Morphisms 02AJ \(\to\) 0254

\(\langle 1 \rangle \oplus \langle 2 \rangle \oplus \langle 3 \rangle \to \mathrm{I}_{20,0}\)

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 \(\{1\} \sqcup \{2, 3\} \sqcup \{4, 5, 6\}\)

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.

\[\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{array}\right)\]
{"matrix": [
  [1, 0, 0],
  [0, 1, 0],
  [0, 1, 0],
  [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]
],
 "row_subdivisions": [],
 "column_subdivisions": []}

Diagonal into the summands \(\{1, 2\} \sqcup \{3, 4, 5, 6\} \sqcup \{7, 8, 9, 10, 11, 12\}\)

A morphism \(\langle 1 \rangle \oplus \langle 2 \rangle \oplus \langle 3 \rangle(2) \to \mathrm{I}_{20,0}\): \(b_T(\varphi x, \varphi y) = 2 \, b_S(x, y)\).

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.

\[\left(\begin{array}{rrr} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{array}\right)\]
{"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, 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]
],
 "row_subdivisions": [],
 "column_subdivisions": []}

Diagonal into the summands \(\{1, 2, 3\} \sqcup \{4, 5, 6, 7, 8, 9\} \sqcup \{10, 11, 12, 13, 14, 15, 16, 17, 18\}\)

A morphism \(\langle 1 \rangle \oplus \langle 2 \rangle \oplus \langle 3 \rangle(3) \to \mathrm{I}_{20,0}\): \(b_T(\varphi x, \varphi y) = 3 \, b_S(x, y)\).

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.

\[\left(\begin{array}{rrr} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{array}\right)\]
{"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, 1],
  [0, 0, 1],
  [0, 0, 1],
  [0, 0, 0],
  [0, 0, 0]
],
 "row_subdivisions": [],
 "column_subdivisions": []}