From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Tue, 14 Aug 2007 05:14:52 +0000
Subject: Initial population.

---
 src/algebra/degred.spad.pamphlet | 99 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 99 insertions(+)
 create mode 100644 src/algebra/degred.spad.pamphlet

(limited to 'src/algebra/degred.spad.pamphlet')

diff --git a/src/algebra/degred.spad.pamphlet b/src/algebra/degred.spad.pamphlet
new file mode 100644
index 00000000..dd903291
--- /dev/null
+++ b/src/algebra/degred.spad.pamphlet
@@ -0,0 +1,99 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra degred.spad}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package DEGRED DegreeReductionPackage}
+<<package DEGRED DegreeReductionPackage>>=
+)abbrev package DEGRED DegreeReductionPackage
+++ This package \undocumented{}
+DegreeReductionPackage(R1, R2): Cat == Capsule where
+    R1: Ring
+    R2: Join(IntegralDomain,OrderedSet)
+ 
+    I    ==> Integer
+    PI   ==> PositiveInteger
+    UP   ==> SparseUnivariatePolynomial
+    RE   ==> Expression R2
+ 
+    Cat == with
+        reduce:  UP R1    ->  Record(pol: UP R1, deg: PI)
+	 	++ reduce(p) \undocumented{}
+        expand:  (RE, PI) ->  List RE
+		++ expand(f,n) \undocumented{}
+ 
+    Capsule == add
+ 
+ 
+        degrees(u: UP R1): List Integer ==
+            l: List Integer := []
+            while u ^= 0 repeat
+              l := concat(degree u,l)
+              u := reductum u
+            l
+        reduce(u: UP R1) ==
+            g := "gcd"/[d for d in degrees u]
+            u := divideExponents(u, g:PI)::(UP R1)
+            [u, g:PI]
+ 
+        import Fraction Integer
+ 
+        rootOfUnity(j:I,n:I):RE ==
+            j = 0 => 1
+            arg:RE := 2*j*pi()/(n::RE)
+            cos arg + (-1)**(1/2) * sin arg
+ 
+        expand(s, g) ==
+            g = 1 => [s]
+            [rootOfUnity(i,g)*s**(1/g) for i in 0..g-1]
+
+@
+\section{License}
+<<license>>=
+--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
+--All rights reserved.
+--
+--Redistribution and use in source and binary forms, with or without
+--modification, are permitted provided that the following conditions are
+--met:
+--
+--    - Redistributions of source code must retain the above copyright
+--      notice, this list of conditions and the following disclaimer.
+--
+--    - Redistributions in binary form must reproduce the above copyright
+--      notice, this list of conditions and the following disclaimer in
+--      the documentation and/or other materials provided with the
+--      distribution.
+--
+--    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
+--      names of its contributors may be used to endorse or promote products
+--      derived from this software without specific prior written permission.
+--
+--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
+--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+@
+<<*>>=
+<<license>>
+
+<<package DEGRED DegreeReductionPackage>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
-- 
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