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

## Synopsis

• Usage:
H = depthZeroTable ()
• Outputs:
• H, ,

## 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 .