\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input r20abugs.input}
\author{Mike Dewar}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1996.
@
<<*>>=
<<license>>


-- This file tests bugs fixed/additions made since release 2.0a.
-- Created by Mike Dewar, 17.5.95

-- Added eval for aggregates
)clear completely
m : Matrix Expression Integer := matrix [[i*x^j for i in 1..3] for j in 1..3]
eval(m,x=0)

-- Added seed function
)clear completely
s:= seed();
r1 := randnum();
for i in 1..10 repeat randnum();
reseed s;
r2 := randnum();
r1 - r2

-- Fixed some problems with %e etc in rules
)clear completely
r3:=rule(3==%pi) -- biblical approximation
numeric(%pi)
numeric(r3(3))

)clear completely
-- Added some extra simplifications
sin(atan(sqrt 3)/2)

)clear completely
-- Fix to poly from Quitte
R := IntegerMod(4)
PolR := UP('X, R)
X : PolR := monomial(1, 1)
a : PolR := 2 * X**2
b : PolR := X**2 + 2*X + 1
-- Used to give a 0 remainder!
qr := monicDivide(a, b)
a - (qr.quotient * b + qr.remainder)

)clear completely
-- This used not to return 0
limit(%e^(1/x^2)/(%e^(1/x^2) + %e^(1/x^4)), x=0)

)clear completely
-- This used to crash because we generated tan(%pi/2)
integrate((sin(t))*sin((%pi-t)/6),t)

)clear completely
-- This used not to return 1.0!
(x+1.0)/(x+1.0)

)clear completely
-- This used to return a formal integral
b := D(Ci(x),x)
integrate(b,x)
-- This used to return -Si(x) rather than log(x) - Si(x)
integrate((1 - sin x)/x,x)

)clear completely
-- This used to return "failed"
limit(erf(x),x=c)

-- Used only to do structural equality for algebraic numbers, now try
-- to do true mathematical equality
(sqrt(2)*sqrt(3)=sqrt(6))@Boolean

-- New case we couldn't handle before
integrate((a + b*x)*exp(-x^2),x)

-- This used to give an infinite recursion
laplace(sin(t)^2/t^(3/2),t,s)

)clear completely
-- The following used to fail
P:=x^4+x^3+x^2+x+1
Q:=x^5+x^4+2*x^3+2*x^2+2*x-2+4*sqrt(-1+sqrt(3))
int := P/Q
int2 := int pretend FRAC POLY IAN
ans:=integrate(int2,x)

@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}