Use precomputed table of marks for functorial composition of species#42443
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mwhansen wants to merge 2 commits into
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Use precomputed table of marks for functorial composition of species#42443mwhansen wants to merge 2 commits into
mwhansen wants to merge 2 commits into
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The subgroup-based algorithm for functorial composition of species computes the table of marks of the symmetric group `S_n` for each coefficient. Computing it from the group is expensive and quickly becomes the limiting factor (and is infeasible past degree ~10). GAP's `tomlib` package ships precomputed tables of marks for the symmetric groups, which are essentially free to look up and available for a much larger range of degrees. Add a cached helper `_table_of_marks_symmetric_group` that uses the library table when available and falls back to computing it from the group otherwise, and use it in `_coefficient_subgroups`.
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`libgap.TableOfMarks("Sn")` raises a GAPError when the GAP tomlib
package is not installed, rather than returning `fail`. Catch the
error so we fall back to computing the table from the symmetric group,
as we already do for degrees that are not in the library.
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Summary
The subgroup-based algorithm for functorial composition of species$S_n$ for every coefficient.
(
LazyCombinatorialSpeciesElement.functorial_composition(..., algorithm="subgroups"))computes the table of marks of the symmetric group
Currently this is computed from the group via
libgap.TableOfMarks(S_n), which isexpensive and quickly becomes the limiting factor — it is effectively infeasible
past degree ~10.
GAP's
tomlibpackage ships precomputed tables of marks for the symmetric groups,which are essentially free to look up and available for a much larger range of degrees.
Measured cost of obtaining the table of marks of$S_n$ :
tomliblookupThis PR adds a cached helper
${1, \dots, n}$ , and
_table_of_marks_symmetric_group(n)that looks up thelibrary table when available and falls back to computing it from the group otherwise,
and uses it in
_coefficient_subgroups. The library tables are representation-compatiblewith the existing code (their underlying group is the natural symmetric group on
RepresentativeTomreturns subgroups of it), so the change istransparent.
Effect
feasible degree for the
"subgroups"algorithm from ~10 to ~13.sage/rings/lazy_species.pypass, and thecoefficients are identical to those computed from the group.
Notes
tomlibcovers a range of small degrees (roughlyTableOfMarksreturnsfailand we fall back to computing from the group, so there isno behavioural regression for any degree.