Module: sage.groups.perm_gps.permgroup_morphism
Author: David Joyner (2006-03-21): first version
sage: G = CyclicPermutationGroup(4) sage: gens = G.gens() sage: H = DihedralGroup(4) sage: g = G([(1,2,3,4)]); g (1,2,3,4) sage: phi = PermutationGroupMorphism_im_gens( G, H, gens, gens) sage: phi.image(G) 'Group([ (1,2,3,4) ])' sage: phi.kernel() Group(()) sage: phi.image(g) '(1,2,3,4)' sage: phi(g) '(1,2,3,4)' sage: phi.range() Dihedral group of order 8 as a permutation group sage: phi.codomain() Dihedral group of order 8 as a permutation group sage: phi.domain() Cyclic group of order 4 as a permutation group
Module-level Functions
x) |
Put a permutation in Gap format, as a string.
f) |
Class: PermutationGroupMap
self, parent) |
Special Functions: _repr_type
Class: PermutationGroupMorphism
sage: G = CyclicPermutationGroup(4) sage: gens = G.gens() sage: H = DihedralGroup(4) sage: g = G([(1,3),(2,4)]); g (1,3)(2,4) sage: phi = PermutationGroupMorphism_im_gens( G, H, gens, gens) sage: phi Homomorphism : Cyclic group of order 4 as a permutation group --> Dihedral group of order 8 as a permutation group sage: phi(g) '(1,3)(2,4)' sage: gens1 = G.gens() sage: gens2 = ((4,3,2,1),) sage: phi = PermutationGroupMorphism_im_gens( G, G, gens1, gens2) sage: g = G([(1,2,3,4)]); g (1,2,3,4) sage: phi(g) '(1,4,3,2)'
AUTHOR: David Joyner (2-2006)
self, G, H, gensG, imgsH) |
Functions: codomain,
domain,
image,
kernel,
range
self, J) |
J must be a subgroup of G. Computes the subgroup of H which is the image of J.
Special Functions: __call__,
__repr__,
__str__,
_latex_
self, g) |
Some python code for wrapping GAP's Images function but only for permutation groups. Returns an error if g is not in G.
sage: G = CyclicPermutationGroup(4) sage: gens = G.gens() sage: H = DihedralGroup(4) sage: phi = PermutationGroupMorphism_im_gens( G, H, gens, gens) sage: g = G([(1,3),(2,4)]); g (1,3)(2,4) sage: phi(g) '(1,3)(2,4)'
Class: PermutationGroupMorphism_from_gap
Basic syntax:
PermutationGroupMorphism_from_gap(domain_group, range_group,'phi:=gap_hom_command;','phi') And don't forget the line: from sage.groups.perm_gps.permgroup_morphism import PermutationGroupMorphism_from_gap to your program.
self, G, H, gap_hom_str, [name=phi]) |
Functions: codomain,
domain,
image,
kernel,
range
self, J) |
J must be a subgroup of G. Computes the subgroup of H which is the image of J.
Special Functions: __call__,
__repr__,
__str__,
_latex_
self, g) |
Some python code for wrapping GAP's Images function but only for permutation groups. Returns an error if g is not in G.
Class: PermutationGroupMorphism_id
self, X) |
Special Functions: _repr_defn
Class: PermutationGroupMorphism_im_gens
sage: G = CyclicPermutationGroup(4) sage: gens = G.gens() sage: H = DihedralGroup(4) sage: g = G([(1,3),(2,4)]); g (1,3)(2,4) sage: phi = PermutationGroupMorphism_im_gens( G, H, gens, gens) sage: phi Homomorphism : Cyclic group of order 4 as a permutation group --> Dihedral group of order 8 as a permutation group sage: phi(g) '(1,3)(2,4)' sage: gens1 = G.gens() sage: gens2 = ((4,3,2,1),) sage: phi = PermutationGroupMorphism_im_gens( G, G, gens1, gens2) sage: g = G([(1,2,3,4)]); g (1,2,3,4) sage: phi(g) '(1,4,3,2)'
AUTHOR: David Joyner (2-2006)
self, G, H, gensG, imgsH) |
Functions: codomain,
domain,
image,
kernel,
range
self, J) |
J must be a subgroup of G. Computes the subgroup of H which is the image of J.
Special Functions: __call__,
__repr__,
__str__,
_latex_
self, g) |
Some python code for wrapping GAP's Images function but only for permutation groups. Returns an error if g is not in G.
sage: G = CyclicPermutationGroup(4) sage: gens = G.gens() sage: H = DihedralGroup(4) sage: phi = PermutationGroupMorphism_im_gens( G, H, gens, gens) sage: g = G([(1,3),(2,4)]); g (1,3)(2,4) sage: phi(g) '(1,3)(2,4)'
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