From 087ef557a5826b106ea3a8a568ebd74a6ca31e5d Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Fri, 10 May 2013 10:16:13 +0000
Subject: 	* algebra/indexedp.spad.pamphlet 
 (IndexedDirectProductOrderedAbelianMonoid) [<]: Rewrite iteratively.

---
 src/ChangeLog                      |  5 +++++
 src/algebra/indexedp.spad.pamphlet | 25 ++++++++++++++-----------
 2 files changed, 19 insertions(+), 11 deletions(-)

diff --git a/src/ChangeLog b/src/ChangeLog
index ac33f792..4534563d 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,8 @@
+2013-05-10  Gabriel Dos Reis  <gdr@integrable-solutions.net>
+
+	* algebra/indexedp.spad.pamphlet
+	(IndexedDirectProductOrderedAbelianMonoid) [<]: Rewrite iteratively.
+
 2013-05-10  Gabriel Dos Reis  <gdr@integrable-solutions.net>
 
 	* algebra/catdef.spad.pamphlet (AbelianMonoid) [opposite?]: New.
diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet
index c296f271..ad4ae9c8 100644
--- a/src/algebra/indexedp.spad.pamphlet
+++ b/src/algebra/indexedp.spad.pamphlet
@@ -249,18 +249,21 @@ IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedType):
 IndexedDirectProductOrderedAbelianMonoid(A:OrderedAbelianMonoid,S:OrderedType):
     Join(OrderedAbelianMonoid,IndexedDirectProductCategory(A,S))
  ==  IndexedDirectProductAbelianMonoid(A,S) add
-    --representations
-       Term:=  Record(k:S,c:A)
-       Rep:=  List Term
-       x,y: %
        x<y ==
-         empty? y => false
-         empty? x => true   -- note careful order of these two lines
-         y.first.k > x.first.k => true
-         y.first.k < x.first.k => false
-         y.first.c > x.first.c => true
-         y.first.c < x.first.c => false
-         x.rest < y.rest
+         u := terms x
+         v := terms y
+         repeat
+           -- note careful order of next two lines
+           empty? v => return false
+           empty? u => return true
+           xt := first u
+           yt := first v
+           index xt < index yt => return true
+           index yt < index xt => return false
+           coefficient xt < coefficient yt => return true
+           coefficient yt < coefficient xt => return false
+           u := rest u
+           v := rest v
 
 @
 \section{domain IDPOAMS IndexedDirectProductOrderedAbelianMonoidSup}
-- 
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