Module: sage.groups.group
Base class for groups
Class: AbelianGroup
Functions: is_abelian
) |
Return True.
Class: AlgebraicGroup
Class: FiniteGroup
Functions: cayley_graph,
is_finite
) |
Returns the cayley graph for this finite group, as a SAGE DiGraph object. To plot the graph with with different colors
sage: D4 = DihedralGroup(4); D4 Dihedral group of order 8 as a permutation group sage: G = D4.cayley_graph() sage: show(G, color_by_label=True, edge_labels=True) sage: A5 = AlternatingGroup(5); A5 Alternating group of order 5!/2 as a permutation group sage: G = A5.cayley_graph() sage: G.show3d(color_by_label=True, edge_size=0.01, edge_size2=0.02, vertex_size=0.03) sage: G.show3d(vertex_size=0.03, edge_size=0.01, edge_size2=0.02, vertex_colors={(1,1,1):G.vertices()}, bgcolor=(0,0,0), color_by_label=True, xres=700, yres=700, iterations=200) # long time (less than a minute)
sage: s1 = SymmetricGroup(1); s = s1.cayley_graph(); s.vertices() [()]
Author Log:
) |
Return True.
Class: Group
Functions: category,
is_abelian,
is_atomic_repr,
is_finite,
is_multiplicative,
order,
quotient,
random_element
) |
The category of all groups
) |
Return True if this group is abelian.
) |
True if the elements of this group have atomic string representations. For example, integers are atomic but polynomials are not.
) |
Returns True if this group is finite.
) |
Returns True if the group operation is given by * (rather than +).
Override for additive groups.
) |
Returns the number of elements of this group, which is either a positive integer or infinity.
) |
Return the quotient of this group by the normal subgroup
.
) |
Return a random element of this group.
Special Functions: __call__,
__contains__,
__init__
) |
Coerce x into this group.
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