On 11/12/2014 10:40 AM, Prof. Dr. Johannes Grabmeier wrote: > There seem to be problems with the various orderings.
I think I also stumbled over this one, but in the Aldor library. > As a partial order is reflexive the basic operation in PartialOrder > is "<=" and hence there are categorial implementations for >, >= and > < there. Well, there are also "strict partial orders", which are then irreflexive. But instead of antisymmetric, they are assymetric. (See for example: Bronstein/Semendrajew: "Taschenbuch der Mathematik" under "Halbordnung".) http://de.wikipedia.org/wiki/Taschenbuch_der_Mathematik The Aldor library seems to build on the concept of an irreflexive partial order. https://github.com/pippijn/aldor/blob/master/aldor/lib/aldor/src/base/sal_order.as#L56 Note in particular that it defines (a:%) > (b:%):Boolean == ~(a <= b) in contrast to (a:%) > (b:%):Boolean == b < a See also https://github.com/pippijn/aldor/blob/master/aldor/lib/aldor/src/base/sal_torder.as#L48 > Perhaps one could think about an Attribute linearilyOrdered or > totallyOrdered Attributes are no longer part of FriCAS. Categories serve the same purpose. Foo has PartialOrder Foo has OrderedSet should basically already give you the "partiallyOrdered" and "linearlyOrdered" properties. Ralf -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
