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authordos-reis <gdr@axiomatics.org>2013-05-11 15:08:29 +0000
committerdos-reis <gdr@axiomatics.org>2013-05-11 15:08:29 +0000
commitd739b05adf4ab0b012db9334ad2e406e5979fdaa (patch)
tree61a88f149f99a03b91fae46d32237cd0ab314d76 /src/algebra/catdef.spad.pamphlet
parentfd5af990d05dc4a3534a1e4d83a6fdbcd150ef6a (diff)
downloadopen-axiom-d739b05adf4ab0b012db9334ad2e406e5979fdaa.tar.gz
Fix location of opposite? implementation
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
-rw-r--r--src/algebra/catdef.spad.pamphlet4
1 files changed, 2 insertions, 2 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet
index a864ed03..fa6edba6 100644
--- a/src/algebra/catdef.spad.pamphlet
+++ b/src/algebra/catdef.spad.pamphlet
@@ -203,7 +203,7 @@ LinearSet(S: SemiGroup): Category == Join(LeftLinearSet S, RightLinearSet S)
-- following domain must be compiled with subsumption disabled
AbelianGroup(): Category == Join(CancellationAbelianMonoid, LeftLinearSet Integer) with
-: % -> % ++ \spad{-x} is the additive inverse of \spad{x}
- "-": (%,%) -> % ++ \spad{x-y} is the difference of \spad{x}
+ -: (%,%) -> % ++ \spad{x-y} is the difference of \spad{x}
++ and \spad{y} i.e. \spad{x + (-y)}.
add
(x:% - y:%):% == x+(-y)
@@ -215,6 +215,7 @@ AbelianGroup(): Category == Join(CancellationAbelianMonoid, LeftLinearSet Intege
zero? n => 0
positive? n => double(n pretend PositiveInteger,x)
double((-n) pretend PositiveInteger,-x)
+ opposite?(x,y) == x = -y
@
@@ -1438,7 +1439,6 @@ OrderedAbelianGroup(): Category ==
positive? x => x
negative? x => -x
0
- opposite?(x,y) == x = -y
@
\section{category OAMON OrderedAbelianMonoid}