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)[source]¶
- Bases: - EuclideanSpace- The vector space \(\RR^{2n}\) equipped with its standard symplectic form. - symplectic_form()[source]¶
- 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 - >>> from sage.all import * >>> M = manifolds.StandardSymplecticSpace(Integer(2), symplectic_name='omega', names=('q', 'p',)); (q, p,) = M._first_ngens(2) >>> omega = M.symplectic_form() >>> omega.display() omega = -dq∧dp