Carlo Romagnano - Wednesday, November 14, 2018 6:43 AM

Jeff Moden - Saturday, November 10, 2018 8:00 AM

I believe you meant "not" rather than "now".

However, your first example is also non-deterministic.  Here's the proof.

Create table dbo.SalesOrderHeader (RN INT IDENTITY(1,1),SomeDate DATETIME);
GO
ALTER TABLE dbo.SalesOrderHeader ADD WhichDay AS datepart(day,'20180131') PERSISTED;

Msg 4936, Level 16, State 1, Line 1
Computed column 'WhichDay' in table 'SalesOrderHeader' cannot be persisted because the column is non-deterministic.

Here an example where it is deterministic:
DROP table dbo.SalesOrderHeader
Create table dbo.SalesOrderHeader (RN INT IDENTITY(1,1),SomeDate DATETIME NOT NULL);
ALTER TABLE dbo.SalesOrderHeader ADD WhichDay AS datepart(d,SomeDate) PERSISTED;
create index idx_SalesOrderHeader ON SalesOrderHeader(WhichDay)
Commands completed successfully.

The difference is the second input parameter:
with string is non-deterministic
with a valid  datetime is deterministic