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| author | dos-reis <gdr@axiomatics.org> | 2011-03-08 04:58:08 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-03-08 04:58:08 +0000 |
| commit | 5a879844f45fd5b566ef61bb3cc9b2a2a0a5c3a7 (patch) | |
| tree | 5d45cbaf2e5fd49cc867509db391f9044b3e2f27 /src/algebra/catdef.spad.pamphlet | |
| parent | b96103f871a1bc514bd9b2ab99fb83fd9e3078f6 (diff) | |
| download | open-axiom-5a879844f45fd5b566ef61bb3cc9b2a2a0a5c3a7.tar.gz | |
* algebra/catdef.spad.pamphlet (SemiRing): New category.
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 20 |
1 files changed, 19 insertions, 1 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index f4447776..fe745809 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -224,7 +224,7 @@ BasicType(): Category == Type with ~=: (%,%) -> Boolean ++ x~=y tests if x and y are not equal. before?: (%,%) -> Boolean ++ \spad{before?(x,y)} holds if the system representation - ++ of \spad{x} is comes before that of \spad{y} in a + ++ of \spad{x} comes before that of \spad{y} in a ++ an implementation defined manner. add x = y == not before?(x,y) and not before?(y,x) @@ -1796,6 +1796,24 @@ RightModule(R:Rng):Category == Join(AbelianGroup, RightLinearSet R) @ +\section{category SRING SemiRing} +<<category SRING SemiRing>>= +)abbrev category SRING SemiRing +++ Author: Gabriel Dos Reis +++ Date Created: March 7, 2011 +++ Date Last Modified: March 7, 2011 +++ Description: +++ The category of all semiring structures, e.g. triples (D,+,*) +++ such that (D,+) is an Abelian monoid and (D,*) is a monoid +++ with the following laws: +++ Axioms: +++ a * (b + c) = (a * b) + (a * c) +++ (b + c) * a = (b * a) + (c * a) +++ 0 * a = 0 +++ a * 0 = 0 +SemiRing(): Category == Join(AbelianMonoid,Monoid) +@ + \section{category RING Ring} <<category RING Ring>>= )abbrev category RING Ring |