Module: sage.groups.matrix_gps.unitary
Unitary Groups
and
These are
unitary matrices with entries in
.
Author Log:
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
Module-level Functions
n, F, [var=a]) |
Return the general unitary group of degree n over the finite field F.
Input:
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] ]
n, F, [var=a]) |
Return the special unitary group of degree
over
.
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
Class: GeneralUnitaryGroup_finite_field
Special Functions: _gap_init_,
_latex_,
_repr_
self) |
Return string that evaluates to creates this group as an element of GAP.
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)
self) |
Return LaTeX string representation of this group.
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}(\mathbf{F}_{7^{2}})
self) |
Return text representatin of self.
sage: G = GU(3,GF(5)) sage: G General Unitary Group of degree 3 over Finite Field of size 5
Class: SpecialUnitaryGroup_finite_field
Special Functions: _gap_init_,
_latex_,
_repr_
self) |
Return string that creates this group in GAP.
sage: SU(3,5)._gap_init_() 'SU(3, 5)'
self) |
Return latex representatin of this group.
sage: G = SU(3,GF(5)) sage: latex(G) ext{SU}_{3}(\mathbf{F}_{5^{2}})
self) |
Return text representation of this special unitary group.
sage: G = SU(3,GF(5)) sage: G Special Unitary Group of degree 3 over Finite Field of size 5
Class: UnitaryGroup_finite_field
Functions: field_of_definition
self) |
Return the field of definition of this general unity group.
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
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