# Updates for twisted Hodge diamonds for complete intersections

The functionality outlined below is implemented in **Twisted Hodge numbers for complete intersections**, which can be used in Sage.
If you use it for your research, please cite it using .

Almost 3 years ago Piet Glas (who did his master thesis under my supervision) and I released code to compute twisted Hodge numbers of complete intersections, based on formulas obtained by Peter Brückmann. It is time to mention some updates about it.

I realised at some point there was a small bug. I never really got around to figuring out its cause until now.

But it is now fixed. The master thesis had the right formula, and the original implementation due to Piet had the right implementation, I just made a silly mistake in the final implementation. As explained in the commit log, I just messed up reading the parentheses in a formula of the paper. It's really like the universe is telling me to never program in Lisp.

The curious thing is that the tests I wrote to compare the two implementations did not catch the discrepancy, so I was unlucky that my tests didn't cover enough ground.

Talking about tests, I have added lots of tests to the code, and they can be run automatically now, so hopefully this will catch any future issues.

Because the fix in the first point was related to characteristic 0 versus characteristic $p$, I decided to extend the computations to also work in positive characteristic. This part is not as seriously tested as the original part, so be careful in using it.

I have created a DOI: . This page also contains information on how to cite the software in case you use it.