[email protected] writes:

| Dear all,
| 
| when trying to implement the order relation on set partitions,
| I found it impossible to use "<=".
| Somehow the interpreter always converts "x<=y" into "not(y<x)",
| even if "<=" is implemented explicitly.
| This is incorrect for a non-linear order.

The names '<', '<=', '>', and '>=' are supposed to be associated with
linear orderings by several components (parser, compiler, interpreter,
algebra, etc.) 

(though OpenAxiom has eliminated some (but not all) of those assumptions
in the parser.)

| What is the recommended way to handle non-linear orders?
| Not to use "<" at all?

Yes.

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