Symplectic vector spaces#


  • Tobias Diez (2021): initial version

class sage.manifolds.differentiable.examples.symplectic_space.StandardSymplecticSpace(dimension: int, name: Optional[str] = None, latex_name: Optional[str] = None, coordinates: str = 'Cartesian', symbols: Optional[str] = None, symplectic_name: Optional[str] = 'omega', symplectic_latex_name: Optional[str] = None, start_index: int = 1, base_manifold: Optional[StandardSymplecticSpace] = None, names: Optional[Tuple[str]] = None)#

Bases: EuclideanSpace

The vector space \(\RR^{2n}\) equipped with its standard symplectic form.


Return the symplectic form.


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