SyzygyData

Current Betti Table Entry:

$$q=0$$

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 · · · ·

Schur Decomposition

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 · · ·

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!