Sage comes with GAP 4.4.10 for computational discrete mathematics, especially group theory.
Here's an example of GAP's IdGroup
function, which uses the
optional small groups database that has to be installed separately, as
explained below.
sage: G = gap('Group((1,2,3)(4,5), (3,4))') sage: G Group( [ (1,2,3)(4,5), (3,4) ] ) sage: G.Center() Group( () ) sage: G.IdGroup() # requires optional database_gap package [ 120, 34 ] sage: G.Order() 120
We can do the same computation in Sage without explicitly invoking the GAP interface as follows:
sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]]) sage: G.center() Permutation Group with generators [()] sage: G.group_id() # requires optional database_gap package [120, 34] sage: n = G.order(); n 120
Note:
For some GAP functionality, you should install two optional
Sage packages.
Type sage -optional
for a list and choose
the one that looks like gap_packages-x.y.z
, then type
sage -i gap_packages-x.y.z
. Do the same
for database_gap-x.y.z
.
Some non-GPL'd GAP packages may be installed by downloading them
from the GAP web site [GAPkg],
and unpacking them in SAGE_ROOT/local/lib/gap-4.4.10/pkg
.
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