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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input equation.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1996.
+@
+<<*>>=
+<<license>>
+--
+--To ease the use of equation (more user friendly applications)
+--I have enhanced the datatype Equation to have more
+--mathematical richness.
+--
+--First of all now you can embed s from S to Equation S
+--as s = s.
+--This allows to easily manipulate equations bring terms
+--from one side to the other by simply adding or multiplying
+--or ... provided, that the equation domain inherits the
+--structure of the underlying S.
+--
+--So I went through the code saying
+--
+--If S has BlaBla then BlaBla
+--
+--for the most important structures, please suggest others
+--if necessary, Steve, do we have a more general method in
+--the new compiler rather than repeating all these
+--definitions as
+--
+--inv(eq) == inv lhs eq = inv rhs eq
+--
+--??
+--
+--
+--Furthermore, we have function to put 0 or 1 on one side
+--and factor the left hand side, after the right hand side
+--is 0 and we have an IntegralDomain.
+--
+--Please comment and test.
+--
+--Johannes
+
+
+eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x)
+--
+--
+--            3      2         4
+--   (1)  - 6x  + 13x  + 4= - x  + 12x
+--                                            Type: Equation Polynomial Integer
+--                                       Time: 1.61 (IN) + 1.47 (OT) = 3.08 sec
+eq2 := x**4+13*x**2-12*x = 6*x**3-4
+--
+--
+--         4      2          3
+--   (2)  x  + 13x  - 12x= 6x  - 4
+--                                            Type: Equation Polynomial Integer
+--                                       Time: 0.16 (IN) + 0.11 (OT) = 0.27 sec
+eq := eq1*y**2+eq2
+--
+--
+--             3      2      2    4      2            4        2     3
+--   (3)  (- 6x  + 13x  + 4)y  + x  + 13x  - 12x= (- x  + 12x)y  + 6x  - 4
+--                                            Type: Equation Polynomial Integer
+--               Time: 0.26 (IN) + 0.01 (EV) + 0.01 (OT) + 1.54 (GC) = 1.82 sec
+swap %
+--
+--
+--            4        2     3           3      2      2    4      2
+--   (4)  (- x  + 12x)y  + 6x  - 4= (- 6x  + 13x  + 4)y  + x  + 13x  - 12x
+--                                            Type: Equation Polynomial Integer
+--                                                   Time: 0.07 (OT) = 0.07 sec
+% + 4
+--
+--
+--            4        2     3       3      2      2    4      2
+--   (5)  (- x  + 12x)y  + 6x = (- 6x  + 13x  + 4)y  + x  + 13x  - 12x + 4
+--                                            Type: Equation Polynomial Integer
+--                                       Time: 0.69 (IN) + 0.01 (OT) = 0.70 sec
+%-6*x**3
+--
+--
+--            4        2       3      2      2    4     3      2
+--   (6)  (- x  + 12x)y = (- 6x  + 13x  + 4)y  + x  - 6x  + 13x  - 12x + 4
+--                                            Type: Equation Polynomial Integer
+--                                       Time: 0.19 (IN) + 0.01 (OT) = 0.20 sec
+leftZero %
+--
+--
+--             4     3      2            2    4     3      2
+--   (7)  0= (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4
+--                                            Type: Equation Polynomial Integer
+--                                       Time: 0.01 (IN) + 0.05 (OT) = 0.06 sec
+swap %
+--
+--
+--          4     3      2            2    4     3      2
+--   (8)  (x  - 6x  + 13x  - 12x + 4)y  + x  - 6x  + 13x  - 12x + 4= 0
+--                                            Type: Equation Polynomial Integer
+--                                                   Time: 0.01 (IN) = 0.01 sec
+factor lhs %
+--
+--
+--               2       2  2
+--   (9)  (x - 2) (x - 1) (y  + 1)
+--                                            Type: Factored Polynomial Integer
+--                           Time: 0.50 (IN) + 0.09 (EV) + 0.30 (OT) = 0.89 sec
+factorAndSplit eq
+--
+--
+--                             2
+--   (10)  [x - 2= 0,x - 1= 0,y  + 1= 0]
+--                                       Type: List Equation Polynomial Integer
+--                                       Time: 0.09 (EV) + 0.21 (OT) = 0.30 sec
+inv (eq :: EQ FRAC POLY INT)
+--
+--
+--                            1                                1
+--   (11)  - ------------------------------------= - ----------------------
+--              3      2      2    4      2            4        2     3
+--           (6x  - 13x  - 4)y  - x  - 13x  + 12x    (x  - 12x)y  - 6x  + 4
+--                                   Type: Equation Fraction Polynomial Integer
+--                                                   Time: 0.03 (IN) = 0.03 sec
+- %
+--
+--
+--                          1                              1
+--   (12)  ------------------------------------= ----------------------
+--            3      2      2    4      2          4        2     3
+--         (6x  - 13x  - 4)y  - x  - 13x  + 12x  (x  - 12x)y  - 6x  + 4
+--                                   Type: Equation Fraction Polynomial Integer
+--                                       Time: 0.01 (IN) + 0.01 (OT) = 0.02 sec
+--
+--
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}