Symplectic vector spaces

AUTHORS:

  • Tobias Diez (2021): initial version

class sage.manifolds.differentiable.examples.symplectic_space.StandardSymplecticSpace(dimension, name=None, latex_name=None, coordinates='Cartesian', symbols=None, symplectic_name='omega', symplectic_latex_name=None, start_index=1, base_manifold=None, names=None)

Bases: sage.manifolds.differentiable.examples.euclidean.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