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如何使用AREL或Squeel翻译给定的查询：

SET @start = '2013-05-14';
SET @end = '2013-11-01';
SET @days = DATEDIFF(@end, @start);
SET @UnusedDays = 0;
SELECT  @UnusedDays := DATEDIFF(end_at,@end) FROM PERIODS WHERE (@end > start_at AND @end <= end_at);
SELECT  @UnusedDays := @UnusedDays + DATEDIFF(@start, start_at) FROM PERIODS WHERE (@start >= start_at AND @start < end_at);
SELECT  @days + @UnusedDays - SUM(DATEDIFF(end_at, start_at)) AS Shortfall
FROM    PERIODS
WHERE   (@start >= start_at AND @start < end_at)
OR      (end_at < @end AND start_at > @start)
OR      (@end > start_at AND @end <= end_at);

将它用作原始 SQL 的解决方案也将受到欢迎，因为到目前为止我无法让它运行。

更新：在SQL 请求中描述了周期模型和目标，以查找周期是否被完全覆盖

UPDATE2：如果我尝试使用原始 sql 查询，例如：

query = %Q[
  SET @start = '2013-05-14';
  SET @end = '2013-11-01';
  SET @days = DATEDIFF(@end, @start);
  SET @UnusedDays = 0;
  SELECT  @UnusedDays := DATEDIFF(end_at,@end) FROM PERIODS WHERE (@end > start_at AND @end <= end_at);
  SELECT  @UnusedDays := @UnusedDays + DATEDIFF(@start, start_at) FROM PERIODS WHERE (@start >= start_at AND @start < end_at);
  SELECT  @days + @UnusedDays - SUM(DATEDIFF(end_at, start_at)) AS Shortfall
  FROM    PERIODS
  WHERE   (@start >= start_at AND @start < end_at)
  OR      (end_at < @end AND start_at > @start)
  OR      (@end > start_at AND @end <= end_at);
]

Period.connection.select_all(query).first.map{|k,v| v }.first == 0

我收到以下错误：

ActiveRecord::StatementInvalid:
       Mysql2::Error: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'SET @end = '2013-11-01';
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