Updating Parts of Documents - Apache Solr Reference Guide - Apache Software Foundation

set	Set or replace the field value(s) with the specified value(s), or remove the values if 'null' or empty list is specified as the new value. May be specified as a single value, or as a list for multivalued fields
add	Adds the specified values to a multivalued field. May be specified as a single value, or as a list.
remove	Removes (all occurrences of) the specified values from a multivalued field. May be specified as a single value, or as a list.
inc	Increments a numeric value by a specific amount. Must be specified as a single numeric value.

Implementation here:
https://issues.apache.org/jira/browse/SOLR-3862

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