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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra cmplxrt.spad}
+\author{Patrizia Gianni}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package CMPLXRT ComplexRootPackage}
+<<package CMPLXRT ComplexRootPackage>>=
+)abbrev package CMPLXRT ComplexRootPackage
+++ Author: P. Gianni
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors: Complex, Float, Fraction, UnivariatePolynomial
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++   This package provides functions complexZeros
+++ for finding the complex zeros
+++ of univariate polynomials with complex rational number coefficients.
+++ The results are to any user specified precision and are returned
+++ as either complex rational number or complex floating point numbers
+++ depending on the type of the second argument which specifies the
+++ precision.
+
+-- Packages for the computation of complex roots of
+-- univariate polynomials with rational or gaussian coefficients.
+
+-- Simplified version, the old original based on Gebauer's solver is
+-- in ocmplxrt spad
+RN     ==> Fraction Integer
+I      ==> Integer
+NF     ==> Float
+
+ComplexRootPackage(UP,Par) : T == C where
+   UP   :   UnivariatePolynomialCategory Complex Integer
+   Par  :   Join(Field, OrderedRing) -- will be Float or RN
+   CP   ==> Complex Par
+   PCI  ==> Polynomial Complex Integer
+
+   T == with
+        complexZeros:(UP,Par)  -> List CP
+          ++ complexZeros(poly, eps) finds the complex zeros of the
+          ++ univariate polynomial poly to precision eps with
+          ++ solutions returned as complex floats or rationals
+          ++ depending on the type of eps.
+
+   C == add
+    complexZeros(p:UP,eps:Par):List CP ==
+      x1:Symbol():=new()
+      x2:Symbol():=new()
+      vv:Symbol():=new()
+      lpf:=factors factor(p)$ComplexFactorization(I,UP)
+      ris:List CP:=empty()
+      for pf in lpf repeat
+          pp:=pf.factor pretend SparseUnivariatePolynomial Complex Integer
+          q:PCI :=multivariate(pp,vv)
+          q:=eval(q,vv,x1::PCI+complex(0,1)*(x2::PCI))
+          p1:=map(real,q)$PolynomialFunctions2(Complex I,I)
+          p2:=map(imag,q)$PolynomialFunctions2(Complex I,I)
+          lz:=innerSolve([p1,p2],[],[x1,x2],
+                          eps)$InnerNumericFloatSolvePackage(I,Par,Par)
+          ris:=append([complex(first z,second z) for z in lz],ris)
+      ris
+
+@
+\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 CMPLXRT ComplexRootPackage>>
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}