can you have complex types which are multivalued?
I'd like to store something like
a tag-name with a corresponding tag-weighting.

How much work it is might depend on how static or dynamic the tag-weighting is.
If it's very static, you could simply use index-time boosts.

can you do sum(*) type queries in lucene/solr? it is efficient ?

If all tag weights were the same, you would get summing for "free" via
lucene scoring I think...

It all depends on the exact details of what you are trying to do, how
many tags, how are the weights calculated, are the sums across all
tags or dynamically determined by some query, etc...

-Yonik

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