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last edited 15 years ago by japp |
Edit detail for #221 'PI' does not have 'OASGP' revision 2 of 6
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Editor: kratt6
Time: 2007/12/13 23:57:44 GMT-8 |
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| Note: Categories of PI | ||
added:
From kratt6 Thu Dec 13 23:57:44 -0800 2007
From: kratt6
Date: Thu, 13 Dec 2007 23:57:44 -0800
Subject: Categories of PI
Message-ID: <20071213235744-0800@axiom-wiki.newsynthesis.org>
Furthermore, we should have::
PositiveInteger: Join(OrderedAbelianSemiGroup,Monoid) with
instead of::
PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid)
as Waldek noticed...
Martin
Strange enough, the current definitions of OrderedAbelianSemiGroup and OrderedAbelianMonoid coincide:
)abbrev category OASGP OrderedAbelianSemiGroup
++ Ordered sets which are also abelian semigroups, such that the addition
++ preserves the ordering.
++ \spad{ x < y => x+z < y+z}
OrderedAbelianSemiGroup(): Category == Join(OrderedSet, AbelianMonoid)
)abbrev category OAMON OrderedAbelianMonoid
++ Ordered sets which are also abelian monoids, such that the addition
++ preserves the ordering.
OrderedAbelianMonoid(): Category ==
Join(OrderedAbelianSemiGroup, AbelianMonoid)
The definition of OASGP should read:
OrderedAbelianSemiGroup(): Category == Join(OrderedSet, AbelianSemiGroup)
Martin
... --Tim Daly, Sun, 30 Oct 2005 11:04:12 -0600 reply
This is a very deep change and I'm going to have to devote
a fair bit of time to testing the system before this one
gets released into the wild.
Tim
Furthermore, we should have:
PositiveInteger: Join(OrderedAbelianSemiGroup,Monoid) with
instead of:
PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid)
as Waldek noticed...
Martin