Vector Bundle Fiber Elements¶
The class VectorBundleFiberElement
implements vectors in the fiber of
a vector bundle.
AUTHORS:
Michael Jung (2019): initial version
-
class
sage.manifolds.vector_bundle_fiber_element.
VectorBundleFiberElement
(parent, name=None, latex_name=None)¶ Bases:
sage.tensor.modules.free_module_element.FiniteRankFreeModuleElement
Vector in a fiber of a vector bundle at the given point.
INPUT:
parent –
VectorBundleFiber
; the fiber to which the vector belongsname
– (default:None
) string; symbol given to the vectorlatex_name
– (default:None
) string; LaTeX symbol to denote the vector; ifNone
,name
will be used
EXAMPLES:
A vector \(v\) in a fiber of a rank 2 vector bundle:
sage: M = Manifold(2, 'M', structure='top') sage: X.<x,y> = M.chart() sage: p = M((1,-1), name='p') sage: E = M.vector_bundle(2, 'E') sage: e = E.local_frame('e') sage: Ep = E.fiber(p) sage: v = Ep((-2,1), name='v'); v Vector v in the fiber of E at Point p on the 2-dimensional topological manifold M sage: v.display() v = -2 e_0 + e_1 sage: v.parent() Fiber of E at Point p on the 2-dimensional topological manifold M sage: v in Ep True
See also
FiniteRankFreeModuleElement
for more documentation.