passagemath-groups

10.8.4 verified Sat May 09 auth: no python

passagemath-groups is a component of the passagemath environment providing group theory and invariant theory functionality, including permutation groups, matrix groups, and algebraic groups. It relies on GAP and libgap. Current version 10.8.4, requiring Python >=3.11 and <3.15. Release cadence follows passagemath releases, typically one or two per year.

pip install passagemath-groups passagemath-sage

Common errors

error ModuleNotFoundError: No module named 'sage' ↓

cause passagemath-sage or sage package not installed.

fix

pip install passagemath-sage

error ImportError: cannot import name 'PermutationGroup' from 'sage' ↓

cause Trying to import directly from sage instead of submodule.

fix

Use from sage.groups.perm_gps.permgroup import PermutationGroup

error RuntimeError: You must install the GAP package 'gap-core' to use this functionality. ↓

cause GAP not installed.

fix

pip install gap-core

Warnings

breaking Python 3.15 not yet supported; passagemath 10.x requires Python 3.11-3.14. ↓

fix Use Python 3.11, 3.12, or 3.14 (if available).

gotcha Do not import directly from passagemath.groups; the package is a namespace only. Use sage submodules instead. ↓

fix Use from sage.groups... import ...

deprecated Some named groups moved or renamed in passagemath 10.x compared to SageMath 9.x. ↓

fix Check sage.groups.perm_gps.permgroup_named for current names.

Imports

PermutationGroup

wrong

from passagemath.groups import PermutationGroup

correct

from sage.groups.perm_gps.permgroup import PermutationGroup

passagemath does not expose group classes at top-level; import from sage submodules.

SymmetricGroup

wrong

from passagemath.groups.perm_gps import SymmetricGroup

correct

from sage.groups.perm_gps.permgroup_named import SymmetricGroup

Named groups live in permgroup_named module.

Quickstart

Create a permutation group on 4 points and compute its order.

from sage.all import *
from sage.groups.perm_gps.permgroup import PermutationGroup
G = PermutationGroup([(1,2), (1,3,4)])
print(G.order())