Unique Index on two columns and vice versa - constraints

Question

I have the following table in postgres 9.5:
CREATE TABLE public.test
(
id bigint NOT NULL DEFAULT nextval('test_id_seq'::regclass),
id1 integer,
id2 integer,
CONSTRAINT test_pkey PRIMARY KEY (id)
);
I want to add restrictions on both columns which only allows recordsets where
the new recordset (id1,id2) is not present and
the new recordset (id1,id2) is not present as (id2,id1) and
id1 and id2 of new recordset are not equal
It should lool like this:
id | id1 | id2
---------------
1 | 1 | 1 <-- invalid (violates restriction 3.)
2 | 1 | 2 <-- valid
3 | 1 | 2 <-- invalid (violates restriction 1.)
4 | 2 | 1 <-- invalid (violates restriction 2.)
5 | 3 | 1 <-- valid
6 | 3 | 2 <-- valid
For restriction 1, I have added:
ALTER TABLE test ADD CONSTRAINT test_id1_id2_unique UNIQUE(id1, id2);
But how to add constraints for 2. and 3.?
Final solution with help of a_horse_with_no_name:
CREATE TABLE public.test(
id bigint NOT NULL DEFAULT nextval('test_id_seq'::regclass),
id1 integer NOT NULL,
id2 integer NOT NULL,
CONSTRAINT test_pkey PRIMARY KEY (id),
CONSTRAINT test_check CHECK (id1 <> id2)
);
CREATE UNIQUE INDEX test_id1_id2_unique
ON public.test
USING btree
((LEAST(id1, id2)), (GREATEST(id1, id2)));

Answer 1

You can create a unique index to cover both 1. and 2.
create unique index on test ( least(id1,id2), greatest(id1,id2) );
For 3. you need a check constraint:
CREATE TABLE public.test
(
id bigint NOT NULL DEFAULT nextval('test_id_seq'::regclass),
id1 integer,
id2 integer,
constraint check_not_equal check (id1 is distinct from id2),
CONSTRAINT test_pkey PRIMARY KEY (id)
);
You probably want both ids to be NOT NULL as well. In that case you could also use check (id1 <> id2)