roosIsotopes -- Creates hashtable of Jan-Erik Roos' quadratic "isotopes"

Synopsis

Usage:

H = depthZeroTable ()
Outputs:
- H, a hash table,

Description

This outputs the examples in Tables B,C,D of Roos' quadratic "isotopes" (see Main Theorem in "Homological properties of the homology algebra of the Koszul complex of a local ring: Examples and questions", Journal of Algebra 465 (2016) 399-436). The key is the alphanumeric name provided by Roos. While these have the same bigraded Poincar\'e series as their corresponding example in Tables 3-7, they have different homology algebra (called "HKR" in Roos). These all have depth zero. The coefficient field is QQ.

i1 : roosIsotopes

                                       2             2   2    2
o1 = HashTable{"46va" => ideal (x*z + u , x*y, x*u, x , y  + z  + z*u)                                          }
                                 2    2    2                             2
               "57v2" => ideal (x  + y  + z , x*y, x*u, y*z, z*u, x*z + u )
                                 2    2                        2
               "59va" => ideal (x  - y , x*y, y*z, z*u, x*z + u , x*u)
                                 2          2                  2
               "62va" => ideal (x  + y*z + u , y*u, z*u, x*y, z , x*u)
                                 2              2        2    2
               "63ne" => ideal (x , x*y, x*z + u , x*u, y  + z , z*u)
                                 2                        2
               "63v4" => ideal (y , x*z + y*u, z*u, x*y, z , x*u)
                                 2                  2         2   2    2
               "63v8" => ideal (x , x*y, x*u, y*u, z , x*z + u , y  + z  + z*u)
                                            2                  2
               "66v5" => ideal (x*y, x*z + u , x*u, y*u, z*u, z )
                                2                  2   2    2
               "68v" => ideal (x , x*y, x*z, x*u, u , y  + z  + z*u)
                                 2    2             2        2
               "71v4" => ideal (x  + u , x*y, x*u, y , y*z, z , z*u)
                                 2         2               2   2   2                   2
               "71v5" => ideal (x  + x*y, x  + y*z, x*y + y , z , z , x*u, z*u, x*z + u )
                                 2   2   2         2
               "71v7" => ideal (x , y , z , x*z + u , x*u, y*z, z*u)
                                  2   2    2                        2
               "71v16" => ideal (x , y  + z , x*y, y*z, z*u, x*z + u , x*u)
                                       2   2         2         2         2                    2               2
               "72v1" => ideal (x*u + u , x  + x*y, y  + x*u, y  + y*z, y  + y*z, y*u + z*u, z  + x*u, z*u + u )
                                       2                         2        2    2
               "72v2e" => ideal (y*z, x  + x*y, x*z + y*u, x*u, z , z*u, x  + u )
                                 2                   2             2
               "75v1" => ideal (y , x*z, y*z + x*u, z , y*u, z*u, u )
                                            2              2             2
               "75v2" => ideal (x*y, x*z + u , x*u, y*z + u , y*u, z*u, z )
                                 2   2   2   2
               "78v1" => ideal (x , y , z , u , x*y, x*z, x*u, y*u)
                                                       2   2         2   2
               "78v2e" => ideal (x*u, x*z + y*u, y*z, x , y , x*y + z , u , z*u)
                                                       2   2         2   2
               "78v3v" => ideal (x*u, x*z + y*u, y*z, x , y , x*z + z , u , z*u)
                                 2   2   2   2
               "81va" => ideal (x , y , z , u , x*y, x*z, x*u, y*u, z*u)

o1 : HashTable

For the programmer

The object roosIsotopes is a hash table.