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Edit detail for #221 'PI' does not have 'OASGP' revision 6 of 6

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Editor: japp
Time: 2008/10/16 11:28:51 GMT-7
Note:

removed:
-From japp Thu Oct 16 11:08:13 -0700 2008
-From: japp
-Date: Thu, 16 Oct 2008 11:08:13 -0700
-Subject: 
-Message-ID: <20081016110813-0700@axiom-wiki.newsynthesis.org>
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-Status: fix proposed => fixed somewhere 
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-
-From japp Thu Oct 16 11:28:36 -0700 2008
-From: japp
-Date: Thu, 16 Oct 2008 11:28:36 -0700
-Subject: 
-Message-ID: <20081016112836-0700@axiom-wiki.newsynthesis.org>
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-Status: fixed somewhere => fix proposed 
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Submitted by : (unknown) at: 2007-11-17T22:11:05-08:00 (14 years ago)
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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

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

Categories of PI --kratt6, Thu, 13 Dec 2007 23:57:44 -0800 reply
Furthermore, we should have:
    PositiveInteger: Join(OrderedAbelianSemiGroup,Monoid) with

instead of:

    PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid)

as Waldek noticed...

Martin

Fixed in OpenAxiom