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| author | dos-reis <gdr@axiomatics.org> | 2012-02-15 07:34:02 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2012-02-15 07:34:02 +0000 |
| commit | d2bcc405fe2c77818ea89966730e78340bd3782d (patch) | |
| tree | e1cdab426f0ba1cb01e8837ccf2126a3e1ded754 /src/algebra/catdef.spad.pamphlet | |
| parent | c80a086d03bf72c9e54ae0625481ac8bf60ae714 (diff) | |
| download | open-axiom-d2bcc405fe2c77818ea89966730e78340bd3782d.tar.gz | |
* algebra/catdef.spad.pamphlet (Ring): Extends SemiRing.
(Dioid): New. Extend OrderedAbelianMonoid and SemiRing.
* algebra/exposed.lsp.pamphlet: Expose Dioid.
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 19 |
1 files changed, 17 insertions, 2 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 6fae2576..00930fb2 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -1831,7 +1831,7 @@ SemiRing(): Category == Join(AbelianMonoid,Monoid) )abbrev category RING Ring ++ Author: ++ Date Created: -++ Date Last Updated: +++ Date Last Updated: February 14, 2012 ++ Basic Functions: ++ Related Constructors: ++ Also See: @@ -1842,7 +1842,7 @@ SemiRing(): Category == Join(AbelianMonoid,Monoid) ++ The category of rings with unity, always associative, but ++ not necessarily commutative. -Ring(): Category == Join(Rng,Monoid,LeftModule(%),CoercibleFrom Integer) with +Ring(): Category == Join(Rng,SemiRing,LeftModule(%),CoercibleFrom Integer) with --operations characteristic: NonNegativeInteger ++ characteristic() returns the characteristic of the ring @@ -1860,6 +1860,19 @@ Ring(): Category == Join(Rng,Monoid,LeftModule(%),CoercibleFrom Integer) with @ +\section{Dioid category} + +<<category DIOID Dioid>>= +)abbrev category DIOID Dioid +++ Author: Gabriel Dos Reis +++ Date Created: February 14, 2012 +++ Date Last Modified: February 14, 2012 +++ Description: +++ Dioid is the class of semirings where the addition operation +++ induces a canonical order relation. +Dioid(): Category == Join(OrderedAbelianMonoid,SemiRing) + +@ \section{category RNG Rng} <<category RNG Rng>>= @@ -2104,7 +2117,9 @@ VectorSpace(S:Field): Category == Module(S) with <<category LINSET LinearSet>> <<category LMODULE LeftModule>> <<category RMODULE RightModule>> +<<category SRING SemiRing>> <<category RING Ring>> +<<category DIOID Dioid>> <<category BMODULE BiModule>> <<category ENTIRER EntireRing>> <<category CHARZ CharacteristicZero>> |