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