\(\langle 1 \rangle \to \begin{pmatrix} -3 & -1 & -1 \\ -1 & -3 & 1 \\ -1 & 1 & -3 \end{pmatrix} \oplus \langle 1 \rangle^{2}\)
Column \(j\) of each matrix gives \(\varphi(e_j)\) in the chosen basis of the target; the subdivisions separate orthogonal summands of the source (columns) and of the target (rows).
Notes
The embeddings of latticedb.summands: each summand of
the source maps by \(x \mapsto (x, \ldots,
x)\) into a set of orthogonal summands of the target.
Diagonal into the summands \(\{2\}\)
Summand \(j\) of the source maps by \(x \mapsto (x, \ldots, x)\) into the orthogonal summands of the target in set \(j\), which are counted from 1 in the order of the basis.
{"matrix": [
[0],
[0],
[0],
[1],
[0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{2, 3\}\)
A morphism \(\langle 1 \rangle(2) \to \begin{pmatrix} -3 & -1 & -1 \\ -1 & -3 & 1 \\ -1 & 1 & -3 \end{pmatrix} \oplus \langle 1 \rangle^{2}\): \(b_T(\varphi x, \varphi y) = 2 \, b_S(x, y)\).
Summand \(j\) of the source maps by \(x \mapsto (x, \ldots, x)\) into the orthogonal summands of the target in set \(j\), which are counted from 1 in the order of the basis.
{"matrix": [
[0],
[0],
[0],
[1],
[1]
],
"row_subdivisions": [],
"column_subdivisions": []}