From ba37f9906f4940389d554897b5c72f731e6c9cbc Mon Sep 17 00:00:00 2001
From: Michael Hemmer <hemmer@mpi-inf.mpg.de>
Date: Mon, 29 Jan 2007 08:51:32 +0000
Subject: [PATCH] moved motivation for Field refining IntegralDomain and not
 EuclideanRing to users manual

---
 .../algebraic_structures.tex                  |  7 ++++++
 .../Algebraic_foundations_ref/Field.tex       | 24 ++++++++++++-------
 2 files changed, 22 insertions(+), 9 deletions(-)

diff --git a/Algebraic_foundations/doc_tex/Algebraic_foundations/algebraic_structures.tex b/Algebraic_foundations/doc_tex/Algebraic_foundations/algebraic_structures.tex
index 2eefcbf9ca0..db367e7b580 100644
--- a/Algebraic_foundations/doc_tex/Algebraic_foundations/algebraic_structures.tex
+++ b/Algebraic_foundations/doc_tex/Algebraic_foundations/algebraic_structures.tex
@@ -41,6 +41,13 @@ corresponds to integral domains in the algebraic sense, the
 distinction results from the fact that some implementations of
 integral domains lack the (algebraically always well defined) integral 
 division.
+Note that \ccc{Field} refines \ccc{IntegralDomain}. This is because 
+most ring-theoretic notions like greatest common divisors become trivial for 
+\ccc{Field}s. Hence we see \ccc{Field} as a refinement of 
+\ccc{IntegralDomain} and not as a 
+refinement of one of the more advanced types of ring. 
+If an algorithm wants to rely on gcd or remainder computation, it is trying 
+to do things it shouldn't do with a \ccc{Field} in the first place. 
 
 
 The main properties of an algebraic structure are collected in the class   
diff --git a/Algebraic_foundations/doc_tex/Algebraic_foundations_ref/Field.tex b/Algebraic_foundations/doc_tex/Algebraic_foundations_ref/Field.tex
index e93e32958c5..19e74996a75 100644
--- a/Algebraic_foundations/doc_tex/Algebraic_foundations_ref/Field.tex
+++ b/Algebraic_foundations/doc_tex/Algebraic_foundations_ref/Field.tex
@@ -3,18 +3,24 @@
 
 \ccDefinition
 
-A model of \ccc{Field} is an IntegralDomain in which every non-zero element has a multiplicative inverse. 
-Thus, one can divide by any non-zero element. Hence division is defined for any divisor != 0. 
-For a Field, we require this division operation to be available through operators / and /=.
+A model of \ccc{Field} is an\ccc{IntegralDomain} in which every non-zero element
+has a multiplicative inverse. 
+Thus, one can divide by any non-zero element. 
+Hence division is defined for any divisor != 0. 
+For a Field, we require this division operation to be available through 
+operators / and /=.
 
-Moreover, \ccc{CGAL::Algebraic_structure_traits< Field >} is a model of \ccc{AlgebraicStructureTraits} providing:\\
-- \ccc{CGAL::Algebraic_structure_traits< Field >::Algebraic_type} derived from \ccc{Field_tag} \\
+Moreover, \ccc{CGAL::Algebraic_structure_traits< Field >} is a model of 
+\ccc{AlgebraicStructureTraits} providing:\\
+- \ccc{CGAL::Algebraic_structure_traits< Field >::Algebraic_type} derived 
+from \ccc{Field_tag} \\
 
 \ccHeading{Remarks:}
-Most ring-theoretic notions like greatest common divisors become trivial for fields. 
-Hence we see Field as a refinement of IntegralDomain and not as a refinement of one of the more advanced 
-types of ring. If an algorithm wants to rely on gcd or remainder computation, it is trying to do things 
-it shouldn't do with a field in the first place. 
+Most ring-theoretic notions like greatest common divisors become trivial for 
+fields. Hence we see Field as a refinement of IntegralDomain and not as a 
+refinement of one of the more advanced types of ring. 
+If an algorithm wants to rely on gcd or remainder computation, it is trying 
+to do things it shouldn't do with a field in the first place. 
   
 \ccRefines
  \ccc{IntegralDomain}