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Is the Koszul operator supported in Sage?

asked 2017-07-05 15:02:17 -0600

updated 2017-07-05 18:45:06 -0600

I would like to use the Koszul operator on differential forms:

$ \kappa( x^\alpha dx_\sigma) = \sum_{i=1}^k \left((-1)^{i+1}x^\alpha x_{\sigma(i)}\right)dx_{\sigma(1)}\wedge\cdots\wedge\widehat{dx_{\sigma(i)}}\wedge\cdots\wedge dx_{\sigma(k)}$

where

$x^{\alpha}dx_{\sigma}:=\left(x_1^{\alpha_1}x_2^{\alpha_2}\dots x_n^{\alpha_n}\right)dx_{\sigma(1)}\wedge\dots\wedge dx_{\sigma(k)}$

and the notation $\widehat{dx_{\sigma(i)}}$ indicates that the term is omitted from the wedge product.

Is there existing code for this map in Sage?

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answered 2017-07-06 13:33:54 -0600

eric_g gravatar image

updated 2017-07-06 13:39:55 -0600

I'm afraid not. The currently available operations on differential forms are listed here.

Would you like to implement the Koszul operator? If yes, visit this page.

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Note that a somehow related operator, the Schouten-Nijenhuis bracket, is currently being implemented, see this discussion.

eric_g gravatar imageeric_g ( 2017-07-06 17:01:36 -0600 )edit

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Asked: 2017-07-05 15:02:17 -0600

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Last updated: Jul 06