SyzygyData

Current Betti Table Entry:

\(n=2\)

\(d=2\)

\(b=0\)

\(p=0\)

\(q=0\)

0 1 2 3
0 1 · · ·
1 · 6 8 3
2 · · · ·
0 1 2 3
0 (0,0,0) · · ·
1 · (2,2,0) (3,2,1) (3,3,2)
2 · · · ·
0 1 2 3
0 1 · · ·
1 · 1 1 1
2 · · · ·
0 1 2 3
0 1 · · ·
1 · 1 1 1
2 · · · ·

Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{0,\lambda}(2,0;2)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{0,0}(2,0;2)\). Here \(\lambda\) is the weight \((\lambda_0,\lambda_1,\lambda_2)\) where \(\lambda_2\) is determined by the fact that \(|\lambda|\) equals \(d(p+q)+b\). The dominant weights are displayed in green. Click on an entry for more info!

-1 0 1
-1 · · ·
0 · 1 ·
1 · · ·

Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{0,\textbf{a}}(2,0;2)\). Here \(\textbf{a}\) is the weight \((a_0,a_1,a_2)\) where \(a_2\) is determined by the fact that \(|\textbf{a}|\) equals \(d(p+q)+b\). Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!

0 1
0 1 ·
1 · ·