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

## Synopsis

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

## 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 .