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()
[ 1 4*a + 4 4*a + 1]
[2*a + 4 2*a + 1 0]
[ 4 3*a 4*a + 2]
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:
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)
...
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]
]
Return string that evaluates to creates this group as an element of GAP.
EXAMPLES:
sage: G = GU(3,GF(7)); G
General Unitary Group of degree 3 over Finite Field of size 7
sage: G._gap_init_()
'GU(3, 7)'
sage: gap(G._gap_init_())
GU(3,7)
Return LaTeX string representation of this group.
EXAMPLES:
sage: G = GU(3,GF(7)); G
General Unitary Group of degree 3 over Finite Field of size 7
sage: latex(G)
\text{GU}_{3}(\Bold{F}_{7^{2}})
Return text representation of self.
EXAMPLES:
sage: G = GU(3,GF(5))
sage: G
General Unitary Group of degree 3 over Finite Field of size 5
Return the special unitary group of degree over
.
EXAMPLES:
sage: SU(3,5)
Special Unitary Group of degree 3 over Finite Field of size 5
sage: SU(3,QQ)
...
NotImplementedError: special unitary group only implemented over finite fields
Return string that creates this group in GAP.
EXAMPLES:
sage: SU(3,5)._gap_init_()
'SU(3, 5)'
Return latex representation of this group.
EXAMPLES:
sage: G = SU(3,GF(5))
sage: latex(G)
ext{SU}_{3}(\Bold{F}_{5^{2}})
Return text representation of this special unitary group.
EXAMPLES:
sage: G = SU(3,GF(5))
sage: G
Special Unitary Group of degree 3 over Finite Field of size 5