Symplectic vector spaces#
AUTHORS:
Tobias Diez (2021): initial version
- class sage.manifolds.differentiable.examples.symplectic_space.StandardSymplecticSpace(dimension: int, name: str | None = None, latex_name: str | None = None, coordinates: str = 'Cartesian', symbols: str | None = None, symplectic_name: str | None = 'omega', symplectic_latex_name: str | None = None, start_index: int = 1, base_manifold: StandardSymplecticSpace | None = None, names: Tuple[str] | None = None)#
Bases:
EuclideanSpace
The vector space \(\RR^{2n}\) equipped with its standard symplectic form.
- symplectic_form()#
Return the symplectic form.
EXAMPLES:
Standard symplectic form on \(\RR^2\):
sage: M.<q, p> = manifolds.StandardSymplecticSpace(2, symplectic_name='omega') sage: omega = M.symplectic_form() sage: omega.display() omega = -dq∧dp