\(\mathrm{I}_{2,0} \to \mathrm{I}_{11,0}\)
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 \(\{1\} \sqcup \{2\}\)
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": [
[1, 0],
[0, 1],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{1, 2\} \sqcup \{3, 4\}\)
A morphism \(\mathrm{I}_{2,0}(2) \to \mathrm{I}_{11,0}\): \(b_T(\varphi x, \varphi y) = 2 \, b_S(x, y)\).
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": [
[1, 0],
[1, 0],
[0, 1],
[0, 1],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{1, 2, 3\} \sqcup \{4, 5, 6\}\)
A morphism \(\mathrm{I}_{2,0}(3) \to \mathrm{I}_{11,0}\): \(b_T(\varphi x, \varphi y) = 3 \, b_S(x, y)\).
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": [
[1, 0],
[1, 0],
[1, 0],
[0, 1],
[0, 1],
[0, 1],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{1, 2, 3, 4\} \sqcup \{5, 6, 7, 8\}\)
A morphism \(\mathrm{I}_{2,0}(4) \to \mathrm{I}_{11,0}\): \(b_T(\varphi x, \varphi y) = 4 \, b_S(x, y)\).
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": [
[1, 0],
[1, 0],
[1, 0],
[1, 0],
[0, 1],
[0, 1],
[0, 1],
[0, 1],
[0, 0],
[0, 0],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{1, 2, 3, 4, 5\} \sqcup \{6, 7, 8, 9, 10\}\)
A morphism \(\mathrm{I}_{2,0}(5) \to \mathrm{I}_{11,0}\): \(b_T(\varphi x, \varphi y) = 5 \, b_S(x, y)\).
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": [
[1, 0],
[1, 0],
[1, 0],
[1, 0],
[1, 0],
[0, 1],
[0, 1],
[0, 1],
[0, 1],
[0, 1],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}