\(\langle 1 \rangle \oplus \langle 2 \rangle^{2} \to \mathrm{I}_{25,0}\)
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 \(\{1\} \sqcup \{2, 3\} \sqcup \{4, 5\}\)
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],
[0, 1, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 1],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[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 \(\{1, 2\} \sqcup \{3, 4, 5, 6\} \sqcup \{7, 8, 9, 10\}\)
A morphism \(\langle 1 \rangle \oplus \langle 2 \rangle^{2}(2) \to \mathrm{I}_{25,0}\): \(b_T(\varphi x, \varphi y) = 2 \, b_S(x, y)\).
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, 0],
[1, 0, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[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 \(\{1, 2, 3\} \sqcup \{4, 5, 6, 7, 8, 9\} \sqcup \{10, 11, 12, 13, 14, 15\}\)
A morphism \(\langle 1 \rangle \oplus \langle 2 \rangle^{2}(3) \to \mathrm{I}_{25,0}\): \(b_T(\varphi x, \varphi y) = 3 \, b_S(x, y)\).
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, 0],
[1, 0, 0],
[1, 0, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[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 \(\{1, 2, 3, 4\} \sqcup \{5, 6, 7, 8, 9, 10, 11, 12\} \sqcup \{13, 14, 15, 16, 17, 18, 19, 20\}\)
A morphism \(\langle 1 \rangle \oplus \langle 2 \rangle^{2}(4) \to \mathrm{I}_{25,0}\): \(b_T(\varphi x, \varphi y) = 4 \, b_S(x, y)\).
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, 0],
[1, 0, 0],
[1, 0, 0],
[1, 0, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{1, 2, 3, 4, 5\} \sqcup \{6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} \sqcup \{16, 17, 18, 19, 20, 21, 22, 23, 24, 25\}\)
A morphism \(\langle 1 \rangle \oplus \langle 2 \rangle^{2}(5) \to \mathrm{I}_{25,0}\): \(b_T(\varphi x, \varphi y) = 5 \, b_S(x, y)\).
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, 0],
[1, 0, 0],
[1, 0, 0],
[1, 0, 0],
[1, 0, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1],
[0, 0, 1]
],
"row_subdivisions": [],
"column_subdivisions": []}