id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
26028 Bug-Fixes and improvements with respect to the bilinear invariant form of classical matrix groups soehms "1) Bug with respect to the symplectic groups:
{{{
#!python
sage: Sp(4, QQ).invariant_form()
[0 0 0 1]
[0 0 1 0]
[0 1 0 0]
[1 0 0 0]
}}}
This bilinear form isn't alternating. Thus Sp(4, QQ) in fact is an orthogonal group!
2) Bug with respect to the unitary groups:
{{{
#!python
sage: G = GU(2,2); G
General Unitary Group of degree 2 over Finite Field in a of size 2^2
sage: m = matrix(G.base_ring(), 2, 2, (1,1,1,0)); m
[1 1]
[1 0]
sage: m in [g.matrix() for g in G]
True
sage: G(m)
Traceback (most recent call last):
...
TypeError: matrix must be unitary
}}}
Note, that this bug is not fixed by ticket #25761. The reason for this bug is this:
{{{
#!python
sage: invariant_form = matrix(G.base_ring(), 2,2, G.gap().InvariantSesquilinearForm()['matrix'].matrix())
sage: invariant_form == G.one().matrix()
False
}}}
Furthermore, There is no method to obtain the invariant from of a unitary group analogues as for symplectic and orthogonal groups.
{{{
#!python
sage: GU(3,2).invariant_form()
Traceback (most recent call last):
...
AttributeError: 'UnitaryMatrixGroup_gap_with_category' object has no attribute 'invariant_form'
}}}
3) Bug with respect to the orthogonal group (but not with respect to the invariant form):
{{{
#!python
sage: GO3_25 = GO(3,25)
sage: GO3_25.order()
240
sage: GO3_5 = GO(3,5)
sage: GO3_5.order()
240
sage: GO3_5.is_isomorphic(GO3_25)
True
}}}
Furthermore, it should be possible to define generic classical matrix groups with respect to a user given invariant bilinear form." defect closed major sage-8.4 group theory fixed matrix groups, unitary, symplectic, orthogonla, classical, invariant bilinear form tscrim Sebastian Oehms Travis Scrimshaw N/A 331e5cbc6327a37bb9b29af7aba236999e8d72b5 #25761