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Navigating ric chains easily - is there a way to do it with the scripting API? (Ideally, I want to go both directions i.e. get_parents & get_children)

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Not at the moment, I'm afraid. See similar question asked here previously.

https://community.developers.refinitiv.com/questions/15389/how-to-get-the-chain-constituents-using-eikon-scri.html

Going from children to parents is not possible even theoretically in the chains data model on Elektron datafeed. You can go from parents to children because children are available in the parents' payload. But there's no way to go from a child to its parents.
It's possible to retrieve the constituents of a stock index as well as the list of indices a stock belongs to, but this capability has nothing to do with chains. It's implemented as part of fundamental and reference dataset outside of and separate from Elektron datafeed.

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