Initial population.

1 files changed, 193 insertions, 0 deletions

diff --git a/src/algebra/funcpkgs.spad.pamphlet b/src/algebra/funcpkgs.spad.pamphlet
new file mode 100644
index 00000000..41f979ef
--- /dev/null
+++ b/src/algebra/funcpkgs.spad.pamphlet
@@ -0,0 +1,193 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra funcpkgs.spad}
+\author{Manuel Bronstein}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package FSUPFACT FunctionSpaceUnivariatePolynomialFactor}
+<<package FSUPFACT FunctionSpaceUnivariatePolynomialFactor>>=
+)abbrev package FSUPFACT FunctionSpaceUnivariatePolynomialFactor
+++ Used internally by IR2F
+++ Author: Manuel Bronstein
+++ Date Created: 12 May 1988
+++ Date Last Updated: 22 September 1993
+++ Keywords: function, space, polynomial, factoring
+FunctionSpaceUnivariatePolynomialFactor(R, F, UP):
+ Exports == Implementation where
+  R : Join(IntegralDomain, OrderedSet, RetractableTo Integer)
+  F : FunctionSpace R
+  UP: UnivariatePolynomialCategory F
+
+  Q   ==> Fraction Integer
+  K   ==> Kernel F
+  AN  ==> AlgebraicNumber
+  PQ  ==> SparseMultivariatePolynomial(Q, K)
+  PR  ==> SparseMultivariatePolynomial(R, K)
+  UPQ ==> SparseUnivariatePolynomial Q
+  UPA ==> SparseUnivariatePolynomial AN
+  FR  ==> Factored UP
+  FRQ ==> Factored UPQ
+  FRA ==> Factored UPA
+
+  Exports ==> with
+    ffactor: UP -> FR
+      ++ ffactor(p) tries to factor a univariate polynomial p over F
+    qfactor: UP -> Union(FRQ, "failed")
+      ++ qfactor(p) tries to factor p over fractions of integers,
+      ++ returning "failed" if it cannot
+    UP2ifCan: UP  -> Union(overq: UPQ, overan: UPA, failed: Boolean)
+      ++ UP2ifCan(x) should be local but conditional.
+    if F has RetractableTo AN then
+      anfactor: UP -> Union(FRA, "failed")
+        ++ anfactor(p) tries to factor p over algebraic numbers,
+        ++ returning "failed" if it cannot
+
+  Implementation ==> add
+    import AlgFactor(UPA)
+    import RationalFactorize(UPQ)
+
+    P2QifCan : PR  -> Union(PQ, "failed")
+    UPQ2UP   : (SparseUnivariatePolynomial PQ, F) -> UP
+    PQ2F     : (PQ, F) -> F
+    ffactor0 : UP -> FR
+
+    dummy := kernel(new()$Symbol)$K
+
+    if F has RetractableTo AN then
+      UPAN2F: UPA -> UP
+      UPQ2AN: UPQ -> UPA
+
+      UPAN2F p ==
+        map(#1::F, p)$UnivariatePolynomialCategoryFunctions2(AN,UPA,F,UP)
+
+      UPQ2AN p ==
+        map(#1::AN, p)$UnivariatePolynomialCategoryFunctions2(Q,UPQ,AN,UPA)
+
+      ffactor p ==
+        (pq := anfactor p) case FRA =>
+                         map(UPAN2F, pq::FRA)$FactoredFunctions2(UPA, UP)
+        ffactor0 p
+
+      anfactor p ==
+        (q := UP2ifCan p) case overq =>
+                     map(UPQ2AN, factor(q.overq))$FactoredFunctions2(UPQ, UPA)
+        q case overan => factor(q.overan)
+        "failed"
+
+      UP2ifCan p ==
+        ansq := 0$UPQ ; ansa := 0$UPA
+        goforq? := true
+        while p ^= 0 repeat
+          if goforq? then
+            rq := retractIfCan(leadingCoefficient p)@Union(Q, "failed")
+            if rq case Q then
+              ansq := ansq + monomial(rq::Q, degree p)
+              ansa := ansa + monomial(rq::Q::AN, degree p)
+            else
+              goforq? := false
+              ra := retractIfCan(leadingCoefficient p)@Union(AN, "failed")
+              if ra case AN then ansa := ansa + monomial(ra::AN, degree p)
+                            else return [true]
+          else
+            ra := retractIfCan(leadingCoefficient p)@Union(AN, "failed")
+            if ra case AN then ansa := ansa + monomial(ra::AN, degree p)
+                          else return [true]
+          p := reductum p
+        goforq? => [ansq]
+        [ansa]
+
+    else
+      UPQ2F: UPQ -> UP
+
+      UPQ2F p ==
+        map(#1::F, p)$UnivariatePolynomialCategoryFunctions2(Q,UPQ,F,UP)
+
+      ffactor p ==
+        (pq := qfactor p) case FRQ =>
+                         map(UPQ2F, pq::FRQ)$FactoredFunctions2(UPQ, UP)
+        ffactor0 p
+
+      UP2ifCan p ==
+        ansq := 0$UPQ
+        while p ^= 0 repeat
+          rq := retractIfCan(leadingCoefficient p)@Union(Q, "failed")
+          if rq case Q then ansq := ansq + monomial(rq::Q, degree p)
+                       else return [true]
+          p := reductum p
+        [ansq]
+
+    ffactor0 p ==
+      smp := numer(ep := p(dummy::F))
+      (q := P2QifCan smp) case "failed" => p::FR
+      map(UPQ2UP(univariate(#1, dummy), denom(ep)::F), factor(q::PQ
+             )$MRationalFactorize(IndexedExponents K, K, Integer,
+                  PQ))$FactoredFunctions2(PQ, UP)
+
+    UPQ2UP(p, d) ==
+      map(PQ2F(#1, d), p)$UnivariatePolynomialCategoryFunctions2(PQ,
+                                   SparseUnivariatePolynomial PQ, F, UP)
+
+    PQ2F(p, d) ==
+      map(#1::F, #1::F, p)$PolynomialCategoryLifting(IndexedExponents K,
+                                                K, Q, PQ, F) / d
+
+    qfactor p ==
+      (q := UP2ifCan p) case overq => factor(q.overq)
+      "failed"
+
+    P2QifCan p ==
+      and/[retractIfCan(c::F)@Union(Q, "failed") case Q
+           for c in coefficients p] =>
+            map(#1::PQ, retract(#1::F)@Q :: PQ,
+              p)$PolynomialCategoryLifting(IndexedExponents K,K,R,PR,PQ)
+      "failed"
+
+@
+\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 FSUPFACT FunctionSpaceUnivariatePolynomialFactor>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}