u + z*u, u )
                                      2   2
                   20 => ideal (x*z, y , z  + y*u, y*u + z*u)
                                      2   2
                   21 => ideal (x*z, y , z , y*u + z*u)
                                 2                         2
                   22 => ideal (x  + x*y, x*u, x*z + y*u, y )
                                           2   2
                   23 => ideal (x*z, x*u, y , z )
                                      2         2
                   24 => ideal (x*z, y , y*z + z , y*u + z*u)
                                 2             2
                   25 => ideal (x , x*y, x*z, u )
                                      2
                   26 => ideal (x*z, y , y*u, z*u)
                                           2
                   27 => ideal (x*y, x*z, y , y*z)
                                 2
                   28 => ideal (x , x*y, x*z, x*u)
                                 2         2         2               2
                   29 => ideal (x  + x*y, y  + x*u, z  + x*u, z*u + u , y*z)
                                       2        2    2    2   2
                   30 => ideal (x*y + u , x*z, x  + z  + u , y , y*u + z*u)
                                 2    2   2    2   2    2                2
                   31 => ideal (x  - y , y  - z , z  - u , x*z + y*u, - x  + x*y - y*z + x*u)
                                 2    2        2              2
                   32 => ideal (x  + z , x*z, y , y*u + z*u, u )
                                 2         2         2         2               2
                   33 => ideal (x  + x*y, y  + y*z, y  + x*u, z  + x*u, z*u + u )
                                 2                2   2        2    2    2
                   34 => ideal (x  + x*y + y*u + u , y , x*z, x  + z  + u , y*u + z*u)
                                 2    2    2   2
                   35 => ideal (x  + z  + u , y , x*z, x*y + y*z + y*u, y*u + z*u)
                                 2    2   2   2
                   36 => ideal (x  + y , z , u , y*z - y*u, x*z + z*u)
                                 2   2
                   37 => ideal (x , y , x*y - z*u, y*z - x*u, x*z - y*z - x*u + y*u)
                                 2   2   2        2
                   38 => ideal (x , y , z , z*u, u )
                                 2          2         2
                   39 => ideal (x  + y*z + u , x*z + z  + y*u, x*y, x*u, z*u)
                                 2           2         2    2   2    2
                   40 => ideal (x  - x*u, - y  + x*u, y  - z , z  - u , x*z + y*u)
                                      2   2        2
                   41 => ideal (x*y, y , z , z*u, u )
                                 2              2
                   42 => ideal (x  + x*y, z*u, y , x*u, x*z + y*u)
                                 2   2             2
                   43 => ideal (x , y , y*z, z*u, u )
                                           2              2    2
                   44 => ideal (x*z, y*z, y , y*u + z*u, z  + u )
                                                  2                    2
                   45 => ideal (x*y + y*z, x*y + z  + y*u, y*u + z*u, y , x*z)
                                 2                  2
                   46 => ideal (x , x*y, y*z, z*u, u )
                                 2         2                     2
                   47 => ideal (x  + x*y, y , x*u, x*z + y*u, - x  + x*z - y*z)
                                      2                    2
                   48 => ideal (x*y, z  + y*u, y*u + z*u, y , x*z)
                                      2   2
                   49 => ideal (x*z, y , z , y*u, z*u)
                                 2             2   2
                   50 => ideal (x , x*y, x*z, y , z )
                                                      2
                   51 => ideal (x*y, x*z, y*z + x*u, z , z*u)
                                 2             2
                   52 => ideal (x , x*y, x*z, y , y*z)
                                 2    2             2
                   53 => ideal (y  - u , x*z, y*z, z , z*u)
                                 2        2   2              2
                   54 => ideal (x , x*z, y , z , y*u + z*u, u )
                                 2                         2   2         2
                   55 => ideal (x  + x*y, x*z + y*u, x*u, y , z , z*u + u )
                                 2          2             2    2   2
                   56 => ideal (x  + x*z + u , x*y, x*u, x  - y , z , z*u)
                                 2          2        2                          2   2    2
                   57 => ideal (x  + y*z + u , x*u, x  + x*y, x*z + y*u, z*u + u , y  + z )
                                 2         2         2   2
                   58 => ideal (x  + x*y, x  + z*u, y , z , x*z + y*u, x*u)
                                 2    2             2
                   59 => ideal (x  - y , x*y, x*u, z , z*u, x*z + y*u)
                                 2          2                        2
                   60 => ideal (x  + y*z + u , x*z + y*u, z*u, x*y, z , x*u)
                                 2    2        2             2
                   61 => ideal (x  - y , x*y, z , x*u, z*u, u )
                                 2    2                        2
                   62 => ideal (x  - y , x*y, x*u, y*z + y*u, z , z*u)
                                 2             2   2
                   63 => ideal (x , x*y, x*u, y , z , z*u)
                                 2    2        2
                   64 => ideal (x  - y , x*y, z , x*u, y*u, z*u)
                                 2             2   2
                   65 => ideal (x , x*y, x*z, y , z  + y*u, y*u + z*u)
                                      2        2        2
                   66 => ideal (x*z, y , y*u, z , z*u, u )
                                           2        2
                   67 => ideal (x*y, x*z, y , y*u, z , z*u)
                                 2             2        2
                   68 => ideal (x , x*y, x*z, y , y*z, z )
                                 2                             2
                   69 => ideal (x , x*z, x*u, x*y - z*u, y*z, z )
                                 2        2      2
                   70 => ideal (x , x*y, x z*u, y , y*z)
                                 2   2   2   2
                   71 => ideal (x , y , z , u , x*y, z*u, y*z + x*u)
                                 2    2                  2
                   72 => ideal (x  - y , x*y, y*z, z*u, z , x*z + y*u, x*u)
                                 2   2   2   2
                   73 => ideal (x , y , z , u , z*u, y*u, x*u)
                                 2         2                       2
                   74 => ideal (x , x*y + z , y*z, x*u, y*u, z*u, u )
                                 2                  2        2
                   75 => ideal (x , x*y, x*z, x*u, y , y*z, u )
                                 2                  2
                   76 => ideal (x , x*y, x*z, x*u, z , z*u, y*u)
                                 2                  2
                   77 => ideal (x , x*y, x*z, x*u, y , y*z, y*u)
                                 2        2   2        2
                   78 => ideal (x , x*y, y , z , z*u, u , x*z + y*u, y*z - x*u)
                                 2                  2        2
                   79 => ideal (x , x*y, x*z, x*u, y , y*u, z , z*u)
                                 2             2             2
                   80 => ideal (x , x*y, x*z, y , y*z, y*u, z , z*u)
                                 2   2   2   2
                   81 => ideal (x , y , z , u , x*y, x*z, y*z - x*u, y*u, z*u)
                                 2                  2        2
                   82 => ideal (x , x*y, x*z, x*u, y , z*u, u , y*z, y*u)
                                 2   2   2   2
                   83 => ideal (x , y , z , u , x*y, x*z, x*u, y*z, y*u, z*u)

    o1 : HashTable

## For the programmer

The object roosTable is a hash table.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/QuadraticIdealExamplesByRoos.m2:243:0.