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How to create a MySQL generated column that uses a join in a concat?

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I have a column that is a concatenation of 5 other columns plus a join to a different table.

UPDATE db.a
JOIN db.b ON fk_b = b.pk
SET concat_field = CONCAT(field1,field2,field3,b.field,field4,field5)

What I would like to do is set the concat_field to a generated column,

concat_field VARCHAR(255) GENERATED ALWAYS AS (CONCAT(fields)) stored,

However while it's easy to do with a straight concat the join is giving me trouble.

How would I turn the update statement into a generated field?

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I don't think this is possible in MySQL due to its computed columns limitations:

Literals, deterministic built-in functions, and operators are permitted. A function is deterministic if, given the same data in tables, multiple invocations produce the same result, independently of the connected user. Examples of functions that are nondeterministic and fail this definition: CONNECTION_ID(), CURRENT_USER(), NOW().

A generated column definition can refer to other generated columns, but only those occurring earlier in the table definition. A generated column definition can refer to any base (nongenerated) column in the table whether its definition occurs earlier or later.

Subqueries are not permitted.

Without the option to use user-defined functions (like in the T-SQL) and refer to columns in other tables, there seems to be no way to circumvent this limitation.

Not sure if it fits your need, but materialized views might be useful in this case.

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