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

Synopsis

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.