These are unitary matrices with entries in
.
AUTHORS:
EXAMPLES:
sage: G = SU(3,GF(5))
sage: G.order()
378000
sage: G
Special Unitary Group of degree 3 over Finite Field of size 5
sage: G._gap_init_()
'SU(3, 5)'
sage: G.random_element()
[4*a + 1 4*a + 4 a + 4]
[3*a + 3 3 3]
[ a + 2 4*a + 1 3*a + 3]
sage: G.base_ring()
Finite Field of size 5
sage: G.field_of_definition()
Finite Field in a of size 5^2
Return the general unitary group of degree n over the finite field F.
INPUT:
Note
This group is also available via groups.matrix.GU().
EXAMPLES:
sage: G = GU(3,GF(7)); G
General Unitary Group of degree 3 over Finite Field of size 7
sage: G.gens()
[
[ a 0 0]
[ 0 1 0]
[ 0 0 5*a],
[6*a 6 1]
[ 6 6 0]
[ 1 0 0]
]
sage: G = GU(2,QQ)
Traceback (most recent call last):
...
NotImplementedError: general unitary group only implemented over finite fields
sage: G = GU(3,GF(5), var='beta')
sage: G.gens()
[
[ beta 0 0]
[ 0 1 0]
[ 0 0 3*beta],
[4*beta 4 1]
[ 4 4 0]
[ 1 0 0]
]
TESTS:
sage: groups.matrix.GU(2, 3)
General Unitary Group of degree 2 over Finite Field of size 3
Bases: sage.groups.matrix_gps.unitary.UnitaryGroup_finite_field
INPUT:
Return the special unitary group of degree over
.
Note
This group is also available via groups.matrix.SU().
EXAMPLES:
sage: SU(3,5)
Special Unitary Group of degree 3 over Finite Field of size 5
sage: SU(3,QQ)
Traceback (most recent call last):
...
NotImplementedError: special unitary group only implemented over finite fields
TESTS:
sage: groups.matrix.SU(2, 3)
Special Unitary Group of degree 2 over Finite Field of size 3
Bases: sage.groups.matrix_gps.unitary.UnitaryGroup_finite_field
INPUT:
Bases: sage.groups.matrix_gps.matrix_group.MatrixGroup_gap_finite_field
INPUT:
Return the field of definition of this general unity group.
EXAMPLES:
sage: G = GU(3,GF(5))
sage: G.field_of_definition()
Finite Field in a of size 5^2
sage: G.base_field()
Finite Field of size 5