Converting SQL to Relational Algebra / Calculus
You have a number of "mistakes" in your SQL, that should be addressed before you translate it to relational algebra.


You don't have a FROM in your SQL. You shouldn't start by JOINing.
You seem to assume that train_code is a text, yet you define it as an integer.
Your table definitions don't define a type for train_code in the journey table, nor for journey_id in the price one.
The tool you're using doesn't understand SERIAL (which is not standard SQL). Just don't use it. Use INTEGER instead.


So, your table definitions just should be:

CREATE TABLE train 
(
  train_code TEXT PRIMARY KEY,
  name TEXT NOT NULL
); 

CREATE TABLE journey 
(
  journey_id INTEGER PRIMARY KEY, 
  int INTEGER,
  train_code TEXT REFERENCES train (train_code)
); 

CREATE TABLE price 
(
  journey_id INTEGER REFERENCES journey (journey_id),
  price INTEGER
); 


This is translated by RelaX to:

group: joanolo (imported from SQL)

train = {
    train_code:string, name:string
}

journey = {
    journey_id:number, int:number, train_code:string
}

price = {
    journey_id:number, price:number
}


On the query side, you need to add a FROM and you just change x IN (a, b) to (x = a OR x = b). You'll end up having the following query:

SELECT 
    train.name
FROM   
    train
    JOIN  journey on train.train_code = journey.train_code
    JOIN  price on price.journey_id = journey.journey_id 
WHERE  
    price.price &gt;= 50 
    AND (journey.train_code = 'NYC' OR journey.train_code = 'SFO') 
    AND  journey.int = 1


This format is understood by RelaX, and will give you the result you're looking for:


  π train.name σ price.price ≥ 50 and (journey.train_code = 'NYC' or journey.train_code = 'SFO' ) and journey.int = 1 train ⨝ train.train_code = journey.train_code journey ⨝ price.journey_id = journey.journey_id price




That is you have one projection (π), equivalent to your SELECT one selection (σ) that filters with the condition in your WHERE clause, and two joins (⨝) which are equivalent to SQL JOIN.