Postgres' inline power operator has incorrect operator precedence

[vegarsti]

In Postgres, x / y ^ z is parsed as (x / y) ^ z when it should be x / (y ^ z):

>>> import sqlglot
>>> import sqlglot
>>> sqlglot.__version__
'12.1.0'
>>> sqlglot.parse_one("select x / y ^ z", read="postgres")
(SELECT expressions:
  (POW this:
    (DIV this:
      (COLUMN this:
        (IDENTIFIER this: x, quoted: False)), expression:
      (COLUMN this:
        (IDENTIFIER this: y, quoted: False))), expression:
    (COLUMN this:
      (IDENTIFIER this: z, quoted: False))))

Docs link: https://www.postgresql.org/docs/15/functions-math.html

Test case in 4eb737d:

sqlglot/tests/dialects/test_postgres.py

Lines 177 to 183 in 4eb737d

	self.validate_all(
	"x / y ^ z",
	write={
	"": "x / POWER(y, z)",
	"postgres": "x / y ^ z",
	},
	)

[vegarsti]

I think this is the culprit:

sqlglot/sqlglot/dialects/postgres.py

Lines 276 to 279 in 6124d0c

	FACTOR = {
	**parser.Parser.FACTOR,
	TokenType.CARET: exp.Pow,
	}

It should have higher precedence than factors

[vegarsti]

Spent some time trying various things with the parser, but not getting anywhere yet.

[tobymao]

i'm looking at this

[vegarsti]

Thanks!