How to filter, order and query LTree in EF Core

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As already described here I'm struggling with LTree and the right way to query. I'm using an object, containing LTree as a column on one of my tables. This is how the object looks like:

using Microsoft.EntityFrameworkCore;

public class MyObject
{
    public Guid Id {get;set;}
    public LTree LTreeColumn {get;set;}
    ....
}

If it is not possible to use the LTree-functions as expected, it's not nice, but also not worst case. But it would be nice, if there is a way, to order and filter a collection, based on LTree.

OrderBy fails, because of missing IComparable implementation. Is there an alternative approach? And how to find the first item on the "tree" given a specific sub-path?

Let's say, I have a structure beginning with Top, followed by Top.One, Top.Two, Top.One.One and so on...

Now I want to find the highest object, beginning with Top in a collection. How can I do this on database and in memory?

And in general (based on a common sub-path) how to evaluate < or > correctly?

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Joshit On

Here's what I figured out so far... If someone knows better or more I highly appreciate another answer.

All LTree-functions will be translated to queries. LTree holds NLevel as a property, which can be used for ordering (as query, not in memory):

var ordered = _dbContext.MyObjects.OrderBy(e=>e.LTreeColumn.NLevel)

Highest in specific path:

var highest = _dbContext.MyObjects.Where(e=>e.LTreeColumn.MatchesLQuery("Top.*"))
    .OrderBy(e=>e.LTreeColumn.NLevel).First();

If I need the level of LTreeColumn in an in-memory collection I use these extension-methods:

public static int GetLTreeLevel(this string lTree)
    => lTree.Split('.').Length;

public static int GetLTreeLevel(this LTree lTree)
    => lTree.ToString().GetLTreeLevel();

Compare the level of two instances of MyObject:

var isHigher = first.LTreeColumn.GetLTreeLevel() < second.LTreeColumn.GetLTreeLevel();