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Integrating differential forms

asked 2021-05-02 21:42:54 +0200

ripple_carry gravatar image

I'd like to integrate dx /\ dy over the unit square. Naively, I would expect the following to work:

E.<x,y> = EuclideanSpace(2) 

phi = E.diff_form(2)
phi[1, 2] = 1

show(integrate(integrate(phi, x, 0, 1), y, 0, 1))

but it fails with:

TypeError: unable to convert 2-form on the Euclidean plane E^2 to a symbolic expression

and I can't find anything about integration in the DiffFormFreeModule documentation. What is the right way to do this?

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answered 2021-05-02 21:59:27 +0200

eric_g gravatar image

Indeed, integration of differential forms is not implemented yet. Meanwhile, you can pass the symbolic expression representing the component $\phi_{12}$, which is returned by phi[1,2].expr(), to integrate: from your example, we get

sage: integrate(integrate(phi[1,2].expr(), x, 0, 1), y, 0, 1)                                       
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Asked: 2021-05-02 21:42:54 +0200

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Last updated: May 02 '21