Atlas of Lie Groups and Representations

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atlas Library · Script File

cell_graph.at

Graph on W-cells of the block of p, numbered as in block_of(p) and W_cells(p).
Similar to builtin print_W_cells@Block and print_W_cells@(RealForm,RealForm)
but using the ordering of parameters from block_of@Param
Source
atlas-scripts/cell_graph.at (75 lines)
Definitions
7
Loads
Loaded by
all.at

Definitions in source order

W_cell_graph_data

L9W_cell_graph_data (Param p) = ([[int]],[[int]])
(cells, induced graph): cells[c] = members of cell c (block_of(p) numbering),
induced[c] = cells d<>c reached by an edge leaving cell c

cell_closure

L19cell_closure ([[int]] induced) = [[int]]
transitive closure of an induced graph on cells (edges go to lower numbers)

W_cell_order

L29W_cell_order (Param p) = [[int]]
transitive closure of the induced graph: all cells reachable from c

cell_reduction

L43cell_reduction ([[int]] induced) = [[int]]
transitive reduction (Hasse diagram) of the induced graph: keep the edge
c->d unless d is reachable from c through another cell

W_cell_graph_dot

L60W_cell_graph_dot (Param p) = string
graphviz file for the graph on cells of block_of(p): one node per cell,
labelled by its number and size, edges the Hasse diagram of the order
(cell 0 at the bottom). W_cell_graph prints the text (no prints needed),
W_cell_graph_dot returns it as a string. Typical usage:
> file.dot W_cell_graph(p)
in console:
dot -Tpdf -o file.pdf file.dot

W_cell_graph

L75W_cell_graph (Param p) = void

Generated from atlas-scripts at commit 648506c (2026-10-13).