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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}
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