# Revision history [back]

### Is the Koszul operator supported in Sage?

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

Is there existing code for this map in Sage?

### Is the Koszul operator supported in Sage?

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

Is there existing code for this map in Sage?