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/cyclotom.spad.pamphlet | 109 +++++++++++++++++++++++++++++++++++++
 1 file changed, 109 insertions(+)
 create mode 100644 src/algebra/cyclotom.spad.pamphlet

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

diff --git a/src/algebra/cyclotom.spad.pamphlet b/src/algebra/cyclotom.spad.pamphlet
new file mode 100644
index 00000000..1d8c77df
--- /dev/null
+++ b/src/algebra/cyclotom.spad.pamphlet
@@ -0,0 +1,109 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra cyclotom.spad}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package CYCLOTOM CyclotomicPolynomialPackage}
+<<package CYCLOTOM CyclotomicPolynomialPackage>>=
+)abbrev package CYCLOTOM CyclotomicPolynomialPackage
+++ This package \undocumented{} 
+CyclotomicPolynomialPackage: public == private where
+  SUP  ==> SparseUnivariatePolynomial(Integer)
+  LSUP ==> List(SUP)
+  NNI  ==> NonNegativeInteger
+  FR   ==> Factored SUP
+  IFP  ==> IntegerFactorizationPackage Integer
+ 
+  public == with
+    cyclotomicDecomposition: Integer -> LSUP
+	++ cyclotomicDecomposition(n) \undocumented{}
+    cyclotomic:              Integer -> SUP
+	++ cyclotomic(n) \undocumented{}
+    cyclotomicFactorization: Integer -> FR
+	++ cyclotomicFactorization(n) \undocumented{}
+ 
+  private == add
+    cyclotomic(n:Integer): SUP ==
+      x,y,z,l: SUP
+      g := factors factor(n)$IFP
+      --Now, for each prime in the factorization apply recursion
+      l := monomial(1,1) - monomial(1,0)
+      for u in g repeat
+         l := (monicDivide(multiplyExponents(l,u.factor::NNI),l)).quotient
+         if u.exponent>1 then
+            l := multiplyExponents(l,((u.factor)**((u.exponent-1)::NNI))::NNI)
+      l
+ 
+    cyclotomicDecomposition(n:Integer):LSUP ==
+      x,y,z: SUP
+      l,ll,m: LSUP
+      rr: Integer
+      g := factors factor(n)$IFP
+      l := [monomial(1,1) - monomial(1,0)]
+      --Now, for each prime in the factorization apply recursion
+      for u in g repeat
+         m := [(monicDivide(
+            multiplyExponents(z,u.factor::NNI),z)).quotient for z in l]
+         for rr in 1..(u.exponent-1) repeat
+            l := append(l,m)
+            m := [multiplyExponents(z,u.factor::NNI) for z in m]
+         l := append(l,m)
+      l
+ 
+    cyclotomicFactorization(n:Integer):FR ==
+      f :  SUP
+      fr : FR := 1$FR
+      for f in cyclotomicDecomposition(n) repeat
+        fr := fr * primeFactor(f,1$Integer)
+      fr
+
+@
+\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 CYCLOTOM CyclotomicPolynomialPackage>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
-- 
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