# Revision history [back]

With Sage 7.5.1, you can use the exterior calculus on manifolds instead of DifferentialForm; the advantage is that the simplification is automatic (no need to invoke simplify_trig by hand): your example becomes:

sage: U = Manifold(2, 'U')
sage: X.<r, theta> = U.chart(r"r:(0,+oo) theta:(0,2*pi):\theta")
sage: x = U.scalar_field(r*cos(theta))
sage: y = U.scalar_field(r*sin(theta))
sage: a = x.differential().wedge(y.differential())
sage: a
2-form on the 2-dimensional differentiable manifold U
sage: a.display()
r dr/\dtheta


With Sage 7.5.1, you can use the exterior calculus on manifolds instead of DifferentialForm; the advantage is that the simplification is automatic (no need to invoke simplify_trig by hand): your example becomes:

sage: U = Manifold(2, 'U')
sage: X.<r, theta> = U.chart(r"r:(0,+oo) theta:(0,2*pi):\theta")
sage: x = U.scalar_field(r*cos(theta))
sage: y = U.scalar_field(r*sin(theta))
sage: a = x.differential().wedge(y.differential())
sage: a
2-form on the 2-dimensional differentiable manifold U
sage: a.display()
r dr/\dtheta


See http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/diff_form.html for more details.